Effect of Temperature on Growth and Sporulation of US-22, US-23, and US-24 Clonal Lineages of Phytophthora infestans and Implications for Late Blight Epidemiology.

PubMed

Seidl Johnson, Anna C; Frost, Kenneth E; Rouse, Douglas I; Gevens, Amanda J

2015-04-01

Epidemics of late blight, caused by Phytophthora infestans (Mont.) de Bary, have been studied by plant pathologists and regarded with great concern by potato and tomato growers since the Irish potato famine in the 1840s. P. infestans populations have continued to evolve, with unique clonal lineages arising which differ in pathogen fitness and pathogenicity, potentially impacting epidemiology. In 2012 and 2013, the US-23 clonal lineage predominated late blight epidemics in most U.S. potato and tomato production regions, including Wisconsin. This lineage was unknown prior to 2009. For isolates of three recently identified clonal lineages of P. infestans (US-22, US-23, and US-24), sporulation rates were experimentally determined on potato and tomato foliage and the effect of temperature on lesion growth rate on tomato was investigated. The US-22 and US-23 isolates had greater lesion growth rates on tomato than US-24 isolates. Sporulation rates for all isolates were greater on potato than tomato, and the US-23 isolates had greater sporulation rates on both tomato and potato than the US-22 and US-24 isolates. Experimentally determined correlates of fitness were input to the LATEBLIGHT model and epidemics were simulated using archived Wisconsin weather data from four growing seasons (2009 to 2012) to investigate the effect of isolates of these new lineages on late blight epidemiology. The fast lesion growth rates of US-22 and US-23 isolates resulted in severe epidemics in all years tested, particularly in 2011. The greater sporulation rates of P. infestans on potato resulted in simulated epidemics that progressed faster than epidemics simulated for tomato; the high sporulation rates of US-23 isolates resulted in simulated epidemics more severe than simulated epidemics of isolates of the US-22 and US-24 isolates and EC-1 clonal lineages on potato and tomato. Additionally, US-23 isolates consistently caused severe simulated epidemics when lesion growth rate and sporulation were input into the model singly or together. Sporangial size of the US-23 isolates was significantly smaller than that of US-22 and US-24 isolates, which may result in more efficient release of sporangia from the tomato or potato canopy. Our experimentally determined correlates of fitness and the simulated epidemics resulting from their incorporation into the LATEBLIGHT model suggest that US-23 isolates of P. infestans may have the greatest fitness among currently prevalent lineages and may be the most likely lineage to persist in the P. infestans population. The US-23 clonal lineage has been documented as the most prevalent lineage in recent years, indicating its overall fitness. In our work, US-23 had the highest epidemic potential among current genotypes. Given that epidemic potential is a component of fitness, this may, in part, explain the current predominance of the US-23 lineage.

Evidence for Emergency Vaccination Having Played a Crucial Role to Control the 1965/66 Foot-and-Mouth Disease Outbreak in Switzerland

PubMed Central

Zingg, Dana; Häsler, Stephan; Schuepbach-Regula, Gertraud; Schwermer, Heinzpeter; Dürr, Salome

2015-01-01

Foot-and-mouth disease (FMD) is a highly contagious disease that caused several large outbreaks in Europe in the last century. The last important outbreak in Switzerland took place in 1965/66 and affected more than 900 premises and more than 50,000 animals were slaughtered. Large-scale emergency vaccination of the cattle and pig population has been applied to control the epidemic. In recent years, many studies have used infectious disease models to assess the impact of different disease control measures, including models developed for diseases exotic for the specific region of interest. Often, the absence of real outbreak data makes a validation of such models impossible. This study aimed to evaluate whether a spatial, stochastic simulation model (the Davis Animal Disease Simulation model) can predict the course of a Swiss FMD epidemic based on the available historic input data on population structure, contact rates, epidemiology of the virus, and quality of the vaccine. In addition, the potential outcome of the 1965/66 FMD epidemic without application of vaccination was investigated. Comparing the model outcomes to reality, only the largest 10% of the simulated outbreaks approximated the number of animals being culled. However, the simulation model highly overestimated the number of culled premises. While the outbreak duration could not be well reproduced by the model compared to the 1965/66 epidemic, it was able to accurately estimate the size of the area infected. Without application of vaccination, the model predicted a much higher mean number of culled animals than with vaccination, demonstrating that vaccination was likely crucial in disease control for the Swiss FMD outbreak in 1965/66. The study demonstrated the feasibility to analyze historical outbreak data with modern analytical tools. However, it also confirmed that predicted epidemics from a most carefully parameterized model cannot integrate all eventualities of a real epidemic. Therefore, decision makers need to be aware that infectious disease models are useful tools to support the decision-making process but their results are not equal valuable as real observations and should always be interpreted with caution. PMID:26697436

Epidemic spreading in time-varying community networks.

PubMed

Ren, Guangming; Wang, Xingyuan

2014-06-01

The spreading processes of many infectious diseases have comparable time scale as the network evolution. Here, we present a simple networks model with time-varying community structure, and investigate susceptible-infected-susceptible epidemic spreading processes in this model. By both theoretic analysis and numerical simulations, we show that the efficiency of epidemic spreading in this model depends intensively on the mobility rate q of the individuals among communities. We also find that there exists a mobility rate threshold qc. The epidemic will survive when q > qc and die when q < qc. These results can help understanding the impacts of human travel on the epidemic spreading in complex networks with community structure.

The threshold of a stochastic SIQS epidemic model

NASA Astrophysics Data System (ADS)

Zhang, Xiao-Bing; Huo, Hai-Feng; Xiang, Hong; Shi, Qihong; Li, Dungang

2017-09-01

In this paper, we present the threshold of a stochastic SIQS epidemic model which determines the extinction and persistence of the disease. Furthermore, we find that noise can suppress the disease outbreak. Numerical simulations are also carried out to confirm the analytical results.

Apollo: Giving application developers a single point of access to public health models using structured vocabularies and Web services

PubMed Central

Wagner, Michael M.; Levander, John D.; Brown, Shawn; Hogan, William R.; Millett, Nicholas; Hanna, Josh

2013-01-01

This paper describes the Apollo Web Services and Apollo-SV, its related ontology. The Apollo Web Services give an end-user application a single point of access to multiple epidemic simulators. An end user can specify an analytic problem—which we define as a configuration and a query of results—exactly once and submit it to multiple epidemic simulators. The end user represents the analytic problem using a standard syntax and vocabulary, not the native languages of the simulators. We have demonstrated the feasibility of this design by implementing a set of Apollo services that provide access to two epidemic simulators and two visualizer services. PMID:24551417

Apollo: giving application developers a single point of access to public health models using structured vocabularies and Web services.

PubMed

Wagner, Michael M; Levander, John D; Brown, Shawn; Hogan, William R; Millett, Nicholas; Hanna, Josh

2013-01-01

This paper describes the Apollo Web Services and Apollo-SV, its related ontology. The Apollo Web Services give an end-user application a single point of access to multiple epidemic simulators. An end user can specify an analytic problem-which we define as a configuration and a query of results-exactly once and submit it to multiple epidemic simulators. The end user represents the analytic problem using a standard syntax and vocabulary, not the native languages of the simulators. We have demonstrated the feasibility of this design by implementing a set of Apollo services that provide access to two epidemic simulators and two visualizer services.

InterSpread Plus: a spatial and stochastic simulation model of disease in animal populations.

PubMed

Stevenson, M A; Sanson, R L; Stern, M W; O'Leary, B D; Sujau, M; Moles-Benfell, N; Morris, R S

2013-04-01

We describe the spatially explicit, stochastic simulation model of disease spread, InterSpread Plus, in terms of its epidemiological framework, operation, and mode of use. The input data required by the model, the method for simulating contact and infection spread, and methods for simulating disease control measures are described. Data and parameters that are essential for disease simulation modelling using InterSpread Plus are distinguished from those that are non-essential, and it is suggested that a rational approach to simulating disease epidemics using this tool is to start with core data and parameters, adding additional layers of complexity if and when the specific requirements of the simulation exercise require it. We recommend that simulation models of disease are best developed as part of epidemic contingency planning so decision makers are familiar with model outputs and assumptions and are well-positioned to evaluate their strengths and weaknesses to make informed decisions in times of crisis. Copyright © 2012 Elsevier B.V. All rights reserved.

Modelling the effect of wheat canopy architecture as affected by sowing density on Septoria tritici epidemics using a coupled epidemic–virtual plant model

PubMed Central

Baccar, Rim; Fournier, Christian; Dornbusch, Tino; Andrieu, Bruno; Gouache, David; Robert, Corinne

2011-01-01

Background and Aims The relationship between Septoria tritici, a splash-dispersed disease, and its host is complex because of the interactions between the dynamic plant architecture and the vertical progress of the disease. The aim of this study was to test the capacity of a coupled virtual wheat–Septoria tritici epidemic model (Septo3D) to simulate disease progress on the different leaf layers for contrasted sowing density treatments. Methods A field experiment was performed with winter wheat ‘Soissons’ grown at three contrasted densities. Plant architecture was characterized to parameterize the wheat model, and disease dynamic was monitored to compare with simulations. Three simulation scenarios, differing in the degree of detail with which plant variability of development was represented, were defined. Key Results Despite architectural differences between density treatments, few differences were found in disease progress; only the lower-density treatment resulted in a slightly higher rate of lesion development. Model predictions were consistent with field measurements but did not reproduce the higher rate of lesion progress in the low density. The canopy reconstruction scenario in which inter-plant variability was taken into account yielded the best agreement between measured and simulated epidemics. Simulations performed with the canopy represented by a population of the same average plant deviated strongly from the observations. Conclusions It was possible to compare the predicted and measured epidemics on detailed variables, supporting the hypothesis that the approach is able to provide new insights into the processes and plant traits that contribute to the epidemics. On the other hand, the complex and dynamic responses to sowing density made it difficult to test the model precisely and to disentangle the various aspects involved. This could be overcome by comparing more contrasted and/or simpler canopy architectures such as those resulting from quasi-isogenic lines differing by single architectural traits. PMID:21724656

Agent-based and phylogenetic analyses reveal how HIV-1 moves between risk groups: injecting drug users sustain the heterosexual epidemic in Latvia

PubMed Central

Graw, Frederik; Leitner, Thomas; Ribeiro, Ruy M.

2012-01-01

Injecting drug users (IDU) are a driving force for the spread of HIV-1 in Latvia and other Baltic States, accounting for a majority of cases. However, in recent years, heterosexual cases have increased disproportionately. It is unclear how the changes in incidence patterns in Latvia can be explained, and how important IDU are for the heterosexual sub-epidemic. We introduce a novel epidemic model and use phylogenetic analyses in parallel to examine the spread of HIV-1 in Latvia between 1987 and 2010. Using a hybrid framework with a mean-field description for the susceptible population and an agent-based model for the infecteds, we track infected individuals and follow transmission histories dynamically formed during the simulation. The agent-based simulations and the phylogenetic analysis show that more than half of the heterosexual transmissions in Latvia were caused by IDU, which sustain the heterosexual epidemic. Indeed, we find that heterosexual clusters are characterized by short transmission chains with up to 63% of the chains dying out after the first introduction. In the simulations, the distribution of transmission chain sizes follows a power law distribution, which is confirmed by the phylogenetic data. Our models indicate that frequent introductions reduced the extinction probability of an autonomously spreading heterosexual HIV-1 epidemic, which now has the potential to dominate the spread of the overall epidemic in the future. Furthermore, our model shows that social heterogeneity of the susceptible population can explain the shift in HIV-1 incidence in Latvia over the course of the epidemic. Thus, the decrease in IDU incidence may be due to local heterogeneities in transmission, rather than the implementation of control measures. Increases in susceptibles, through social or geographic movement of IDU, could lead to a boost in HIV-1 infections in this risk group. Targeting individuals that bridge social groups would help prevent further spread of the epidemic. PMID:22664069

Agent-based and phylogenetic analyses reveal how HIV-1 moves between risk groups: injecting drug users sustain the heterosexual epidemic in Latvia.

PubMed

Graw, Frederik; Leitner, Thomas; Ribeiro, Ruy M

2012-06-01

Injecting drug users (IDUs) are a driving force for the spread of HIV-1 in Latvia and other Baltic States, accounting for a majority of cases. However, in recent years, heterosexual cases have increased disproportionately. It is unclear how the changes in incidence patterns in Latvia can be explained, and how important IDUs are for the heterosexual sub-epidemic. We introduce a novel epidemic model and use phylogenetic analyses in parallel to examine the spread of HIV-1 in Latvia between 1987 and 2010. Using a hybrid framework with a mean-field description for the susceptible population and an agent-based model for the infecteds, we track infected individuals and follow transmission histories dynamically formed during the simulation. The agent-based simulations and the phylogenetic analysis show that more than half of the heterosexual transmissions in Latvia were caused by IDU, which sustain the heterosexual epidemic. Indeed, we find that heterosexual clusters are characterized by short transmission chains with up to 63% of the chains dying out after the first introduction. In the simulations, the distribution of transmission chain sizes follows a power law distribution, which is confirmed by the phylogenetic data. Our models indicate that frequent introductions reduced the extinction probability of an autonomously spreading heterosexual HIV-1 epidemic, which now has the potential to dominate the spread of the overall epidemic in the future. Furthermore, our model shows that social heterogeneity of the susceptible population can explain the shift in HIV-1 incidence in Latvia over the course of the epidemic. Thus, the decrease in IDU incidence may be due to local heterogeneities in transmission, rather than the implementation of control measures. Increases in susceptibles, through social or geographic movement of IDU, could lead to a boost in HIV-1 infections in this risk group. Targeting individuals that bridge social groups would help prevent further spread of the epidemic. Copyright © 2012 Elsevier B.V. All rights reserved.

Modeling Epidemics Spreading on Social Contact Networks.

PubMed

Zhang, Zhaoyang; Wang, Honggang; Wang, Chonggang; Fang, Hua

2015-09-01

Social contact networks and the way people interact with each other are the key factors that impact on epidemics spreading. However, it is challenging to model the behavior of epidemics based on social contact networks due to their high dynamics. Traditional models such as susceptible-infected-recovered (SIR) model ignore the crowding or protection effect and thus has some unrealistic assumption. In this paper, we consider the crowding or protection effect and develop a novel model called improved SIR model. Then, we use both deterministic and stochastic models to characterize the dynamics of epidemics on social contact networks. The results from both simulations and real data set conclude that the epidemics are more likely to outbreak on social contact networks with higher average degree. We also present some potential immunization strategies, such as random set immunization, dominating set immunization, and high degree set immunization to further prove the conclusion.

Modeling Epidemics Spreading on Social Contact Networks

PubMed Central

ZHANG, ZHAOYANG; WANG, HONGGANG; WANG, CHONGGANG; FANG, HUA

2016-01-01

Social contact networks and the way people interact with each other are the key factors that impact on epidemics spreading. However, it is challenging to model the behavior of epidemics based on social contact networks due to their high dynamics. Traditional models such as susceptible-infected-recovered (SIR) model ignore the crowding or protection effect and thus has some unrealistic assumption. In this paper, we consider the crowding or protection effect and develop a novel model called improved SIR model. Then, we use both deterministic and stochastic models to characterize the dynamics of epidemics on social contact networks. The results from both simulations and real data set conclude that the epidemics are more likely to outbreak on social contact networks with higher average degree. We also present some potential immunization strategies, such as random set immunization, dominating set immunization, and high degree set immunization to further prove the conclusion. PMID:27722037

Approximation of epidemic models by diffusion processes and their statistical inference.

PubMed

Guy, Romain; Larédo, Catherine; Vergu, Elisabeta

2015-02-01

Multidimensional continuous-time Markov jump processes [Formula: see text] on [Formula: see text] form a usual set-up for modeling [Formula: see text]-like epidemics. However, when facing incomplete epidemic data, inference based on [Formula: see text] is not easy to be achieved. Here, we start building a new framework for the estimation of key parameters of epidemic models based on statistics of diffusion processes approximating [Formula: see text]. First, previous results on the approximation of density-dependent [Formula: see text]-like models by diffusion processes with small diffusion coefficient [Formula: see text], where [Formula: see text] is the population size, are generalized to non-autonomous systems. Second, our previous inference results on discretely observed diffusion processes with small diffusion coefficient are extended to time-dependent diffusions. Consistent and asymptotically Gaussian estimates are obtained for a fixed number [Formula: see text] of observations, which corresponds to the epidemic context, and for [Formula: see text]. A correction term, which yields better estimates non asymptotically, is also included. Finally, performances and robustness of our estimators with respect to various parameters such as [Formula: see text] (the basic reproduction number), [Formula: see text], [Formula: see text] are investigated on simulations. Two models, [Formula: see text] and [Formula: see text], corresponding to single and recurrent outbreaks, respectively, are used to simulate data. The findings indicate that our estimators have good asymptotic properties and behave noticeably well for realistic numbers of observations and population sizes. This study lays the foundations of a generic inference method currently under extension to incompletely observed epidemic data. Indeed, contrary to the majority of current inference techniques for partially observed processes, which necessitates computer intensive simulations, our method being mostly an analytical approach requires only the classical optimization steps.

Epidemic spreading in time-varying community networks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ren, Guangming, E-mail: wangxy@dlut.edu.cn, E-mail: ren-guang-ming@163.com; Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024; Wang, Xingyuan, E-mail: wangxy@dlut.edu.cn, E-mail: ren-guang-ming@163.com

2014-06-15

The spreading processes of many infectious diseases have comparable time scale as the network evolution. Here, we present a simple networks model with time-varying community structure, and investigate susceptible-infected-susceptible epidemic spreading processes in this model. By both theoretic analysis and numerical simulations, we show that the efficiency of epidemic spreading in this model depends intensively on the mobility rate q of the individuals among communities. We also find that there exists a mobility rate threshold q{sub c}. The epidemic will survive when q > q{sub c} and die when q < q{sub c}. These results can help understanding the impacts of human travel onmore » the epidemic spreading in complex networks with community structure.« less

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks.

PubMed

Hasegawa, Takehisa; Nemoto, Koji

2017-08-01

This study focuses on investigating the manner in which a prompt quarantine measure suppresses epidemics in networks. A simple and ideal quarantine measure is considered in which an individual is detected with a probability immediately after it becomes infected and the detected one and its neighbors are promptly isolated. The efficiency of this quarantine in suppressing a susceptible-infected-removed (SIR) model is tested in random graphs and uncorrelated scale-free networks. Monte Carlo simulations are used to show that the prompt quarantine measure outperforms random and acquaintance preventive vaccination schemes in terms of reducing the number of infected individuals. The epidemic threshold for the SIR model is analytically derived under the quarantine measure, and the theoretical findings indicate that prompt executions of quarantines are highly effective in containing epidemics. Even if infected individuals are detected with a very low probability, the SIR model under a prompt quarantine measure has finite epidemic thresholds in fat-tailed scale-free networks in which an infected individual can always cause an outbreak of a finite relative size without any measure. The numerical simulations also demonstrate that the present quarantine measure is effective in suppressing epidemics in real networks.

Efficiency of prompt quarantine measures on a susceptible-infected-removed model in networks

NASA Astrophysics Data System (ADS)

Hasegawa, Takehisa; Nemoto, Koji

2017-08-01

This study focuses on investigating the manner in which a prompt quarantine measure suppresses epidemics in networks. A simple and ideal quarantine measure is considered in which an individual is detected with a probability immediately after it becomes infected and the detected one and its neighbors are promptly isolated. The efficiency of this quarantine in suppressing a susceptible-infected-removed (SIR) model is tested in random graphs and uncorrelated scale-free networks. Monte Carlo simulations are used to show that the prompt quarantine measure outperforms random and acquaintance preventive vaccination schemes in terms of reducing the number of infected individuals. The epidemic threshold for the SIR model is analytically derived under the quarantine measure, and the theoretical findings indicate that prompt executions of quarantines are highly effective in containing epidemics. Even if infected individuals are detected with a very low probability, the SIR model under a prompt quarantine measure has finite epidemic thresholds in fat-tailed scale-free networks in which an infected individual can always cause an outbreak of a finite relative size without any measure. The numerical simulations also demonstrate that the present quarantine measure is effective in suppressing epidemics in real networks.

Epidemic spreading and global stability of an SIS model with an infective vector on complex networks

NASA Astrophysics Data System (ADS)

Kang, Huiyan; Fu, Xinchu

2015-10-01

In this paper, we present a new SIS model with delay on scale-free networks. The model is suitable to describe some epidemics which are not only transmitted by a vector but also spread between individuals by direct contacts. In view of the biological relevance and real spreading process, we introduce a delay to denote average incubation period of disease in a vector. By mathematical analysis, we obtain the epidemic threshold and prove the global stability of equilibria. The simulation shows the delay will effect the epidemic spreading. Finally, we investigate and compare two major immunization strategies, uniform immunization and targeted immunization.

Analysis of a novel stochastic SIRS epidemic model with two different saturated incidence rates

NASA Astrophysics Data System (ADS)

Chang, Zhengbo; Meng, Xinzhu; Lu, Xiao

2017-04-01

This paper presents a stochastic SIRS epidemic model with two different nonlinear incidence rates and double epidemic asymmetrical hypothesis, and we devote to develop a mathematical method to obtain the threshold of the stochastic epidemic model. We firstly investigate the boundness and extinction of the stochastic system. Furthermore, we use Ito's formula, the comparison theorem and some new inequalities techniques of stochastic differential systems to discuss persistence in mean of two diseases on three cases. The results indicate that stochastic fluctuations can suppress the disease outbreak. Finally, numerical simulations about different noise disturbance coefficients are carried out to illustrate the obtained theoretical results.

Estimating the epidemic threshold on networks by deterministic connections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Kezan, E-mail: lkzzr@sohu.com; Zhu, Guanghu; Fu, Xinchu

2014-12-15

For many epidemic networks some connections between nodes are treated as deterministic, while the remainder are random and have different connection probabilities. By applying spectral analysis to several constructed models, we find that one can estimate the epidemic thresholds of these networks by investigating information from only the deterministic connections. Nonetheless, in these models, generic nonuniform stochastic connections and heterogeneous community structure are also considered. The estimation of epidemic thresholds is achieved via inequalities with upper and lower bounds, which are found to be in very good agreement with numerical simulations. Since these deterministic connections are easier to detect thanmore » those stochastic connections, this work provides a feasible and effective method to estimate the epidemic thresholds in real epidemic networks.« less

The basic reproduction number R0 and effectiveness of reactive interventions during dengue epidemics: the 2002 dengue outbreak in Easter Island, Chile.

PubMed

Chowell, Gerardo; Fuentes, R; Olea, A; Aguilera, X; Nesse, H; Hyman, J M

2013-01-01

We use a stochastic simulation model to explore the effect of reactive intervention strategies during the 2002 dengue outbreak in the small population of Easter Island, Chile. We quantified the effect of interventions on the transmission dynamics and epidemic size as a function of the simulated control intensity levels and the timing of initiation of control interventions. Because no dengue outbreaks had been reported prior to 2002 in Easter Island, the 2002 epidemic provided a unique opportunity to estimate the basic reproduction number R0 during the initial epidemic phase, prior to the start of control interventions. We estimated R0 at 27.2 (95%CI: 14.8, 49.3). We found that the final epidemic size is highly sensitive to the timing of start of interventions. However, even when the control interventions start several weeks after the epidemic onset, reactive intervention efforts can have a significant impact on the final epidemic size. Our results indicate that the rapid implementation of control interventions can have a significant effect in reducing the epidemic size of dengue epidemics.

Modeling epidemics on adaptively evolving networks: A data-mining perspective.

PubMed

Kattis, Assimakis A; Holiday, Alexander; Stoica, Ana-Andreea; Kevrekidis, Ioannis G

2016-01-01

The exploration of epidemic dynamics on dynamically evolving ("adaptive") networks poses nontrivial challenges to the modeler, such as the determination of a small number of informative statistics of the detailed network state (that is, a few "good observables") that usefully summarize the overall (macroscopic, systems-level) behavior. Obtaining reduced, small size accurate models in terms of these few statistical observables--that is, trying to coarse-grain the full network epidemic model to a small but useful macroscopic one--is even more daunting. Here we describe a data-based approach to solving the first challenge: the detection of a few informative collective observables of the detailed epidemic dynamics. This is accomplished through Diffusion Maps (DMAPS), a recently developed data-mining technique. We illustrate the approach through simulations of a simple mathematical model of epidemics on a network: a model known to exhibit complex temporal dynamics. We discuss potential extensions of the approach, as well as possible shortcomings.

Recalibrating disease parameters for increasing realism in modeling epidemics in closed settings.

PubMed

Bioglio, Livio; Génois, Mathieu; Vestergaard, Christian L; Poletto, Chiara; Barrat, Alain; Colizza, Vittoria

2016-11-14

The homogeneous mixing assumption is widely adopted in epidemic modelling for its parsimony and represents the building block of more complex approaches, including very detailed agent-based models. The latter assume homogeneous mixing within schools, workplaces and households, mostly for the lack of detailed information on human contact behaviour within these settings. The recent data availability on high-resolution face-to-face interactions makes it now possible to assess the goodness of this simplified scheme in reproducing relevant aspects of the infection dynamics. We consider empirical contact networks gathered in different contexts, as well as synthetic data obtained through realistic models of contacts in structured populations. We perform stochastic spreading simulations on these contact networks and in populations of the same size under a homogeneous mixing hypothesis. We adjust the epidemiological parameters of the latter in order to fit the prevalence curve of the contact epidemic model. We quantify the agreement by comparing epidemic peak times, peak values, and epidemic sizes. Good approximations of the peak times and peak values are obtained with the homogeneous mixing approach, with a median relative difference smaller than 20 % in all cases investigated. Accuracy in reproducing the peak time depends on the setting under study, while for the peak value it is independent of the setting. Recalibration is found to be linear in the epidemic parameters used in the contact data simulations, showing changes across empirical settings but robustness across groups and population sizes. An adequate rescaling of the epidemiological parameters can yield a good agreement between the epidemic curves obtained with a real contact network and a homogeneous mixing approach in a population of the same size. The use of such recalibrated homogeneous mixing approximations would enhance the accuracy and realism of agent-based simulations and limit the intrinsic biases of the homogeneous mixing.

Cholera epidemic in Haiti, 2010: using a transmission model to explain spatial spread of disease and identify optimal control interventions.

PubMed

Tuite, Ashleigh R; Tien, Joseph; Eisenberg, Marisa; Earn, David J D; Ma, Junling; Fisman, David N

2011-05-03

Haiti is in the midst of a cholera epidemic. Surveillance data for formulating models of the epidemic are limited, but such models can aid understanding of epidemic processes and help define control strategies. To predict, by using a mathematical model, the sequence and timing of regional cholera epidemics in Haiti and explore the potential effects of disease-control strategies. Compartmental mathematical model allowing person-to-person and waterborne transmission of cholera. Within- and between-region epidemic spread was modeled, with the latter dependent on population sizes and distance between regional centroids (a "gravity" model). Haiti, 2010 to 2011. Haitian hospitalization data, 2009 census data, literature-derived parameter values, and model calibration. Dates of epidemic onset and hospitalizations. The plausible range for cholera's basic reproductive number (R(0), defined as the number of secondary cases per primary case in a susceptible population without intervention) was 2.06 to 2.78. The order and timing of regional cholera outbreaks predicted by the gravity model were closely correlated with empirical observations. Analysis of changes in disease dynamics over time suggests that public health interventions have substantially affected this epidemic. A limited vaccine supply provided late in the epidemic was projected to have a modest effect. Assumptions were simplified, which was necessary for modeling. Projections are based on the initial dynamics of the epidemic, which may change. Despite limited surveillance data from the cholera epidemic in Haiti, a model simulating between-region disease transmission according to population and distance closely reproduces reported disease patterns. This model is a tool that planners, policymakers, and medical personnel seeking to manage the epidemic could use immediately.

Simulations of a epidemic model with parameters variation analysis for the dengue fever

NASA Astrophysics Data System (ADS)

Jardim, C. L. T. F.; Prates, D. B.; Silva, J. M.; Ferreira, L. A. F.; Kritz, M. V.

2015-09-01

Mathematical models can be widely found in the literature for describing and analyzing epidemics. The models that use differential equations to represent mathematically such description are specially sensible to parameters involved in the modelling. In this work, an already developed model, called SIR, is analyzed when applied to a scenario of a dengue fever epidemic. Such choice is powered by the existence of useful tools presented by a variation of this original model, which allow an inclusion of different aspects of the dengue fever disease, as its seasonal characteristics, the presence of more than one strain of the vector and of the biological factor of cross-immunity. The analysis and results interpretation are performed through numerical solutions of the model in question, and a special attention is given to the different solutions generated by the use of different values for the parameters present in this model. Slight variations are performed either dynamically or statically in those parameters, mimicking hypothesized changes in the biological scenario of this simulation and providing a source of evaluation of how those changes would affect the outcomes of the epidemic in a population.

A Parallel Sliding Region Algorithm to Make Agent-Based Modeling Possible for a Large-Scale Simulation: Modeling Hepatitis C Epidemics in Canada.

PubMed

Wong, William W L; Feng, Zeny Z; Thein, Hla-Hla

2016-11-01

Agent-based models (ABMs) are computer simulation models that define interactions among agents and simulate emergent behaviors that arise from the ensemble of local decisions. ABMs have been increasingly used to examine trends in infectious disease epidemiology. However, the main limitation of ABMs is the high computational cost for a large-scale simulation. To improve the computational efficiency for large-scale ABM simulations, we built a parallelizable sliding region algorithm (SRA) for ABM and compared it to a nonparallelizable ABM. We developed a complex agent network and performed two simulations to model hepatitis C epidemics based on the real demographic data from Saskatchewan, Canada. The first simulation used the SRA that processed on each postal code subregion subsequently. The second simulation processed the entire population simultaneously. It was concluded that the parallelizable SRA showed computational time saving with comparable results in a province-wide simulation. Using the same method, SRA can be generalized for performing a country-wide simulation. Thus, this parallel algorithm enables the possibility of using ABM for large-scale simulation with limited computational resources.

Dynamic behavior of the interaction between epidemics and cascades on heterogeneous networks

NASA Astrophysics Data System (ADS)

Jiang, Lurong; Jin, Xinyu; Xia, Yongxiang; Ouyang, Bo; Wu, Duanpo

2014-12-01

Epidemic spreading and cascading failure are two important dynamical processes on complex networks. They have been investigated separately for a long time. But in the real world, these two dynamics sometimes may interact with each other. In this paper, we explore a model combined with the SIR epidemic spreading model and a local load sharing cascading failure model. There exists a critical value of the tolerance parameter for which the epidemic with high infection probability can spread out and infect a fraction of the network in this model. When the tolerance parameter is smaller than the critical value, the cascading failure cuts off the abundance of paths and blocks the spreading of the epidemic locally. While the tolerance parameter is larger than the critical value, the epidemic spreads out and infects a fraction of the network. A method for estimating the critical value is proposed. In simulations, we verify the effectiveness of this method in the uncorrelated configuration model (UCM) scale-free networks.

Stability and bifurcation for an SEIS epidemic model with the impact of media

NASA Astrophysics Data System (ADS)

Huo, Hai-Feng; Yang, Peng; Xiang, Hong

2018-01-01

A novel SEIS epidemic model with the impact of media is introduced. By analyzing the characteristic equation of equilibrium, the basic reproduction number is obtained and the stability of the steady states is proved. The occurrence of a forward, backward and Hopf bifurcation is derived. Numerical simulations and sensitivity analysis are performed. Our results manifest that media can regard as a good indicator in controlling the emergence and spread of the epidemic disease.

Second look at the spread of epidemics on networks

NASA Astrophysics Data System (ADS)

Kenah, Eben; Robins, James M.

2007-09-01

In an important paper, Newman [Phys. Rev. E66, 016128 (2002)] claimed that a general network-based stochastic Susceptible-Infectious-Removed (SIR) epidemic model is isomorphic to a bond percolation model, where the bonds are the edges of the contact network and the bond occupation probability is equal to the marginal probability of transmission from an infected node to a susceptible neighbor. In this paper, we show that this isomorphism is incorrect and define a semidirected random network we call the epidemic percolation network that is exactly isomorphic to the SIR epidemic model in any finite population. In the limit of a large population, (i) the distribution of (self-limited) outbreak sizes is identical to the size distribution of (small) out-components, (ii) the epidemic threshold corresponds to the phase transition where a giant strongly connected component appears, (iii) the probability of a large epidemic is equal to the probability that an initial infection occurs in the giant in-component, and (iv) the relative final size of an epidemic is equal to the proportion of the network contained in the giant out-component. For the SIR model considered by Newman, we show that the epidemic percolation network predicts the same mean outbreak size below the epidemic threshold, the same epidemic threshold, and the same final size of an epidemic as the bond percolation model. However, the bond percolation model fails to predict the correct outbreak size distribution and probability of an epidemic when there is a nondegenerate infectious period distribution. We confirm our findings by comparing predictions from percolation networks and bond percolation models to the results of simulations. In the Appendix, we show that an isomorphism to an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model.

On the modeling of epidemics under the influence of risk perception

NASA Astrophysics Data System (ADS)

de Lillo, S.; Fioriti, G.; Prioriello, M. L.

An epidemic spreading model is presented in the framework of the kinetic theory of active particles. The model is characterized by the influence of risk perception which can reduce the diffusion of infection. The evolution of the system is modeled through nonlinear interactions, whose output is described by stochastic games. The results of numerical simulations are discussed for different initial conditions.

Epidemic Process over the Commute Network in a Metropolitan Area

PubMed Central

Yashima, Kenta; Sasaki, Akira

2014-01-01

An understanding of epidemiological dynamics is important for prevention and control of epidemic outbreaks. However, previous studies tend to focus only on specific areas, indicating that application to another area or intervention strategy requires a similar time-consuming simulation. Here, we study the epidemic dynamics of the disease-spread over a commute network, using the Tokyo metropolitan area as an example, in an attempt to elucidate the general properties of epidemic spread over a commute network that could be used for a prediction in any metropolitan area. The model is formulated on the basis of a metapopulation network in which local populations are interconnected by actual commuter flows in the Tokyo metropolitan area and the spread of infection is simulated by an individual-based model. We find that the probability of a global epidemic as well as the final epidemic sizes in both global and local populations, the timing of the epidemic peak, and the time at which the epidemic reaches a local population are mainly determined by the joint distribution of the local population sizes connected by the commuter flows, but are insensitive to geographical or topological structure of the network. Moreover, there is a strong relation between the population size and the time that the epidemic reaches this local population and we are able to determine the reason for this relation as well as its dependence on the commute network structure and epidemic parameters. This study shows that the model based on the connection between the population size classes is sufficient to predict both global and local epidemic dynamics in metropolitan area. Moreover, the clear relation of the time taken by the epidemic to reach each local population can be used as a novel measure for intervention; this enables efficient intervention strategies in each local population prior to the actual arrival. PMID:24905831

Hop limited epidemic-like information spreading in mobile social networks with selfish nodes

NASA Astrophysics Data System (ADS)

Wu, Yahui; Deng, Su; Huang, Hongbin

2013-07-01

Similar to epidemics, information can be transmitted directly among users in mobile social networks. Different from epidemics, we can control the spreading process by adjusting the corresponding parameters (e.g., hop count) directly. This paper proposes a theoretical model to evaluate the performance of an epidemic-like spreading algorithm, in which the maximal hop count of the information is limited. In addition, our model can be used to evaluate the impact of users’ selfish behavior. Simulations show the accuracy of our theoretical model. Numerical results show that the information hop count can have an important impact. In addition, the impact of selfish behavior is related to the information hop count.

Impact of delay on disease outbreak in a spatial epidemic model

NASA Astrophysics Data System (ADS)

Zhao, Xia-Xia; Wang, Jian-Zhong

2015-04-01

One of the central issues in studying epidemic spreading is the mechanism on disease outbreak. In this paper, we investigate the effects of time delay on disease outbreak in spatial epidemics based on a reaction-diffusion model. By mathematical analysis and numerical simulations, we show that when time delay is more than a critical value, the disease outbreaks. The obtained results show that the time delay is an important factor in the spread of the disease, which may provide new insights on disease control.

Modeling Epidemics with Dynamic Small-World Networks

NASA Astrophysics Data System (ADS)

Kaski, Kimmo; Saramäki, Jari

2005-06-01

In this presentation a minimal model for describing the spreading of an infectious disease, such as influenza, is discussed. Here it is assumed that spreading takes place on a dynamic small-world network comprising short- and long-range infection events. Approximate equations for the epidemic threshold as well as the spreading dynamics are derived and they agree well with numerical discrete time-step simulations. Also the dependence of the epidemic saturation time on the initial conditions is analysed and a comparison with real-world data is made.

Epidemic outbreaks and its control using a fractional order model with seasonality and stochastic infection

NASA Astrophysics Data System (ADS)

He, Shaobo; Banerjee, Santo

2018-07-01

A fractional-order SIR epidemic model is proposed under the influence of both parametric seasonality and the external noise. The integer order SIR epidemic model originally is stable. By introducing seasonality and noise force to the model, behaviors of the system is changed. It is shown that the system has rich dynamical behaviors with different system parameters, fractional derivative order and the degree of seasonality and noise. Complexity of the stochastic model is investigated by using multi-scale fuzzy entropy. Finally, hard limiter controlled system is designed and simulation results show the ratio of infected individuals can converge to a small enough target ρ, which means the epidemic outbreak can be under control by the implementation of some effective medical and health measures.

A Computer Simulation of Employee Vaccination to Mitigate an Influenza Epidemic

PubMed Central

Lee, Bruce Y.; Brown, Shawn T.; Cooley, Philip C.; Zimmerman, Richard K.; Wheaton, William D.; Zimmer, Shanta M.; Grefenstette, John J.; Assi, Tina-Marie; Furphy, Timothy J.; Wagener, Diane K.; Burke, Donald S.

2010-01-01

Background Determining the effects of varying vaccine coverage, compliance, administration rates, prioritization, and timing among employees during an influenza pandemic. Methods As part of the Models of Infectious Disease Agent Study (MIDAS) network’s H1N1 influenza planning efforts, an agent-based computer simulation model (ABM) was developed of the Washington, DC metropolitan region, encompassing five metropolitan statistical areas. Each simulation run involved introducing 100 infectious individuals to initiate a 1.3 reproductive rate (R0) epidemic, consistent with H1N1 parameters to date. Another set of scenarios represented a R0=1.6 epidemic. Results An unmitigated epidemic resulted in substantial productivity losses (a mean of $112.6 million for a serologic 15% attack rate and $193.8 million for a serologic 25% attack rate), even with the relatively low estimated mortality impact of H1N1. While vaccinating Advisory Committee on Immunization Practices (ACIP) priority groups resulted in the largest savings, vaccinating all remaining workers captured additional savings and, in fact, reduced healthcare workers’ and critical infrastructure workers’ chances of infection. While employee vaccination compliance affected the epidemic, once 20% compliance was achieved, additional increases in compliance provided less incremental benefit. Even though a vast majority of the workplaces in the DC Metro region had fewer than 100 employees, focusing on vaccinating only those in larger firms (≥100 employees) was just as effective in mitigating the epidemic as trying to vaccinate all workplaces. Conclusions Timely vaccination of at least 20% of the large company workforce can play an important role in epidemic mitigation. PMID:20042311

Epidemic spreading in weighted networks: an edge-based mean-field solution.

PubMed

Yang, Zimo; Zhou, Tao

2012-05-01

Weight distribution greatly impacts the epidemic spreading taking place on top of networks. This paper presents a study of a susceptible-infected-susceptible model on regular random networks with different kinds of weight distributions. Simulation results show that the more homogeneous weight distribution leads to higher epidemic prevalence, which, unfortunately, could not be captured by the traditional mean-field approximation. This paper gives an edge-based mean-field solution for general weight distribution, which can quantitatively reproduce the simulation results. This method could be applied to characterize the nonequilibrium steady states of dynamical processes on weighted networks.

Modeling epidemic spread with awareness and heterogeneous transmission rates in networks.

PubMed

Shang, Yilun

2013-06-01

During an epidemic outbreak in a human population, susceptibility to infection can be reduced by raising awareness of the disease. In this paper, we investigate the effects of three forms of awareness (i.e., contact, local, and global) on the spread of a disease in a random network. Connectivity-correlated transmission rates are assumed. By using the mean-field theory and numerical simulation, we show that both local and contact awareness can raise the epidemic thresholds while the global awareness cannot, which mirrors the recent results of Wu et al. The obtained results point out that individual behaviors in the presence of an infectious disease has a great influence on the epidemic dynamics. Our method enriches mean-field analysis in epidemic models.

Epidemic dynamics and endemic states in complex networks

NASA Astrophysics Data System (ADS)

Pastor-Satorras, Romualdo; Vespignani, Alessandro

2001-06-01

We study by analytical methods and large scale simulations a dynamical model for the spreading of epidemics in complex networks. In networks with exponentially bounded connectivity we recover the usual epidemic behavior with a threshold defining a critical point below that the infection prevalence is null. On the contrary, on a wide range of scale-free networks we observe the absence of an epidemic threshold and its associated critical behavior. This implies that scale-free networks are prone to the spreading and the persistence of infections whatever spreading rate the epidemic agents might possess. These results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks.

A nonlinear SIR with stability

NASA Astrophysics Data System (ADS)

Trisilowati, Darti, I.; Fitri, S.

2014-02-01

The aim of this work is to develop a mathematical model of a nonlinear susceptible-infectious-removed (SIR) epidemic model with vaccination. We analyze the stability of the model by linearizing the model around the equilibrium point. Then, diphtheria data from East Java province is fitted to the model. From these estimated parameters, we investigate which parameters that play important role in the epidemic model. Some numerical simulations are given to illustrate the analytical results and the behavior of the model.

Epidemic spreading with activity-driven awareness diffusion on multiplex network.

PubMed

Guo, Quantong; Lei, Yanjun; Jiang, Xin; Ma, Yifang; Huo, Guanying; Zheng, Zhiming

2016-04-01

There has been growing interest in exploring the interplay between epidemic spreading with human response, since it is natural for people to take various measures when they become aware of epidemics. As a proper way to describe the multiple connections among people in reality, multiplex network, a set of nodes interacting through multiple sets of edges, has attracted much attention. In this paper, to explore the coupled dynamical processes, a multiplex network with two layers is built. Specifically, the information spreading layer is a time varying network generated by the activity driven model, while the contagion layer is a static network. We extend the microscopic Markov chain approach to derive the epidemic threshold of the model. Compared with extensive Monte Carlo simulations, the method shows high accuracy for the prediction of the epidemic threshold. Besides, taking different spreading models of awareness into consideration, we explored the interplay between epidemic spreading with awareness spreading. The results show that the awareness spreading can not only enhance the epidemic threshold but also reduce the prevalence of epidemics. When the spreading of awareness is defined as susceptible-infected-susceptible model, there exists a critical value where the dynamical process on the awareness layer can control the onset of epidemics; while if it is a threshold model, the epidemic threshold emerges an abrupt transition with the local awareness ratio α approximating 0.5. Moreover, we also find that temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is threshold model. Given that the threshold model is a widely used model for social contagion, this is an important and meaningful result. Our results could also lead to interesting future research about the different time-scales of structural changes in multiplex networks.

Epidemic spreading with activity-driven awareness diffusion on multiplex network

NASA Astrophysics Data System (ADS)

Guo, Quantong; Lei, Yanjun; Jiang, Xin; Ma, Yifang; Huo, Guanying; Zheng, Zhiming

2016-04-01

There has been growing interest in exploring the interplay between epidemic spreading with human response, since it is natural for people to take various measures when they become aware of epidemics. As a proper way to describe the multiple connections among people in reality, multiplex network, a set of nodes interacting through multiple sets of edges, has attracted much attention. In this paper, to explore the coupled dynamical processes, a multiplex network with two layers is built. Specifically, the information spreading layer is a time varying network generated by the activity driven model, while the contagion layer is a static network. We extend the microscopic Markov chain approach to derive the epidemic threshold of the model. Compared with extensive Monte Carlo simulations, the method shows high accuracy for the prediction of the epidemic threshold. Besides, taking different spreading models of awareness into consideration, we explored the interplay between epidemic spreading with awareness spreading. The results show that the awareness spreading can not only enhance the epidemic threshold but also reduce the prevalence of epidemics. When the spreading of awareness is defined as susceptible-infected-susceptible model, there exists a critical value where the dynamical process on the awareness layer can control the onset of epidemics; while if it is a threshold model, the epidemic threshold emerges an abrupt transition with the local awareness ratio α approximating 0.5. Moreover, we also find that temporal changes in the topology hinder the spread of awareness which directly affect the epidemic threshold, especially when the awareness layer is threshold model. Given that the threshold model is a widely used model for social contagion, this is an important and meaningful result. Our results could also lead to interesting future research about the different time-scales of structural changes in multiplex networks.

Is it growing exponentially fast? -- Impact of assuming exponential growth for characterizing and forecasting epidemics with initial near-exponential growth dynamics.

PubMed

Chowell, Gerardo; Viboud, Cécile

2016-10-01

The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing models that capture the baseline transmission characteristics in order to generate reliable epidemic forecasts. Improved models for epidemic forecasting could be achieved by identifying signature features of epidemic growth, which could inform the design of models of disease spread and reveal important characteristics of the transmission process. In particular, it is often taken for granted that the early growth phase of different growth processes in nature follow early exponential growth dynamics. In the context of infectious disease spread, this assumption is often convenient to describe a transmission process with mass action kinetics using differential equations and generate analytic expressions and estimates of the reproduction number. In this article, we carry out a simulation study to illustrate the impact of incorrectly assuming an exponential-growth model to characterize the early phase (e.g., 3-5 disease generation intervals) of an infectious disease outbreak that follows near-exponential growth dynamics. Specifically, we assess the impact on: 1) goodness of fit, 2) bias on the growth parameter, and 3) the impact on short-term epidemic forecasts. Designing transmission models and statistical approaches that more flexibly capture the profile of epidemic growth could lead to enhanced model fit, improved estimates of key transmission parameters, and more realistic epidemic forecasts.

Decisions on control of foot-and-mouth disease informed using model predictions.

PubMed

Halasa, T; Willeberg, P; Christiansen, L E; Boklund, A; Alkhamis, M; Perez, A; Enøe, C

2013-11-01

The decision on whether or not to change the control strategy, such as introducing emergency vaccination, is perhaps one of the most difficult decisions faced by the veterinary authorities during a foot-and-mouth disease (FMD) epidemic. A simple tool that may predict the epidemic outcome and consequences would be useful to assist the veterinary authorities in the decision-making process. A previously proposed simple quantitative tool based on the first 14 days outbreaks (FFO) of FMD was used with results from an FMD simulation exercise. Epidemic outcomes included the number of affected herds, epidemic duration, geographical size and costs. The first 14 days spatial spread (FFS) was also included to further support the prediction. The epidemic data was obtained from a Danish version (DTU-DADS) of a pre-existing FMD simulation model (Davis Animal Disease Spread - DADS) adapted to model the spread of FMD in Denmark. The European Union (EU) and Danish regulations for FMD control were used in the simulation. The correlations between FFO and FFS and the additional number of affected herds after day 14 following detection of the first infected herd were 0.66 and 0.82, respectively. The variation explained by the FFO at day 14 following detection was high (P-value<0.001). This indicates that the FFO may take a part in the decision of whether or not to intensify FMD control, for instance by introducing emergency vaccination and/or pre-emptive depopulation, which might prevent a "catastrophic situation". A significant part of the variation was explained by supplementing the model with the FFS (P-value<0.001). Furthermore, the type of the index-herd was also a significant predictor of the epidemic outcomes (P-value<0.05). The results of the current study suggest that national veterinary authorities should consider to model their national situation and to use FFO and FFS to help planning and updating their contingency plans and FMD emergency control strategies. Copyright © 2013 Elsevier B.V. All rights reserved.

Mathematical models to characterize early epidemic growth: A Review

PubMed Central

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-01-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-15 Ebola epidemic in West Africa. PMID:27451336

Mathematical models to characterize early epidemic growth: A review

NASA Astrophysics Data System (ADS)

Chowell, Gerardo; Sattenspiel, Lisa; Bansal, Shweta; Viboud, Cécile

2016-09-01

There is a long tradition of using mathematical models to generate insights into the transmission dynamics of infectious diseases and assess the potential impact of different intervention strategies. The increasing use of mathematical models for epidemic forecasting has highlighted the importance of designing reliable models that capture the baseline transmission characteristics of specific pathogens and social contexts. More refined models are needed however, in particular to account for variation in the early growth dynamics of real epidemics and to gain a better understanding of the mechanisms at play. Here, we review recent progress on modeling and characterizing early epidemic growth patterns from infectious disease outbreak data, and survey the types of mathematical formulations that are most useful for capturing a diversity of early epidemic growth profiles, ranging from sub-exponential to exponential growth dynamics. Specifically, we review mathematical models that incorporate spatial details or realistic population mixing structures, including meta-population models, individual-based network models, and simple SIR-type models that incorporate the effects of reactive behavior changes or inhomogeneous mixing. In this process, we also analyze simulation data stemming from detailed large-scale agent-based models previously designed and calibrated to study how realistic social networks and disease transmission characteristics shape early epidemic growth patterns, general transmission dynamics, and control of international disease emergencies such as the 2009 A/H1N1 influenza pandemic and the 2014-2015 Ebola epidemic in West Africa.

The threshold of a stochastic avian-human influenza epidemic model with psychological effect

NASA Astrophysics Data System (ADS)

Zhang, Fengrong; Zhang, Xinhong

2018-02-01

In this paper, a stochastic avian-human influenza epidemic model with psychological effect in human population and saturation effect within avian population is investigated. This model describes the transmission of avian influenza among avian population and human population in random environments. For stochastic avian-only system, persistence in the mean and extinction of the infected avian population are studied. For the avian-human influenza epidemic system, sufficient conditions for the existence of an ergodic stationary distribution are obtained. Furthermore, a threshold of this stochastic model which determines the outcome of the disease is obtained. Finally, numerical simulations are given to support the theoretical results.

Dynamics of epidemic spreading with vaccination: Impact of social pressure and engagement

NASA Astrophysics Data System (ADS)

Pires, Marcelo A.; Crokidakis, Nuno

2017-02-01

In this work we consider a model of epidemic spreading coupled with an opinion dynamics in a fully-connected population. Regarding the opinion dynamics, the individuals may be in two distinct states, namely in favor or against a vaccination campaign. Individuals against the vaccination follow a standard SIS model, whereas the pro-vaccine individuals can also be in a third compartment, namely Vaccinated. In addition, the opinions change according to the majority-rule dynamics in groups with three individuals. We also consider that the vaccine can give permanent or temporary immunization to the individuals. By means of analytical calculations and computer simulations, we show that the opinion dynamics can drastically affect the disease propagation, and that the engagement of the pro-vaccine individuals can be crucial for stopping the epidemic spreading. The full numerical code for simulating the model is available from the authors' webpage.

Effects of distribution of infection rate on epidemic models

NASA Astrophysics Data System (ADS)

Lachiany, Menachem; Louzoun, Yoram

2016-08-01

A goal of many epidemic models is to compute the outcome of the epidemics from the observed infected early dynamics. However, often, the total number of infected individuals at the end of the epidemics is much lower than predicted from the early dynamics. This discrepancy is argued to result from human intervention or nonlinear dynamics not incorporated in standard models. We show that when variability in infection rates is included in standard susciptible-infected-susceptible (SIS ) and susceptible-infected-recovered (SIR ) models the total number of infected individuals in the late dynamics can be orders lower than predicted from the early dynamics. This discrepancy holds for SIS and SIR models, where the assumption that all individuals have the same sensitivity is eliminated. In contrast with network models, fixed partnerships are not assumed. We derive a moment closure scheme capturing the distribution of sensitivities. We find that the shape of the sensitivity distribution does not affect R0 or the number of infected individuals in the early phases of the epidemics. However, a wide distribution of sensitivities reduces the total number of removed individuals in the SIR model and the steady-state infected fraction in the SIS model. The difference between the early and late dynamics implies that in order to extrapolate the expected effect of the epidemics from the initial phase of the epidemics, the rate of change in the average infectivity should be computed. These results are supported by a comparison of the theoretical model to the Ebola epidemics and by numerical simulation.

Discrete Event Modeling and Massively Parallel Execution of Epidemic Outbreak Phenomena

DOE Office of Scientific and Technical Information (OSTI.GOV)

Perumalla, Kalyan S; Seal, Sudip K

2011-01-01

In complex phenomena such as epidemiological outbreaks, the intensity of inherent feedback effects and the significant role of transients in the dynamics make simulation the only effective method for proactive, reactive or post-facto analysis. The spatial scale, runtime speed, and behavioral detail needed in detailed simulations of epidemic outbreaks make it necessary to use large-scale parallel processing. Here, an optimistic parallel execution of a new discrete event formulation of a reaction-diffusion simulation model of epidemic propagation is presented to facilitate in dramatically increasing the fidelity and speed by which epidemiological simulations can be performed. Rollback support needed during optimistic parallelmore » execution is achieved by combining reverse computation with a small amount of incremental state saving. Parallel speedup of over 5,500 and other runtime performance metrics of the system are observed with weak-scaling execution on a small (8,192-core) Blue Gene / P system, while scalability with a weak-scaling speedup of over 10,000 is demonstrated on 65,536 cores of a large Cray XT5 system. Scenarios representing large population sizes exceeding several hundreds of millions of individuals in the largest cases are successfully exercised to verify model scalability.« less

Development of a Novel Rabies Simulation Model for Application in a Non-endemic Environment

PubMed Central

Dürr, Salome; Ward, Michael P.

2015-01-01

Domestic dog rabies is an endemic disease in large parts of the developing world and also epidemic in previously free regions. For example, it continues to spread in eastern Indonesia and currently threatens adjacent rabies-free regions with high densities of free-roaming dogs, including remote northern Australia. Mathematical and simulation disease models are useful tools to provide insights on the most effective control strategies and to inform policy decisions. Existing rabies models typically focus on long-term control programs in endemic countries. However, simulation models describing the dog rabies incursion scenario in regions where rabies is still exotic are lacking. We here describe such a stochastic, spatially explicit rabies simulation model that is based on individual dog information collected in two remote regions in northern Australia. Illustrative simulations produced plausible results with epidemic characteristics expected for rabies outbreaks in disease free regions (mean R0 1.7, epidemic peak 97 days post-incursion, vaccination as the most effective response strategy). Systematic sensitivity analysis identified that model outcomes were most sensitive to seven of the 30 model parameters tested. This model is suitable for exploring rabies spread and control before an incursion in populations of largely free-roaming dogs that live close together with their owners. It can be used for ad-hoc contingency or response planning prior to and shortly after incursion of dog rabies in previously free regions. One challenge that remains is model parameterisation, particularly how dogs’ roaming and contacts and biting behaviours change following a rabies incursion in a previously rabies free population. PMID:26114762

Effects of Variant Rates and Noise on Epidemic Spreading

NASA Astrophysics Data System (ADS)

Li, Wei; Gao, Zong-Mao; Gu, Jiao

2011-05-01

We introduce variant rates, for both infection and recovery and noise into the susceptible-infected-removed (SIR) model for epidemic spreading. The changing rates are taken mainly due to the changing profiles of an epidemic during its evolution. However, the noise parameter which is taken from a given distribution, i.e. Gaussian can describe the fluctuations of the infection and recovery rates. The numerical simulations show that the SIR model with variant rates and noise and can improve the fitting with real SARS data in the near-stationary stage.

Epidemic forecasting is messier than weather forecasting: The role of human behavior and internet data streams in epidemic forecast

DOE PAGES

Moran, Kelly Renee; Fairchild, Geoffrey; Generous, Nicholas; ...

2016-11-14

Mathematical models, such as those that forecast the spread of epidemics or predict the weather, must overcome the challenges of integrating incomplete and inaccurate data in computer simulations, estimating the probability of multiple possible scenarios, incorporating changes in human behavior and/or the pathogen, and environmental factors. In the past 3 decades, the weather forecasting community has made significant advances in data collection, assimilating heterogeneous data steams into models and communicating the uncertainty of their predictions to the general public. Epidemic modelers are struggling with these same issues in forecasting the spread of emerging diseases, such as Zika virus infection andmore » Ebola virus disease. While weather models rely on physical systems, data from satellites, and weather stations, epidemic models rely on human interactions, multiple data sources such as clinical surveillance and Internet data, and environmental or biological factors that can change the pathogen dynamics. We describe some of similarities and differences between these 2 fields and how the epidemic modeling community is rising to the challenges posed by forecasting to help anticipate and guide the mitigation of epidemics. Here, we conclude that some of the fundamental differences between these 2 fields, such as human behavior, make disease forecasting more challenging than weather forecasting.« less

Epidemic forecasting is messier than weather forecasting: The role of human behavior and internet data streams in epidemic forecast

DOE Office of Scientific and Technical Information (OSTI.GOV)

Moran, Kelly Renee; Fairchild, Geoffrey; Generous, Nicholas

Mathematical models, such as those that forecast the spread of epidemics or predict the weather, must overcome the challenges of integrating incomplete and inaccurate data in computer simulations, estimating the probability of multiple possible scenarios, incorporating changes in human behavior and/or the pathogen, and environmental factors. In the past 3 decades, the weather forecasting community has made significant advances in data collection, assimilating heterogeneous data steams into models and communicating the uncertainty of their predictions to the general public. Epidemic modelers are struggling with these same issues in forecasting the spread of emerging diseases, such as Zika virus infection andmore » Ebola virus disease. While weather models rely on physical systems, data from satellites, and weather stations, epidemic models rely on human interactions, multiple data sources such as clinical surveillance and Internet data, and environmental or biological factors that can change the pathogen dynamics. We describe some of similarities and differences between these 2 fields and how the epidemic modeling community is rising to the challenges posed by forecasting to help anticipate and guide the mitigation of epidemics. Here, we conclude that some of the fundamental differences between these 2 fields, such as human behavior, make disease forecasting more challenging than weather forecasting.« less

Epidemic Forecasting is Messier Than Weather Forecasting: The Role of Human Behavior and Internet Data Streams in Epidemic Forecast

PubMed Central

Moran, Kelly R.; Fairchild, Geoffrey; Generous, Nicholas; Hickmann, Kyle; Osthus, Dave; Priedhorsky, Reid; Hyman, James; Del Valle, Sara Y.

2016-01-01

Mathematical models, such as those that forecast the spread of epidemics or predict the weather, must overcome the challenges of integrating incomplete and inaccurate data in computer simulations, estimating the probability of multiple possible scenarios, incorporating changes in human behavior and/or the pathogen, and environmental factors. In the past 3 decades, the weather forecasting community has made significant advances in data collection, assimilating heterogeneous data steams into models and communicating the uncertainty of their predictions to the general public. Epidemic modelers are struggling with these same issues in forecasting the spread of emerging diseases, such as Zika virus infection and Ebola virus disease. While weather models rely on physical systems, data from satellites, and weather stations, epidemic models rely on human interactions, multiple data sources such as clinical surveillance and Internet data, and environmental or biological factors that can change the pathogen dynamics. We describe some of similarities and differences between these 2 fields and how the epidemic modeling community is rising to the challenges posed by forecasting to help anticipate and guide the mitigation of epidemics. We conclude that some of the fundamental differences between these 2 fields, such as human behavior, make disease forecasting more challenging than weather forecasting. PMID:28830111

Inference of Transmission Network Structure from HIV Phylogenetic Trees

DOE PAGES

Giardina, Federica; Romero-Severson, Ethan Obie; Albert, Jan; ...

2017-01-13

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic.more » Second, we implemented an inference method based on approximate Bayesian computation (ABC) to discriminate among three well-studied network models and jointly estimate both network parameters and key epidemiological quantities such as the infection rate. Our ABC framework used both topological and distance-based tree statistics for comparison between simulated and observed trees. Overall, our simulations showed that a virus time-scaled phylogeny (genealogy) may be substantially different from the between-host transmission tree. This has important implications for the interpretation of what a phylogeny reveals about the underlying epidemic contact network. In particular, we found that while the within-host evolutionary process obscures the transmission tree, the diversification process and infectivity dynamics also add discriminatory power to differentiate between different types of contact networks. We also found that the possibility to differentiate contact networks depends on how far an epidemic has progressed, where distance-based tree statistics have more power early in an epidemic. Finally, we applied our ABC inference on two different outbreaks from the Swedish HIV-1 epidemic.« less

Inference of Transmission Network Structure from HIV Phylogenetic Trees

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giardina, Federica; Romero-Severson, Ethan Obie; Albert, Jan

Phylogenetic inference is an attractive means to reconstruct transmission histories and epidemics. However, there is not a perfect correspondence between transmission history and virus phylogeny. Both node height and topological differences may occur, depending on the interaction between within-host evolutionary dynamics and between-host transmission patterns. To investigate these interactions, we added a within-host evolutionary model in epidemiological simulations and examined if the resulting phylogeny could recover different types of contact networks. To further improve realism, we also introduced patient-specific differences in infectivity across disease stages, and on the epidemic level we considered incomplete sampling and the age of the epidemic.more » Second, we implemented an inference method based on approximate Bayesian computation (ABC) to discriminate among three well-studied network models and jointly estimate both network parameters and key epidemiological quantities such as the infection rate. Our ABC framework used both topological and distance-based tree statistics for comparison between simulated and observed trees. Overall, our simulations showed that a virus time-scaled phylogeny (genealogy) may be substantially different from the between-host transmission tree. This has important implications for the interpretation of what a phylogeny reveals about the underlying epidemic contact network. In particular, we found that while the within-host evolutionary process obscures the transmission tree, the diversification process and infectivity dynamics also add discriminatory power to differentiate between different types of contact networks. We also found that the possibility to differentiate contact networks depends on how far an epidemic has progressed, where distance-based tree statistics have more power early in an epidemic. Finally, we applied our ABC inference on two different outbreaks from the Swedish HIV-1 epidemic.« less

Recurrent epidemic cycles driven by intervention in a population of two susceptibility types

NASA Astrophysics Data System (ADS)

Juanico, Drandreb Earl O.

2014-03-01

Epidemics have been known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, infectious diseases like influenza continue to appear intermittently over time. I have undertaken an analysis of a stochastic epidemic model to explore the hypothesis that intervention efforts actually drive epidemic cycles. Time series from simulations of the model reveal oscillations exhibiting a similar temporal signature as influenza epidemics. The power-spectral density indicates a resonant frequency, which approximately corresponds to the apparent annual seasonality of influenza in temperate zones. Asymptotic solution to the backward Kolmogorov equation of the dynamics corresponds to an exponentially-decaying mean-exit time as a function of the intervention rate. Intervention must be implemented at a sufficiently high rate to extinguish the infection. The results demonstrate that intervention efforts can induce epidemic cycles, and that the temporal signature of cycles can provide early warning of imminent outbreaks.

Inferring Epidemic Contact Structure from Phylogenetic Trees

PubMed Central

Leventhal, Gabriel E.; Kouyos, Roger; Stadler, Tanja; von Wyl, Viktor; Yerly, Sabine; Böni, Jürg; Cellerai, Cristina; Klimkait, Thomas; Günthard, Huldrych F.; Bonhoeffer, Sebastian

2012-01-01

Contact structure is believed to have a large impact on epidemic spreading and consequently using networks to model such contact structure continues to gain interest in epidemiology. However, detailed knowledge of the exact contact structure underlying real epidemics is limited. Here we address the question whether the structure of the contact network leaves a detectable genetic fingerprint in the pathogen population. To this end we compare phylogenies generated by disease outbreaks in simulated populations with different types of contact networks. We find that the shape of these phylogenies strongly depends on contact structure. In particular, measures of tree imbalance allow us to quantify to what extent the contact structure underlying an epidemic deviates from a null model contact network and illustrate this in the case of random mixing. Using a phylogeny from the Swiss HIV epidemic, we show that this epidemic has a significantly more unbalanced tree than would be expected from random mixing. PMID:22412361

Sudden transitions in coupled opinion and epidemic dynamics with vaccination

NASA Astrophysics Data System (ADS)

Pires, Marcelo A.; Oestereich, André L.; Crokidakis, Nuno

2018-05-01

This work consists of an epidemic model with vaccination coupled with an opinion dynamics. Our objective was to study how disease risk perception can influence opinions about vaccination and therefore the spreading of the disease. Differently from previous works we have considered continuous opinions. The epidemic spreading is governed by an SIS-like model with an extra vaccinated state. In our model individuals vaccinate with a probability proportional to their opinions. The opinions change due to peer influence in pairwise interactions. The epidemic feedback to the opinion dynamics acts as an external field increasing the vaccination probability. We performed Monte Carlo simulations in fully-connected populations. Interestingly we observed the emergence of a first-order phase transition, besides the usual active-absorbing phase transition presented in the SIS model. Our simulations also show that with a certain combination of parameters, an increment in the initial fraction of the population that is pro-vaccine has a twofold effect: it can lead to smaller epidemic outbreaks in the short term, but it also contributes to the survival of the chain of infections in the long term. Our results also suggest that it is possible that more effective vaccines can decrease the long-term vaccine coverage. This is a counterintuitive outcome, but it is in line with empirical observations that vaccines can become a victim of their own success.

Concurrency-Induced Transitions in Epidemic Dynamics on Temporal Networks.

PubMed

Onaga, Tomokatsu; Gleeson, James P; Masuda, Naoki

2017-09-08

Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically investigate the effects of concurrency, the number of neighbors that a node has at a given time point, on the epidemic threshold in the stochastic susceptible-infected-susceptible dynamics on temporal network models. We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when the node's concurrency is low, but can also enhance epidemics when the concurrency is high. We analytically determine different phases of this concurrency-induced transition, and confirm our results with numerical simulations.

Concurrency-Induced Transitions in Epidemic Dynamics on Temporal Networks

NASA Astrophysics Data System (ADS)

Onaga, Tomokatsu; Gleeson, James P.; Masuda, Naoki

2017-09-01

Social contact networks underlying epidemic processes in humans and animals are highly dynamic. The spreading of infections on such temporal networks can differ dramatically from spreading on static networks. We theoretically investigate the effects of concurrency, the number of neighbors that a node has at a given time point, on the epidemic threshold in the stochastic susceptible-infected-susceptible dynamics on temporal network models. We show that network dynamics can suppress epidemics (i.e., yield a higher epidemic threshold) when the node's concurrency is low, but can also enhance epidemics when the concurrency is high. We analytically determine different phases of this concurrency-induced transition, and confirm our results with numerical simulations.

Controlling disease outbreaks in wildlife using limited culling: modelling classical swine fever incursions in wild pigs in Australia.

PubMed

Cowled, Brendan D; Garner, M Graeme; Negus, Katherine; Ward, Michael P

2012-01-16

Disease modelling is one approach for providing new insights into wildlife disease epidemiology. This paper describes a spatio-temporal, stochastic, susceptible- exposed-infected-recovered process model that simulates the potential spread of classical swine fever through a documented, large and free living wild pig population following a simulated incursion. The study area (300 000 km2) was in northern Australia. Published data on wild pig ecology from Australia, and international Classical Swine Fever data was used to parameterise the model. Sensitivity analyses revealed that herd density (best estimate 1-3 pigs km-2), daily herd movement distances (best estimate approximately 1 km), probability of infection transmission between herds (best estimate 0.75) and disease related herd mortality (best estimate 42%) were highly influential on epidemic size but that extraordinary movements of pigs and the yearly home range size of a pig herd were not. CSF generally established (98% of simulations) following a single point introduction. CSF spread at approximately 9 km2 per day with low incidence rates (< 2 herds per day) in an epidemic wave along contiguous habitat for several years, before dying out (when the epidemic arrived at the end of a contiguous sub-population or at a low density wild pig area). The low incidence rate indicates that surveillance for wildlife disease epidemics caused by short lived infections will be most efficient when surveillance is based on detection and investigation of clinical events, although this may not always be practical. Epidemics could be contained and eradicated with culling (aerial shooting) or vaccination when these were adequately implemented. It was apparent that the spatial structure, ecology and behaviour of wild populations must be accounted for during disease management in wildlife. An important finding was that it may only be necessary to cull or vaccinate relatively small proportions of a population to successfully contain and eradicate some wildlife disease epidemics.

Controlling disease outbreaks in wildlife using limited culling: modelling classical swine fever incursions in wild pigs in Australia

PubMed Central

2012-01-01

Disease modelling is one approach for providing new insights into wildlife disease epidemiology. This paper describes a spatio-temporal, stochastic, susceptible- exposed-infected-recovered process model that simulates the potential spread of classical swine fever through a documented, large and free living wild pig population following a simulated incursion. The study area (300 000 km2) was in northern Australia. Published data on wild pig ecology from Australia, and international Classical Swine Fever data was used to parameterise the model. Sensitivity analyses revealed that herd density (best estimate 1-3 pigs km-2), daily herd movement distances (best estimate approximately 1 km), probability of infection transmission between herds (best estimate 0.75) and disease related herd mortality (best estimate 42%) were highly influential on epidemic size but that extraordinary movements of pigs and the yearly home range size of a pig herd were not. CSF generally established (98% of simulations) following a single point introduction. CSF spread at approximately 9 km2 per day with low incidence rates (< 2 herds per day) in an epidemic wave along contiguous habitat for several years, before dying out (when the epidemic arrived at the end of a contiguous sub-population or at a low density wild pig area). The low incidence rate indicates that surveillance for wildlife disease epidemics caused by short lived infections will be most efficient when surveillance is based on detection and investigation of clinical events, although this may not always be practical. Epidemics could be contained and eradicated with culling (aerial shooting) or vaccination when these were adequately implemented. It was apparent that the spatial structure, ecology and behaviour of wild populations must be accounted for during disease management in wildlife. An important finding was that it may only be necessary to cull or vaccinate relatively small proportions of a population to successfully contain and eradicate some wildlife disease epidemics. PMID:22243996

Recurrent dynamics in an epidemic model due to stimulated bifurcation crossovers

NASA Astrophysics Data System (ADS)

Juanico, Drandreb Earl

2015-05-01

Epidemics are known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, peaks of activity for infectious diseases like influenza reappear over time. Analysis of a stochastic model is here undertaken to explore a proposed cycle-generating mechanism - the bifurcation crossover. Time series from simulations of the model exhibit oscillations similar to the temporal signature of influenza activity. Power-spectral density indicates a resonant frequency, which corresponds to the annual seasonality of influenza in temperate zones. The study finds that intervention actions influence the extinguishability of epidemic activity. Asymptotic solution to a backward Kolmogorov equation corresponds to a mean extinction time that is a function of both intervention efficacy and population size. Intervention efficacy must be greater than a certain threshold to increase the chances of extinguishing the epidemic. Agreement of the model with several phenomenological features of epidemic cycles lends to it a tractability that may serve as early warning of imminent outbreaks.

Recurrent dynamics in an epidemic model due to stimulated bifurcation crossovers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Juanico, Drandreb Earl; National Institute of Physics, University of the Philippines, Diliman, Quezon City, Philippines 1101

Epidemics are known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, peaks of activity for infectious diseases like influenza reappear over time. Analysis of a stochastic model is here undertaken to explore a proposed cycle-generating mechanism – the bifurcation crossover. Time series from simulations of the model exhibit oscillations similar to the temporal signature of influenza activity. Power-spectral density indicates a resonant frequency, which corresponds to the annual seasonality of influenza in temperate zones. The study finds that intervention actions influence the extinguishability of epidemic activity. Asymptotic solution to a backwardmore » Kolmogorov equation corresponds to a mean extinction time that is a function of both intervention efficacy and population size. Intervention efficacy must be greater than a certain threshold to increase the chances of extinguishing the epidemic. Agreement of the model with several phenomenological features of epidemic cycles lends to it a tractability that may serve as early warning of imminent outbreaks.« less

The impact of regional climate change on malaria risk due to greenhouse forcing and land-use changes in tropical Africa.

PubMed

Ermert, Volker; Fink, Andreas H; Morse, Andrew P; Paeth, Heiko

2012-01-01

Climate change will probably alter the spread and transmission intensity of malaria in Africa. In this study, we assessed potential changes in the malaria transmission via an integrated weather-disease model. We simulated mosquito biting rates using the Liverpool Malaria Model (LMM). The input data for the LMM were bias-corrected temperature and precipitation data from the regional model (REMO) on a 0.5° latitude-longitude grid. A Plasmodium falciparum infection model expands the LMM simulations to incorporate information on the infection rate among children. Malaria projections were carried out with this integrated weather-disease model for 2001 to 2050 according to two climate scenarios that include the effect of anthropogenic land-use and land-cover changes on climate. Model-based estimates for the present climate (1960 to 2000) are consistent with observed data for the spread of malaria in Africa. In the model domain, the regions where malaria is epidemic are located in the Sahel as well as in various highland territories. A decreased spread of malaria over most parts of tropical Africa is projected because of simulated increased surface temperatures and a significant reduction in annual rainfall. However, the likelihood of malaria epidemics is projected to increase in the southern part of the Sahel. In most of East Africa, the intensity of malaria transmission is expected to increase. Projections indicate that highland areas that were formerly unsuitable for malaria will become epidemic, whereas in the lower-altitude regions of the East African highlands, epidemic risk will decrease. We project that climate changes driven by greenhouse-gas and land-use changes will significantly affect the spread of malaria in tropical Africa well before 2050. The geographic distribution of areas where malaria is epidemic might have to be significantly altered in the coming decades.

Effects of superspreaders in spread of epidemic

NASA Astrophysics Data System (ADS)

Fujie, Ryo; Odagaki, Takashi

2007-02-01

Within the standard SIR model with spatial structure, we propose two models for the superspreader. In one model, superspreaders have intrinsically strong infectiousness. In other model, they have many social connections. By Monte Carlo simulation, we obtain the percolation probability, the propagation speed, the epidemic curve, the distribution of secondary infected and the propagation path as functions of population and the density of superspreaders. By comparing the results with the data of SARS in Singapore 2003, we conclude that the latter model can explain the observation.

Dynamical behavior of susceptible-infected-recovered-susceptible epidemic model on weighted networks

NASA Astrophysics Data System (ADS)

Wu, Qingchu; Zhang, Fei

2018-02-01

We study susceptible-infected-recovered-susceptible epidemic model in weighted, regular, and random complex networks. We institute a pairwise-type mathematical model with a general transmission rate to evaluate the influence of the link-weight distribution on the spreading process. Furthermore, we develop a dimensionality reduction approach to derive the condition for the contagion outbreak. Finally, we analyze the influence of the heterogeneity of weight distribution on the outbreak condition for the scenario with a linear transmission rate. Our theoretical analysis is in agreement with stochastic simulations, showing that the heterogeneity of link-weight distribution can have a significant effect on the epidemic dynamics.

Incorporating individual health-protective decisions into disease transmission models: a mathematical framework.

PubMed

Durham, David P; Casman, Elizabeth A

2012-03-07

It is anticipated that the next generation of computational epidemic models will simulate both infectious disease transmission and dynamic human behaviour change. Individual agents within a simulation will not only infect one another, but will also have situational awareness and a decision algorithm that enables them to modify their behaviour. This paper develops such a model of behavioural response, presenting a mathematical interpretation of a well-known psychological model of individual decision making, the health belief model, suitable for incorporation within an agent-based disease-transmission model. We formalize the health belief model and demonstrate its application in modelling the prevalence of facemask use observed over the course of the 2003 Hong Kong SARS epidemic, a well-documented example of behaviour change in response to a disease outbreak.

Incorporating individual health-protective decisions into disease transmission models: a mathematical framework

PubMed Central

Durham, David P.; Casman, Elizabeth A.

2012-01-01

It is anticipated that the next generation of computational epidemic models will simulate both infectious disease transmission and dynamic human behaviour change. Individual agents within a simulation will not only infect one another, but will also have situational awareness and a decision algorithm that enables them to modify their behaviour. This paper develops such a model of behavioural response, presenting a mathematical interpretation of a well-known psychological model of individual decision making, the health belief model, suitable for incorporation within an agent-based disease-transmission model. We formalize the health belief model and demonstrate its application in modelling the prevalence of facemask use observed over the course of the 2003 Hong Kong SARS epidemic, a well-documented example of behaviour change in response to a disease outbreak. PMID:21775324

Infection Threshold for an Epidemic Model in Site and Bond Percolation Worlds

NASA Astrophysics Data System (ADS)

Sakisaka, Yukio; Yoshimura, Jin; Takeuchi, Yasuhiro; Sugiura, Koji; Tainaka, Kei-ichi

2010-02-01

We investigate an epidemic model on a square lattice with two protection treatments: prevention and quarantine. To explore the effects of both treatments, we apply the site and bond percolations. Computer simulations reveal that the threshold between endemic and disease-free phases can be represented by a single scaling law. The mean-field theory qualitatively predicts such infection dynamics and the scaling law.

Impact of Information based Classification on Network Epidemics

PubMed Central

Mishra, Bimal Kumar; Haldar, Kaushik; Sinha, Durgesh Nandini

2016-01-01

Formulating mathematical models for accurate approximation of malicious propagation in a network is a difficult process because of our inherent lack of understanding of several underlying physical processes that intrinsically characterize the broader picture. The aim of this paper is to understand the impact of available information in the control of malicious network epidemics. A 1-n-n-1 type differential epidemic model is proposed, where the differentiality allows a symptom based classification. This is the first such attempt to add such a classification into the existing epidemic framework. The model is incorporated into a five class system called the DifEpGoss architecture. Analysis reveals an epidemic threshold, based on which the long-term behavior of the system is analyzed. In this work three real network datasets with 22002, 22469 and 22607 undirected edges respectively, are used. The datasets show that classification based prevention given in the model can have a good role in containing network epidemics. Further simulation based experiments are used with a three category classification of attack and defense strengths, which allows us to consider 27 different possibilities. These experiments further corroborate the utility of the proposed model. The paper concludes with several interesting results. PMID:27329348

Spreading dynamics of a SIQRS epidemic model on scale-free networks

NASA Astrophysics Data System (ADS)

Li, Tao; Wang, Yuanmei; Guan, Zhi-Hong

2014-03-01

In order to investigate the influence of heterogeneity of the underlying networks and quarantine strategy on epidemic spreading, a SIQRS epidemic model on the scale-free networks is presented. Using the mean field theory the spreading dynamics of the virus is analyzed. The spreading critical threshold and equilibria are derived. Theoretical results indicate that the critical threshold value is significantly dependent on the topology of the underlying networks and quarantine rate. The existence of equilibria is determined by threshold value. The stability of disease-free equilibrium and the permanence of the disease are proved. Numerical simulations confirmed the analytical results.

Modeling of contact tracing in social networks

NASA Astrophysics Data System (ADS)

Tsimring, Lev S.; Huerta, Ramón

2003-07-01

Spreading of certain infections in complex networks is effectively suppressed by using intelligent strategies for epidemic control. One such standard epidemiological strategy consists in tracing contacts of infected individuals. In this paper, we use a recently introduced generalization of the standard susceptible-infectious-removed stochastic model for epidemics in sparse random networks which incorporates an additional (traced) state. We describe a deterministic mean-field description which yields quantitative agreement with stochastic simulations on random graphs. We also discuss the role of contact tracing in epidemics control in small-world and scale-free networks. Effectiveness of contact tracing grows as the rewiring probability is reduced.

SEIIrR: Drug abuse model with rehabilitation

NASA Astrophysics Data System (ADS)

Sutanto, Azizah, Afina; Widyaningsih, Purnami; Saputro, Dewi Retno Sari

2017-05-01

Drug abuse in the world quite astonish and tend to increase. The increase and decrease on the number of drug abusers showed a pattern of spread that had the same characteristics with patterns of spread of infectious disease. The susceptible infected removed (SIR) and susceptible exposed infected removed (SEIR) epidemic models for infectious disease was developed to study social epidemic. In this paper, SEIR model for disease epidemic was developed to study drug abuse epidemic with rehabilitation treatment. The aims of this paper were to analogize susceptible exposed infected isolated recovered (SEIIrR) model on the drug abusers, to determine solutions of the model, to determine equilibrium point, and to do simulation on β. The solutions of SEIIrR model was determined by using fourth order of Runge-Kutta algorithm, equilibrium point obtained was free-drug equilibrium point. Solutions of SEIIrR showed that the model was able to suppress the spread of drug abuse. The increasing value of contact rate was not affect the number of infected individuals due to rehabilitation treatment.

Simulated effect of pig-population density on epidemic size and choice of control strategy for classical swine fever epidemics in The Netherlands.

PubMed

Mangen, M-J J; Nielen, M; Burrell, A M

2002-12-18

We examined the importance of pig-population density in the area of an outbreak of classical swine fever (CSF) for the spread of the infection and the choice of control measures. A spatial, stochastic, dynamic epidemiological simulation model linked to a sector-level market-and-trade model for The Netherlands were used. Outbreaks in sparsely and densely populated areas were compared under four different control strategies and with two alternative trade assumptions. The obligatory control strategy required by current EU legislation was predicted to be enough to eradicate an epidemic starting in an area with sparse pig population. By contrast, additional control measures would be necessary if the outbreak began in an area with high pig density. The economic consequences of using preventive slaughter rather than emergency vaccination as an additional control measure depended strongly on the reactions of trading partners. Reducing the number of animal movements significantly reduced the size and length of epidemics in areas with high pig density. The phenomenon of carrier piglets was included in the model with realistic probabilities of infection by this route, but it made a negligible contribution to the spread of the infection.

Disease properties, geography, and mitigation strategies in a simulation spread of rinderpest across the United States

PubMed Central

2011-01-01

For the past decade, the Food and Agriculture Organization of the United Nations has been working toward eradicating rinderpest through vaccination and intense surveillance by 2012. Because of the potential severity of a rinderpest epidemic, it is prudent to prepare for an unexpected outbreak in animal populations. There is no immunity to the disease among the livestock or wildlife in the United States (US). If rinderpest were to emerge in the US, the loss in livestock could be devastating. We predict the potential spread of rinderpest using a two-stage model for the spread of a multi-host infectious disease among agricultural animals in the US. The model incorporates large-scale interactions among US counties and the small-scale dynamics of disease spread within a county. The model epidemic was seeded in 16 locations and there was a strong dependence of the overall epidemic size on the starting location. The epidemics were classified according to overall size into small epidemics of 100 to 300 animals (failed epidemics), epidemics infecting 3 000 to 30 000 animals (medium epidemics), and the large epidemics infecting around one million beef cattle. The size of the rinderpest epidemics were directly related to the origin of the disease and whether or not the disease moved into certain key counties in high-livestock-density areas of the US. The epidemic size also depended upon response time and effectiveness of movement controls. PMID:21435236

Risk perception in epidemic modeling

NASA Astrophysics Data System (ADS)

Bagnoli, Franco; Liò, Pietro; Sguanci, Luca

2007-12-01

We investigate the effects of risk perception in a simple model of epidemic spreading. We assume that the perception of the risk of being infected depends on the fraction of neighbors that are ill. The effect of this factor is to decrease the infectivity, that therefore becomes a dynamical component of the model. We study the problem in the mean-field approximation and by numerical simulations for regular, random, and scale-free networks. We show that for homogeneous and random networks, there is always a value of perception that stops the epidemics. In the “worst-case” scenario of a scale-free network with diverging input connectivity, a linear perception cannot stop the epidemics; however, we show that a nonlinear increase of the perception risk may lead to the extinction of the disease. This transition is discontinuous, and is not predicted by the mean-field analysis.

Stochastic Models of Emerging Infectious Disease Transmission on Adaptive Random Networks

PubMed Central

Pipatsart, Navavat; Triampo, Wannapong

2017-01-01

We presented adaptive random network models to describe human behavioral change during epidemics and performed stochastic simulations of SIR (susceptible-infectious-recovered) epidemic models on adaptive random networks. The interplay between infectious disease dynamics and network adaptation dynamics was investigated in regard to the disease transmission and the cumulative number of infection cases. We found that the cumulative case was reduced and associated with an increasing network adaptation probability but was increased with an increasing disease transmission probability. It was found that the topological changes of the adaptive random networks were able to reduce the cumulative number of infections and also to delay the epidemic peak. Our results also suggest the existence of a critical value for the ratio of disease transmission and adaptation probabilities below which the epidemic cannot occur. PMID:29075314

Estimation of Hepatitis C Disease Burden and Budget Impact of Treatment Using Health Economic Modeling.

PubMed

Chhatwal, Jagpreet; Chen, Qiushi; Aggarwal, Rakesh

2018-06-01

Oral direct-acting antiviral agents have revolutionized treatment of hepatitis C virus (HCV) infection. Nonetheless, barriers exist to elimination of HCV as a public health threat including low uptake of treatment, limited budget allocations for HCV treatment, and low awareness rates of HCV status among infected people. Mathematical modeling provides a systematic framework to analyze and compare potential solutions and elimination strategies by simulating the HCV epidemic under different conditions. Such models evaluate impact of interventions in advance of implementation. This article describes key components of developing an HCV burden model and illustrates its use by simulating the HCV epidemic in the United States. Copyright © 2018 Elsevier Inc. All rights reserved.

The effects of global awareness on the spreading of epidemics in multiplex networks

NASA Astrophysics Data System (ADS)

Zang, Haijuan

2018-02-01

It is increasingly recognized that understanding the complex interplay patterns between epidemic spreading and human behavioral is a key component of successful infection control efforts. In particular, individuals can obtain the information about epidemics and respond by altering their behaviors, which can affect the spreading dynamics as well. Besides, because the existence of herd-like behaviors, individuals are very easy to be influenced by the global awareness information. Here, in this paper, we propose a global awareness controlled spreading model (GACS) to explore the interplay between the coupled dynamical processes. Using the global microscopic Markov chain approach, we obtain the analytical results for the epidemic thresholds, which shows a high accuracy by comparison with lots of Monte Carlo simulations. Furthermore, considering other classical models used to describe the coupled dynamical processes, including the local awareness controlled contagion spreading (LACS) model, Susceptible-Infected-Susceptible-Unaware-Aware-Unaware (SIS-UAU) model and the single layer occasion, we make a detailed comparisons between the GACS with them. Although the comparisons and results depend on the parameters each model has, the GACS model always shows a strong restrain effects on epidemic spreading process. Our results give us a better understanding of the coupled dynamical processes and highlights the importance of considering the spreading of global awareness in the control of epidemics.

Mathematical modeling, analysis and Markov Chain Monte Carlo simulation of Ebola epidemics

NASA Astrophysics Data System (ADS)

Tulu, Thomas Wetere; Tian, Boping; Wu, Zunyou

Ebola virus infection is a severe infectious disease with the highest case fatality rate which become the global public health treat now. What makes the disease the worst of all is no specific effective treatment available, its dynamics is not much researched and understood. In this article a new mathematical model incorporating both vaccination and quarantine to study the dynamics of Ebola epidemic has been developed and comprehensively analyzed. The existence as well as uniqueness of the solution to the model is also verified and the basic reproduction number is calculated. Besides, stability conditions are also checked and finally simulation is done using both Euler method and one of the top ten most influential algorithm known as Markov Chain Monte Carlo (MCMC) method. Different rates of vaccination to predict the effect of vaccination on the infected individual over time and that of quarantine are discussed. The results show that quarantine and vaccination are very effective ways to control Ebola epidemic. From our study it was also seen that there is less possibility of an individual for getting Ebola virus for the second time if they survived his/her first infection. Last but not least real data has been fitted to the model, showing that it can used to predict the dynamic of Ebola epidemic.

The impact of awareness on epidemic spreading in networks.

PubMed

Wu, Qingchu; Fu, Xinchu; Small, Michael; Xu, Xin-Jian

2012-03-01

We explore the impact of awareness on epidemic spreading through a population represented by a scale-free network. Using a network mean-field approach, a mathematical model for epidemic spreading with awareness reactions is proposed and analyzed. We focus on the role of three forms of awareness including local, global, and contact awareness. By theoretical analysis and simulation, we show that the global awareness cannot decrease the likelihood of an epidemic outbreak while both the local awareness and the contact awareness can. Also, the influence degree of the local awareness on disease dynamics is closely related with the contact awareness.

Forecast and control of epidemics in a globalized world

PubMed Central

Hufnagel, L.; Brockmann, D.; Geisel, T.

2004-01-01

The rapid worldwide spread of severe acute respiratory syndrome demonstrated the potential threat an infectious disease poses in a closely interconnected and interdependent world. Here we introduce a probabilistic model that describes the worldwide spread of infectious diseases and demonstrate that a forecast of the geographical spread of epidemics is indeed possible. This model combines a stochastic local infection dynamics among individuals with stochastic transport in a worldwide network, taking into account national and international civil aviation traffic. Our simulations of the severe acute respiratory syndrome outbreak are in surprisingly good agreement with published case reports. We show that the high degree of predictability is caused by the strong heterogeneity of the network. Our model can be used to predict the worldwide spread of future infectious diseases and to identify endangered regions in advance. The performance of different control strategies is analyzed, and our simulations show that a quick and focused reaction is essential to inhibiting the global spread of epidemics. PMID:15477600

Modeling the impact of interventions on an epidemic of ebola in sierra leone and liberia.

PubMed

Rivers, Caitlin M; Lofgren, Eric T; Marathe, Madhav; Eubank, Stephen; Lewis, Bryan L

2014-11-06

An Ebola outbreak of unparalleled size is currently affecting several countries in West Africa, and international efforts to control the outbreak are underway. However, the efficacy of these interventions, and their likely impact on an Ebola epidemic of this size, is unknown. Forecasting and simulation of these interventions may inform public health efforts. We use existing data from Liberia and Sierra Leone to parameterize a mathematical model of Ebola and use this model to forecast the progression of the epidemic, as well as the efficacy of several interventions, including increased contact tracing, improved infection control practices, the use of a hypothetical pharmaceutical intervention to improve survival in hospitalized patients. Model forecasts until Dec. 31, 2014 show an increasingly severe epidemic with no sign of having reached a peak. Modeling results suggest that increased contact tracing, improved infection control, or a combination of the two can have a substantial impact on the number of Ebola cases, but these interventions are not sufficient to halt the progress of the epidemic. The hypothetical pharmaceutical intervention, while impacting mortality, had a smaller effect on the forecasted trajectory of the epidemic. Near-term, practical interventions to address the ongoing Ebola epidemic may have a beneficial impact on public health, but they will not result in the immediate halting, or even obvious slowing of the epidemic. A long-term commitment of resources and support will be necessary to address the outbreak.

Modeling the impact of interventions on an epidemic of ebola in sierra leone and liberia.

PubMed

Rivers, Caitlin M; Lofgren, Eric T; Marathe, Madhav; Eubank, Stephen; Lewis, Bryan L

2014-10-16

An Ebola outbreak of unparalleled size is currently affecting several countries in West Africa, and international efforts to control the outbreak are underway. However, the efficacy of these interventions, and their likely impact on an Ebola epidemic of this size, is unknown. Forecasting and simulation of these interventions may inform public health efforts. We use existing data from Liberia and Sierra Leone to parameterize a mathematical model of Ebola and use this model to forecast the progression of the epidemic, as well as the efficacy of several interventions, including increased contact tracing, improved infection control practices, the use of a hypothetical pharmaceutical intervention to improve survival in hospitalized patients. Model forecasts until Dec. 31, 2014 show an increasingly severe epidemic with no sign of having reached a peak. Modeling results suggest that increased contact tracing, improved infection control, or a combination of the two can have a substantial impact on the number of Ebola cases, but these interventions are not sufficient to halt the progress of the epidemic. The hypothetical pharmaceutical intervention, while impacting mortality, had a smaller effect on the forecasted trajectory of the epidemic. Near-term, practical interventions to address the ongoing Ebola epidemic may have a beneficial impact on public health, but they will not result in the immediate halting, or even obvious slowing of the epidemic. A long-term commitment of resources and support will be necessary to address the outbreak.

On the existence of a threshold for preventive behavioral responses to suppress epidemic spreading.

PubMed

Sahneh, Faryad Darabi; Chowdhury, Fahmida N; Scoglio, Caterina M

2012-01-01

The spontaneous behavioral responses of individuals to the progress of an epidemic are recognized to have a significant impact on how the infection spreads. One observation is that, even if the infection strength is larger than the classical epidemic threshold, the initially growing infection can diminish as the result of preventive behavioral patterns adopted by the individuals. In order to investigate such dynamics of the epidemic spreading, we use a simple behavioral model coupled with the individual-based SIS epidemic model where susceptible individuals adopt a preventive behavior when sensing infection. We show that, given any infection strength and contact topology, there exists a region in the behavior-related parameter space such that infection cannot survive in long run and is completely contained. Several simulation results, including a spreading scenario in a realistic contact network from a rural district in the State of Kansas, are presented to support our analytical arguments.

Understanding the effects of different HIV transmission models in individual-based microsimulation of HIV epidemic dynamics in people who inject drugs

PubMed Central

MONTEIRO, J.F.G.; ESCUDERO, D.J.; WEINREB, C.; FLANIGAN, T.; GALEA, S.; FRIEDMAN, S.R.; MARSHALL, B.D.L.

2017-01-01

SUMMARY We investigated how different models of HIV transmission, and assumptions regarding the distribution of unprotected sex and syringe-sharing events (‘risk acts’), affect quantitative understanding of HIV transmission process in people who inject drugs (PWID). The individual-based model simulated HIV transmission in a dynamic sexual and injecting network representing New York City. We constructed four HIV transmission models: model 1, constant probabilities; model 2, random number of sexual and parenteral acts; model 3, viral load individual assigned; and model 4, two groups of partnerships (low and high risk). Overall, models with less heterogeneity were more sensitive to changes in numbers risk acts, producing HIV incidence up to four times higher than that empirically observed. Although all models overestimated HIV incidence, micro-simulations with greater heterogeneity in the HIV transmission modelling process produced more robust results and better reproduced empirical epidemic dynamics. PMID:26753627

The GLEaMviz computational tool, a publicly available software to explore realistic epidemic spreading scenarios at the global scale

PubMed Central

2011-01-01

Background Computational models play an increasingly important role in the assessment and control of public health crises, as demonstrated during the 2009 H1N1 influenza pandemic. Much research has been done in recent years in the development of sophisticated data-driven models for realistic computer-based simulations of infectious disease spreading. However, only a few computational tools are presently available for assessing scenarios, predicting epidemic evolutions, and managing health emergencies that can benefit a broad audience of users including policy makers and health institutions. Results We present "GLEaMviz", a publicly available software system that simulates the spread of emerging human-to-human infectious diseases across the world. The GLEaMviz tool comprises three components: the client application, the proxy middleware, and the simulation engine. The latter two components constitute the GLEaMviz server. The simulation engine leverages on the Global Epidemic and Mobility (GLEaM) framework, a stochastic computational scheme that integrates worldwide high-resolution demographic and mobility data to simulate disease spread on the global scale. The GLEaMviz design aims at maximizing flexibility in defining the disease compartmental model and configuring the simulation scenario; it allows the user to set a variety of parameters including: compartment-specific features, transition values, and environmental effects. The output is a dynamic map and a corresponding set of charts that quantitatively describe the geo-temporal evolution of the disease. The software is designed as a client-server system. The multi-platform client, which can be installed on the user's local machine, is used to set up simulations that will be executed on the server, thus avoiding specific requirements for large computational capabilities on the user side. Conclusions The user-friendly graphical interface of the GLEaMviz tool, along with its high level of detail and the realism of its embedded modeling approach, opens up the platform to simulate realistic epidemic scenarios. These features make the GLEaMviz computational tool a convenient teaching/training tool as well as a first step toward the development of a computational tool aimed at facilitating the use and exploitation of computational models for the policy making and scenario analysis of infectious disease outbreaks. PMID:21288355

[Epidemiological dynamics of Dengue on Easter Island].

PubMed

Canals, Mauricio; González, Christian; Canals, Andrea; Figueroa, Daniela

2012-08-01

Dengue is considered an emerging disease with an increasing prevalence especially in South America. In 2002, an epidemic of classic Dengue (DENV-1) occurred unexpectedly on Easter Island, where it had never been detected before. It reappeared in 2006-2007 and 2008, 2009 and 2011. The aim of this study was to estimate the most relevant parameters of the epidemiological dynamics of transmission of Dengue on Easter Island and to model the dynamics since 2002, comparing the predictions with the actual situation observed. Of the total cases, 52.27% were females and 47.73% men. The average age of infection was 31.38 ± 18.37 years, similar in men and women. We estimated the reproductive number R0 = 3.005 with an IC0,95 = [1.92, 4.61]. The inter-epidemic period reached an estimated T = 5.20 to 6.8 years. The case simulation showed recurrent epidemics with decreasing magnitude (damped oscillations), which is a known phenomenon in models of dengue and malaria. There was good qualitative fit to the epidemiological dynamics from 2002 onwards. It accurately predicted the rise in cases between 2006 and 2011. The predicted number of cases during the 2002 epidemic is greater than the confirmed cases and the predicted epidemic was faster than notified cases. Interepidemic period in the simulation was 6.72 years between 2002 and 2008 and 4.68 years between 2008 and 2013. From the theoretical perspective, the first epidemic had affected 94% of the population (approximately 3500 cases), but 639 were reported suggesting underreporting and a lot of sub-clinical cases occurred. Future epidemic of decreasing size are expected, although the main danger are epidemics of hemorrhagic dengue fever resulting from the introduction of different dengue virus serotypes.

Epidemic Model with Isolation in Multilayer Networks

NASA Astrophysics Data System (ADS)

Zuzek, L. G. Alvarez; Stanley, H. E.; Braunstein, L. A.

2015-07-01

The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network, and we use an isolation parameter w to measure the effect of quarantining infected individuals from both layers during an isolation period tw. We call this process the Susceptible-Infected-Isolated-Recovered (SIIR) model. Using the framework of link percolation we find that isolation increases the critical epidemic threshold of the disease because the time in which infection can spread is reduced. In this scenario we find that this threshold increases with w and tw. When the isolation period is maximum there is a critical threshold for w above which the disease never becomes an epidemic. We simulate the process and find an excellent agreement with the theoretical results.

A computer simulation of employee vaccination to mitigate an influenza epidemic.

PubMed

Lee, Bruce Y; Brown, Shawn T; Cooley, Philip C; Zimmerman, Richard K; Wheaton, William D; Zimmer, Shanta M; Grefenstette, John J; Assi, Tina-Marie; Furphy, Timothy J; Wagener, Diane K; Burke, Donald S

2010-03-01

Better understanding the possible effects of vaccinating employees is important and can help policymakers and businesses plan vaccine distribution and administration logistics, especially with the current H1N1 influenza vaccine in short supply. This article aims to determine the effects of varying vaccine coverage, compliance, administration rates, prioritization, and timing among employees during an influenza pandemic. As part of the H1N1 influenza planning efforts of the Models of Infectious Disease Agent Study network, an agent-based computer simulation model was developed for the Washington DC metropolitan region, encompassing five metropolitan statistical areas. Each simulation run involved introducing 100 infectious individuals to initiate a 1.3 reproductive-rate (R(0)) epidemic, consistent with H1N1 parameters to date. Another set of scenarios represented a R(0)=1.6 epidemic. An unmitigated epidemic resulted in substantial productivity losses (a mean of $112.6 million for a serologic 15% attack rate and $193.8 million for a serologic 25% attack rate), even with the relatively low estimated mortality impact of H1N1. Although vaccinating Advisory Committee on Immunization Practices-defined priority groups resulted in the largest savings, vaccinating all remaining workers captured additional savings and, in fact, reduced healthcare workers' and critical infrastructure workers' chances of infection. Moreover, although employee vaccination compliance affected the epidemic, once 20% compliance was achieved, additional increases in compliance provided less incremental benefit. Even though a vast majority of the workplaces in the DC metropolitan region had fewer than 100 employees, focusing on vaccinating only those in larger firms (> or =100 employees) was just as effective in mitigating the epidemic as trying to vaccinate employees in all workplaces. Timely vaccination of at least 20% of the large-company workforce can play an important role in epidemic mitigation. Copyright (c) 2010 American Journal of Preventive Medicine. Published by Elsevier Inc. All rights reserved.

Interplay between the local information based behavioral responses and the epidemic spreading in complex networks.

PubMed

Liu, Can; Xie, Jia-Rong; Chen, Han-Shuang; Zhang, Hai-Feng; Tang, Ming

2015-10-01

The spreading of an infectious disease can trigger human behavior responses to the disease, which in turn plays a crucial role on the spreading of epidemic. In this study, to illustrate the impacts of the human behavioral responses, a new class of individuals, S(F), is introduced to the classical susceptible-infected-recovered model. In the model, S(F) state represents that susceptible individuals who take self-initiate protective measures to lower the probability of being infected, and a susceptible individual may go to S(F) state with a response rate when contacting an infectious neighbor. Via the percolation method, the theoretical formulas for the epidemic threshold as well as the prevalence of epidemic are derived. Our finding indicates that, with the increasing of the response rate, the epidemic threshold is enhanced and the prevalence of epidemic is reduced. The analytical results are also verified by the numerical simulations. In addition, we demonstrate that, because the mean field method neglects the dynamic correlations, a wrong result based on the mean field method is obtained-the epidemic threshold is not related to the response rate, i.e., the additional S(F) state has no impact on the epidemic threshold.

Optimization model of vaccination strategy for dengue transmission

NASA Astrophysics Data System (ADS)

Widayani, H.; Kallista, M.; Nuraini, N.; Sari, M. Y.

2014-02-01

Dengue fever is emerging tropical and subtropical disease caused by dengue virus infection. The vaccination should be done as a prevention of epidemic in population. The host-vector model are modified with consider a vaccination factor to prevent the occurrence of epidemic dengue in a population. An optimal vaccination strategy using non-linear objective function was proposed. The genetic algorithm programming techniques are combined with fourth-order Runge-Kutta method to construct the optimal vaccination. In this paper, the appropriate vaccination strategy by using the optimal minimum cost function which can reduce the number of epidemic was analyzed. The numerical simulation for some specific cases of vaccination strategy is shown.

Lattice model for influenza spreading with spontaneous behavioral changes.

PubMed

Fierro, Annalisa; Liccardo, Antonella

2013-01-01

Individual behavioral response to the spreading of an epidemic plays a crucial role in the progression of the epidemic itself. The risk perception induces individuals to adopt a protective behavior, as for instance reducing their social contacts, adopting more restrictive hygienic measures or undergoing prophylaxis procedures. In this paper, starting with a previously developed lattice-gas SIR model, we construct a coupled behavior-disease model for influenza spreading with spontaneous behavioral changes. The focus is on self-initiated behavioral changes that alter the susceptibility to the disease, without altering the contact patterns among individuals. Three different mechanisms of awareness spreading are analyzed: the local spreading due to the presence in the neighborhood of infective individuals; the global spreading due to the news published by the mass media and to educational campaigns implemented at institutional level; the local spreading occurring through the "thought contagion" among aware and unaware individuals. The peculiarity of the present approach is that the awareness spreading model is calibrated on available data on awareness and concern of the population about the risk of contagion. In particular, the model is validated against the A(H1N1) epidemic outbreak in Italy during the 2009/2010 season, by making use of the awareness data gathered by the behavioral risk factor surveillance system (PASSI). We find that, increasing the accordance between the simulated awareness spreading and the PASSI data on risk perception, the agreement between simulated and experimental epidemiological data improves as well. Furthermore, we show that, within our model, the primary mechanism to reproduce a realistic evolution of the awareness during an epidemic, is the one due to globally available information. This result highlights how crucial is the role of mass media and educational campaigns in influencing the epidemic spreading of infectious diseases.

Epidemic Forecasting is Messier Than Weather Forecasting: The Role of Human Behavior and Internet Data Streams in Epidemic Forecast.

PubMed

Moran, Kelly R; Fairchild, Geoffrey; Generous, Nicholas; Hickmann, Kyle; Osthus, Dave; Priedhorsky, Reid; Hyman, James; Del Valle, Sara Y

2016-12-01

Mathematical models, such as those that forecast the spread of epidemics or predict the weather, must overcome the challenges of integrating incomplete and inaccurate data in computer simulations, estimating the probability of multiple possible scenarios, incorporating changes in human behavior and/or the pathogen, and environmental factors. In the past 3 decades, the weather forecasting community has made significant advances in data collection, assimilating heterogeneous data steams into models and communicating the uncertainty of their predictions to the general public. Epidemic modelers are struggling with these same issues in forecasting the spread of emerging diseases, such as Zika virus infection and Ebola virus disease. While weather models rely on physical systems, data from satellites, and weather stations, epidemic models rely on human interactions, multiple data sources such as clinical surveillance and Internet data, and environmental or biological factors that can change the pathogen dynamics. We describe some of similarities and differences between these 2 fields and how the epidemic modeling community is rising to the challenges posed by forecasting to help anticipate and guide the mitigation of epidemics. We conclude that some of the fundamental differences between these 2 fields, such as human behavior, make disease forecasting more challenging than weather forecasting. Published by Oxford University Press for the Infectious Diseases Society of America 2016. This work is written by (a) US Government employee(s) and is in the public domain in the US.

Analysis and optimization of cross-immunity epidemic model on complex networks

NASA Astrophysics Data System (ADS)

Chen, Chao; Zhang, Hao; Wu, Yin-Hua; Feng, Wei-Qiang; Zhang, Jian

2015-09-01

There are various infectious diseases in real world, and these diseases often spread on a network of population and compete for the limited hosts. Cross-immunity is an important disease competing pattern, which has attracted the attention of many researchers. In this paper, we discovered an important conclusion for two cross-immunity epidemics on a network. When the infectious ability of the second epidemic takes a fixed value, the infectious ability of the first epidemic has an optimal value which minimizes the sum of the infection sizes of the two epidemics. We also proposed a simple mathematical analysis method for the infection size of the second epidemic using the cavity method. The proposed method and conclusion are verified by simulation results. Minor inaccuracies of the existing mathematical methods for the infection size of the second epidemic are also found and discussed in experiments, which have not been noticed in existing research.

Epidemic spread in bipartite network by considering risk awareness

NASA Astrophysics Data System (ADS)

Han, She; Sun, Mei; Ampimah, Benjamin Chris; Han, Dun

2018-02-01

Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. Exploring the interplay between human awareness and epidemic spreading is a topic that has been receiving increasing attention. Considering the fact, some well-known diseases only spread between different species we propose a theoretical analysis of the Susceptible-Infected-Susceptible (SIS) epidemic spread from the perspective of bipartite network and risk aversion. Using mean field theory, the epidemic threshold is calculated theoretically. Simulation results are consistent with the proposed analytic model. The results show that, the final infection density is negative linear with the value of individuals' risk awareness. Therefore, the epidemic spread could be effectively suppressed by improving individuals' risk awareness.

Simulating the epidemiological and economic effects of an African swine fever epidemic in industrialized swine populations.

PubMed

Halasa, Tariq; Bøtner, Anette; Mortensen, Sten; Christensen, Hanne; Toft, Nils; Boklund, Anette

2016-09-25

African swine fever (ASF) is a notifiable infectious disease with a considerable impact on animal health and is currently one of the most important emerging diseases of domestic pigs. ASF was introduced into Georgia in 2007 and subsequently spread to the Russian Federation and several Eastern European countries. Consequently, there is a non-negligible risk of ASF spread towards Western Europe. Therefore it is important to develop tools to improve our understanding of the spread and control of ASF for contingency planning. A stochastic and dynamic spatial spread model (DTU-DADS) was adjusted to simulate the spread of ASF virus between domestic swine herds exemplified by the Danish swine population. ASF was simulated to spread via animal movement, low- or medium-risk contacts and local spread. Each epidemic was initiated in a randomly selected herd - either in a nucleus herd, a sow herd, a randomly selected herd or in multiple herds simultaneously. A sensitivity analysis was conducted on input parameters. Given the inputs and assumptions of the model, epidemics of ASF in Denmark are predicted to be small, affecting about 14 herds in the worst-case scenario. The duration of an epidemic is predicted to vary from 1 to 76days. Substantial economic damages are predicted, with median direct costs and export losses of €12 and €349 million, respectively, when epidemics were initiated in multiple herds. Each infectious herd resulted in 0 to 2 new infected herds varying from 0 to 5 new infected herds, depending on the index herd type. Copyright © 2016 Elsevier B.V. All rights reserved.

How to Estimate Epidemic Risk from Incomplete Contact Diaries Data?

PubMed

Mastrandrea, Rossana; Barrat, Alain

2016-06-01

Social interactions shape the patterns of spreading processes in a population. Techniques such as diaries or proximity sensors allow to collect data about encounters and to build networks of contacts between individuals. The contact networks obtained from these different techniques are however quantitatively different. Here, we first show how these discrepancies affect the prediction of the epidemic risk when these data are fed to numerical models of epidemic spread: low participation rate, under-reporting of contacts and overestimation of contact durations in contact diaries with respect to sensor data determine indeed important differences in the outcomes of the corresponding simulations with for instance an enhanced sensitivity to initial conditions. Most importantly, we investigate if and how information gathered from contact diaries can be used in such simulations in order to yield an accurate description of the epidemic risk, assuming that data from sensors represent the ground truth. The contact networks built from contact sensors and diaries present indeed several structural similarities: this suggests the possibility to construct, using only the contact diary network information, a surrogate contact network such that simulations using this surrogate network give the same estimation of the epidemic risk as simulations using the contact sensor network. We present and compare several methods to build such surrogate data, and show that it is indeed possible to obtain a good agreement between the outcomes of simulations using surrogate and sensor data, as long as the contact diary information is complemented by publicly available data describing the heterogeneity of the durations of human contacts.

How to Estimate Epidemic Risk from Incomplete Contact Diaries Data?

PubMed Central

Mastrandrea, Rossana; Barrat, Alain

2016-01-01

Social interactions shape the patterns of spreading processes in a population. Techniques such as diaries or proximity sensors allow to collect data about encounters and to build networks of contacts between individuals. The contact networks obtained from these different techniques are however quantitatively different. Here, we first show how these discrepancies affect the prediction of the epidemic risk when these data are fed to numerical models of epidemic spread: low participation rate, under-reporting of contacts and overestimation of contact durations in contact diaries with respect to sensor data determine indeed important differences in the outcomes of the corresponding simulations with for instance an enhanced sensitivity to initial conditions. Most importantly, we investigate if and how information gathered from contact diaries can be used in such simulations in order to yield an accurate description of the epidemic risk, assuming that data from sensors represent the ground truth. The contact networks built from contact sensors and diaries present indeed several structural similarities: this suggests the possibility to construct, using only the contact diary network information, a surrogate contact network such that simulations using this surrogate network give the same estimation of the epidemic risk as simulations using the contact sensor network. We present and compare several methods to build such surrogate data, and show that it is indeed possible to obtain a good agreement between the outcomes of simulations using surrogate and sensor data, as long as the contact diary information is complemented by publicly available data describing the heterogeneity of the durations of human contacts. PMID:27341027

Bursty communication patterns facilitate spreading in a threshold-based epidemic dynamics.

PubMed

Takaguchi, Taro; Masuda, Naoki; Holme, Petter

2013-01-01

Records of social interactions provide us with new sources of data for understanding how interaction patterns affect collective dynamics. Such human activity patterns are often bursty, i.e., they consist of short periods of intense activity followed by long periods of silence. This burstiness has been shown to affect spreading phenomena; it accelerates epidemic spreading in some cases and slows it down in other cases. We investigate a model of history-dependent contagion. In our model, repeated interactions between susceptible and infected individuals in a short period of time is needed for a susceptible individual to contract infection. We carry out numerical simulations on real temporal network data to find that bursty activity patterns facilitate epidemic spreading in our model.

Mathematical Analysis of an Epidemic System in the Presence of Optimal Control and Population Dispersal

NASA Astrophysics Data System (ADS)

Nandi, Swapan Kumar; Jana, Soovoojeet; Mandal, Manotosh; Kar, T. K.

In this paper, we proposed and analyzed a susceptible-infected-recovered (SIR) type epidemic model to investigate the effect of transport-related infectious diseases namely tuberculosis, measles, rubella, influenza, sexually transmitted diseases, etc. The existence and stability criteria of both the diseases include free equilibrium point and endemic equilibrium point which are established and the threshold parametric condition for which the system passes through a transcritical bifurcation is also obtained. Optimal control strategy for control parameters is formulated and solved both theoretically and numerically. Lastly, we not only illustrate our theoretical results through graphical illustrations but also computer simulation is used to show that our model would be a good model to study the SARS epidemic in 2003.

Optimization of seasonal ARIMA models using differential evolution - simulated annealing (DESA) algorithm in forecasting dengue cases in Baguio City

NASA Astrophysics Data System (ADS)

Addawe, Rizavel C.; Addawe, Joel M.; Magadia, Joselito C.

2016-10-01

Accurate forecasting of dengue cases would significantly improve epidemic prevention and control capabilities. This paper attempts to provide useful models in forecasting dengue epidemic specific to the young and adult population of Baguio City. To capture the seasonal variations in dengue incidence, this paper develops a robust modeling approach to identify and estimate seasonal autoregressive integrated moving average (SARIMA) models in the presence of additive outliers. Since the least squares estimators are not robust in the presence of outliers, we suggest a robust estimation based on winsorized and reweighted least squares estimators. A hybrid algorithm, Differential Evolution - Simulated Annealing (DESA), is used to identify and estimate the parameters of the optimal SARIMA model. The method is applied to the monthly reported dengue cases in Baguio City, Philippines.

Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules

NASA Astrophysics Data System (ADS)

Zhang, Yue; Li, Yang; Zhang, Qingling; Li, Aihua

2018-07-01

In this paper, the threshold behavior of a susceptible-infected-recovered (SIR) epidemic model with stochastic perturbation is investigated. Firstly, it is obtained that the system has a unique global positive solution with any positive initial value. Random effect may lead to disease extinction under a simple condition. Subsequently, sufficient condition for persistence has been established in the mean of the disease. Finally, some numerical simulations are carried out to confirm the analytical results.

The Impact of Heterogeneity and Awareness in Modeling Epidemic Spreading on Multiplex Networks

PubMed Central

Scatà, Marialisa; Di Stefano, Alessandro; Liò, Pietro; La Corte, Aurelio

2016-01-01

In the real world, dynamic processes involving human beings are not disjoint. To capture the real complexity of such dynamics, we propose a novel model of the coevolution of epidemic and awareness spreading processes on a multiplex network, also introducing a preventive isolation strategy. Our aim is to evaluate and quantify the joint impact of heterogeneity and awareness, under different socioeconomic conditions. Considering, as case study, an emerging public health threat, Zika virus, we introduce a data-driven analysis by exploiting multiple sources and different types of data, ranging from Big Five personality traits to Google Trends, related to different world countries where there is an ongoing epidemic outbreak. Our findings demonstrate how the proposed model allows delaying the epidemic outbreak and increasing the resilience of nodes, especially under critical economic conditions. Simulation results, using data-driven approach on Zika virus, which has a growing scientific research interest, are coherent with the proposed analytic model. PMID:27848978

Fitting mechanistic epidemic models to data: A comparison of simple Markov chain Monte Carlo approaches.

PubMed

Li, Michael; Dushoff, Jonathan; Bolker, Benjamin M

2018-07-01

Simple mechanistic epidemic models are widely used for forecasting and parameter estimation of infectious diseases based on noisy case reporting data. Despite the widespread application of models to emerging infectious diseases, we know little about the comparative performance of standard computational-statistical frameworks in these contexts. Here we build a simple stochastic, discrete-time, discrete-state epidemic model with both process and observation error and use it to characterize the effectiveness of different flavours of Bayesian Markov chain Monte Carlo (MCMC) techniques. We use fits to simulated data, where parameters (and future behaviour) are known, to explore the limitations of different platforms and quantify parameter estimation accuracy, forecasting accuracy, and computational efficiency across combinations of modeling decisions (e.g. discrete vs. continuous latent states, levels of stochasticity) and computational platforms (JAGS, NIMBLE, Stan).

Epidemic spreading by objective traveling

NASA Astrophysics Data System (ADS)

Tang, Ming; Liu, Zonghua; Li, Baowen

2009-07-01

A fundamental feature of agent traveling in social networks is that traveling is usually not a random walk but with a specific destination and goes through the shortest path from starting to destination. A serious consequence of the objective traveling is that it may result in a fast epidemic spreading, such as SARS etc. In this letter we present a reaction-traveling model to study how the objective traveling influences the epidemic spreading. We consider a random scale-free meta-population network with sub-population at each node. Through a SIS model we theoretically prove that near the threshold of epidemic outbreak, the objective traveling can significantly enhance the final infected population and the infected fraction at a node is proportional to its betweenness for the traveling agents and approximately proportional to its degree for the non-traveling agents. Numerical simulations have confirmed the theoretical predictions.

Interplay between cost and benefits triggers nontrivial vaccination uptake

NASA Astrophysics Data System (ADS)

Steinegger, Benjamin; Cardillo, Alessio; Rios, Paolo De Los; Gómez-Gardeñes, Jesús; Arenas, Alex

2018-03-01

The containment of epidemic spreading is a major challenge in science. Vaccination, whenever available, is the best way to prevent the spreading, because it eventually immunizes individuals. However, vaccines are not perfect, and total immunization is not guaranteed. Imperfect immunization has driven the emergence of antivaccine movements that totally alter the predictions about the epidemic incidence. Here, we propose a mathematically solvable mean-field vaccination model to mimic the spontaneous adoption of vaccines against influenzalike diseases and the expected epidemic incidence. The results are in agreement with extensive Monte Carlo simulations of the epidemics and vaccination coevolutionary processes. Interestingly, the results reveal a nonmonotonic behavior on the vaccination coverage that increases with the imperfection of the vaccine and after decreases. This apparent counterintuitive behavior is analyzed and understood from stability principles of the proposed mathematical model.

Spread of Zika virus in the Americas.

PubMed

Zhang, Qian; Sun, Kaiyuan; Chinazzi, Matteo; Pastore Y Piontti, Ana; Dean, Natalie E; Rojas, Diana Patricia; Merler, Stefano; Mistry, Dina; Poletti, Piero; Rossi, Luca; Bray, Margaret; Halloran, M Elizabeth; Longini, Ira M; Vespignani, Alessandro

2017-05-30

We use a data-driven global stochastic epidemic model to analyze the spread of the Zika virus (ZIKV) in the Americas. The model has high spatial and temporal resolution and integrates real-world demographic, human mobility, socioeconomic, temperature, and vector density data. We estimate that the first introduction of ZIKV to Brazil likely occurred between August 2013 and April 2014 (90% credible interval). We provide simulated epidemic profiles of incident ZIKV infections for several countries in the Americas through February 2017. The ZIKV epidemic is characterized by slow growth and high spatial and seasonal heterogeneity, attributable to the dynamics of the mosquito vector and to the characteristics and mobility of the human populations. We project the expected timing and number of pregnancies infected with ZIKV during the first trimester and provide estimates of microcephaly cases assuming different levels of risk as reported in empirical retrospective studies. Our approach represents a modeling effort aimed at understanding the potential magnitude and timing of the ZIKV epidemic and it can be potentially used as a template for the analysis of future mosquito-borne epidemics.

Spread of Zika virus in the Americas

PubMed Central

Zhang, Qian; Sun, Kaiyuan; Chinazzi, Matteo; Pastore y Piontti, Ana; Dean, Natalie E.; Rojas, Diana Patricia; Merler, Stefano; Mistry, Dina; Poletti, Piero; Rossi, Luca; Bray, Margaret; Halloran, M. Elizabeth; Longini, Ira M.; Vespignani, Alessandro

2017-01-01

We use a data-driven global stochastic epidemic model to analyze the spread of the Zika virus (ZIKV) in the Americas. The model has high spatial and temporal resolution and integrates real-world demographic, human mobility, socioeconomic, temperature, and vector density data. We estimate that the first introduction of ZIKV to Brazil likely occurred between August 2013 and April 2014 (90% credible interval). We provide simulated epidemic profiles of incident ZIKV infections for several countries in the Americas through February 2017. The ZIKV epidemic is characterized by slow growth and high spatial and seasonal heterogeneity, attributable to the dynamics of the mosquito vector and to the characteristics and mobility of the human populations. We project the expected timing and number of pregnancies infected with ZIKV during the first trimester and provide estimates of microcephaly cases assuming different levels of risk as reported in empirical retrospective studies. Our approach represents a modeling effort aimed at understanding the potential magnitude and timing of the ZIKV epidemic and it can be potentially used as a template for the analysis of future mosquito-borne epidemics. PMID:28442561

A novel epidemic spreading model with decreasing infection rate based on infection times

NASA Astrophysics Data System (ADS)

Huang, Yunhan; Ding, Li; Feng, Yun

2016-02-01

A new epidemic spreading model where individuals can be infected repeatedly is proposed in this paper. The infection rate decreases according to the times it has been infected before. This phenomenon may be caused by immunity or heightened alertness of individuals. We introduce a new parameter called decay factor to evaluate the decrease of infection rate. Our model bridges the Susceptible-Infected-Susceptible(SIS) model and the Susceptible-Infected-Recovered(SIR) model by this parameter. The proposed model has been studied by Monte-Carlo numerical simulation. It is found that initial infection rate has greater impact on peak value comparing with decay factor. The effect of decay factor on final density and threshold of outbreak is dominant but weakens significantly when considering birth and death rates. Besides, simulation results show that the influence of birth and death rates on final density is non-monotonic in some circumstances.

Two-stage effects of awareness cascade on epidemic spreading in multiplex networks

NASA Astrophysics Data System (ADS)

Guo, Quantong; Jiang, Xin; Lei, Yanjun; Li, Meng; Ma, Yifang; Zheng, Zhiming

2015-01-01

Human awareness plays an important role in the spread of infectious diseases and the control of propagation patterns. The dynamic process with human awareness is called awareness cascade, during which individuals exhibit herd-like behavior because they are making decisions based on the actions of other individuals [Borge-Holthoefer et al., J. Complex Networks 1, 3 (2013), 10.1093/comnet/cnt006]. In this paper, to investigate the epidemic spreading with awareness cascade, we propose a local awareness controlled contagion spreading model on multiplex networks. By theoretical analysis using a microscopic Markov chain approach and numerical simulations, we find the emergence of an abrupt transition of epidemic threshold βc with the local awareness ratio α approximating 0.5 , which induces two-stage effects on epidemic threshold and the final epidemic size. These findings indicate that the increase of α can accelerate the outbreak of epidemics. Furthermore, a simple 1D lattice model is investigated to illustrate the two-stage-like sharp transition at αc≈0.5 . The results can give us a better understanding of why some epidemics cannot break out in reality and also provide a potential access to suppressing and controlling the awareness cascading systems.

Bayesian inference in an extended SEIR model with nonparametric disease transmission rate: an application to the Ebola epidemic in Sierra Leone.

PubMed

Frasso, Gianluca; Lambert, Philippe

2016-10-01

SummaryThe 2014 Ebola outbreak in Sierra Leone is analyzed using a susceptible-exposed-infectious-removed (SEIR) epidemic compartmental model. The discrete time-stochastic model for the epidemic evolution is coupled to a set of ordinary differential equations describing the dynamics of the expected proportions of subjects in each epidemic state. The unknown parameters are estimated in a Bayesian framework by combining data on the number of new (laboratory confirmed) Ebola cases reported by the Ministry of Health and prior distributions for the transition rates elicited using information collected by the WHO during the follow-up of specific Ebola cases. The time-varying disease transmission rate is modeled in a flexible way using penalized B-splines. Our framework represents a valuable stochastic tool for the study of an epidemic dynamic even when only irregularly observed and possibly aggregated data are available. Simulations and the analysis of the 2014 Sierra Leone Ebola data highlight the merits of the proposed methodology. In particular, the flexible modeling of the disease transmission rate makes the estimation of the effective reproduction number robust to the misspecification of the initial epidemic states and to underreporting of the infectious cases. © The Author 2016. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

Extinction and persistence of a stochastic nonlinear SIS epidemic model with jumps

NASA Astrophysics Data System (ADS)

Ge, Qing; Ji, Guilin; Xu, Jiabo; Fan, Xiaolin

2016-11-01

In this paper, Brownian motion and L e ´ vy jumps are introduced to a SIS type epidemic model with nonlinear incidence rate. The dynamical behavior of the considered model is investigated. In order to reveal the extinction and permanence of the disease, two threshold values R˜0 ,R¯0 are showed. We find that if R˜0 < 1, the disease may die out, and when R¯0 > 1, the disease may be persistent. Finally, the numerical simulations are presented to illustrate our mathematical results.

Modular programming for tuberculosis control, the "AuTuMN" platform.

PubMed

Trauer, James McCracken; Ragonnet, Romain; Doan, Tan Nhut; McBryde, Emma Sue

2017-08-07

Tuberculosis (TB) is now the world's leading infectious killer and major programmatic advances will be needed if we are to meet the ambitious new End TB Targets. Although mathematical models are powerful tools for TB control, such models must be flexible enough to capture the complexity and heterogeneity of the global TB epidemic. This includes simulating a disease that affects age groups and other risk groups differently, has varying levels of infectiousness depending upon the organ involved and varying outcomes from treatment depending on the drug resistance pattern of the infecting strain. We adopted sound basic principles of software engineering to develop a modular software platform for simulation of TB control interventions ("AuTuMN"). These included object-oriented programming, logical linkage between modules and consistency of code syntax and variable naming. The underlying transmission dynamic model incorporates optional stratification by age, risk group, strain and organ involvement, while our approach to simulating time-variant programmatic parameters better captures the historical progression of the epidemic. An economic model is overlaid upon this epidemiological model which facilitates comparison between new and existing technologies. A "Model runner" module allows for predictions of future disease burden trajectories under alternative scenario situations, as well as uncertainty, automatic calibration, cost-effectiveness and optimisation. The model has now been used to guide TB control strategies across a range of settings and countries, with our modular approach enabling repeated application of the tool without the need for extensive modification for each application. The modular construction of the platform minimises errors, enhances readability and collaboration between multiple programmers and enables rapid adaptation to answer questions in a broad range of contexts without the need for extensive re-programming. Such features are particularly important in simulating an epidemic as complex and diverse as TB.

Epidemic spreading on adaptively weighted scale-free networks.

PubMed

Sun, Mengfeng; Zhang, Haifeng; Kang, Huiyan; Zhu, Guanghu; Fu, Xinchu

2017-04-01

We introduce three modified SIS models on scale-free networks that take into account variable population size, nonlinear infectivity, adaptive weights, behavior inertia and time delay, so as to better characterize the actual spread of epidemics. We develop new mathematical methods and techniques to study the dynamics of the models, including the basic reproduction number, and the global asymptotic stability of the disease-free and endemic equilibria. We show the disease-free equilibrium cannot undergo a Hopf bifurcation. We further analyze the effects of local information of diseases and various immunization schemes on epidemic dynamics. We also perform some stochastic network simulations which yield quantitative agreement with the deterministic mean-field approach.

Stochastic analysis of a novel nonautonomous periodic SIRI epidemic system with random disturbances

NASA Astrophysics Data System (ADS)

Zhang, Weiwei; Meng, Xinzhu

2018-02-01

In this paper, a new stochastic nonautonomous SIRI epidemic model is formulated. Given that the incidence rates of diseases may change with the environment, we propose a novel type of transmission function. The main aim of this paper is to obtain the thresholds of the stochastic SIRI epidemic model. To this end, we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable Lyapunov functions and using stochastic analysis technique. Furthermore, we show that the stochastic system has at least one nontrivial positive periodic solution. Finally, numerical simulations are introduced to illustrate our results.

Comparing control strategies against foot-and-mouth disease: will vaccination be cost-effective in Denmark?

PubMed

Boklund, A; Halasa, T; Christiansen, L E; Enøe, C

2013-09-01

Recent outbreaks of foot-and-mouth disease (FMD) in Europe have highlighted the need for assessment of control strategies to optimise control of the spread of FMD. Our objectives were to assess the epidemiological and financial impact of simulated FMD outbreaks in Denmark and the effect of using ring depopulation or emergency vaccination to control these outbreaks. Two stochastic simulation models (InterSpreadPlus (ISP) and the modified Davis Animal Disease Simulation model (DTU-DADS)) were used to simulate the spread of FMD in Denmark using different control strategies. Each epidemic was initiated in one herd (index herd), and a total of 5000 index herds were used. Four types of control measures were investigated: (1) a basic scenario including depopulation of detected herds, 3 km protection and 10 km surveillance zones, movement tracing and a three-day national standstill, (2) the basic scenario plus depopulation in ring zones around detected herds (Depop), (3) the basic scenario plus protective vaccination within ring zones around detected herds, and (4) the basic scenario plus protective vaccination within ring zones around detected herds. Disease spread was simulated through direct animal movements, medium-risk contacts (veterinarians, artificial inseminators or milk controllers), low-risk contacts (animal feed and rendering trucks, technicians or visitors), market contacts, abattoir trucks, milk tanks, or local spread. The two simulation models showed different results in terms of the estimated numbers. However, the tendencies in terms of recommendations of strategies were similar for both models. Comparison of the different control strategies showed that, from an epidemiological point of view, protective vaccination would be preferable if the epidemic started in a cattle herd in an area with a high density of cattle, whereas if the epidemic started in an area with a low density of cattle or in other species, protective vaccination or depopulation would have almost the same preventive effect. Implementing additional control measures either 14 days after detection of the first infected herd or when 10 herds have been diagnosed would be more efficient than implementing additional control measures when more herds have been diagnosed. Protective vaccination scenarios would never be cost-effective, whereas depopulation or suppressive vaccination scenarios would most often be recommended. Looking at the median estimates of the cost-benefit analysis, depopulation in zones would most often be recommended, although, in extreme epidemics, suppressive vaccination scenarios could be less expensive. The vast majority of the costs and losses associated with a Danish epidemic could be attributed to export losses. Copyright © 2013 Elsevier B.V. All rights reserved.

Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees

PubMed Central

2011-01-01

Background The spread of infectious diseases crucially depends on the pattern of contacts between individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. However, there are few empirical studies available that provide estimates of the number and duration of contacts between social groups. Moreover, their space and time resolutions are limited, so that data are not explicit at the person-to-person level, and the dynamic nature of the contacts is disregarded. In this study, we aimed to assess the role of data-driven dynamic contact patterns between individuals, and in particular of their temporal aspects, in shaping the spread of a simulated epidemic in the population. Methods We considered high-resolution data about face-to-face interactions between the attendees at a conference, obtained from the deployment of an infrastructure based on radiofrequency identification (RFID) devices that assessed mutual face-to-face proximity. The spread of epidemics along these interactions was simulated using an SEIR (Susceptible, Exposed, Infectious, Recovered) model, using both the dynamic network of contacts defined by the collected data, and two aggregated versions of such networks, to assess the role of the data temporal aspects. Results We show that, on the timescales considered, an aggregated network taking into account the daily duration of contacts is a good approximation to the full resolution network, whereas a homogeneous representation that retains only the topology of the contact network fails to reproduce the size of the epidemic. Conclusions These results have important implications for understanding the level of detail needed to correctly inform computational models for the study and management of real epidemics. Please see related article BMC Medicine, 2011, 9:88 PMID:21771290

Bayesian Tracking of Emerging Epidemics Using Ensemble Optimal Statistical Interpolation

PubMed Central

Cobb, Loren; Krishnamurthy, Ashok; Mandel, Jan; Beezley, Jonathan D.

2014-01-01

We present a preliminary test of the Ensemble Optimal Statistical Interpolation (EnOSI) method for the statistical tracking of an emerging epidemic, with a comparison to its popular relative for Bayesian data assimilation, the Ensemble Kalman Filter (EnKF). The spatial data for this test was generated by a spatial susceptible-infectious-removed (S-I-R) epidemic model of an airborne infectious disease. Both tracking methods in this test employed Poisson rather than Gaussian noise, so as to handle epidemic data more accurately. The EnOSI and EnKF tracking methods worked well on the main body of the simulated spatial epidemic, but the EnOSI was able to detect and track a distant secondary focus of infection that the EnKF missed entirely. PMID:25113590

Mathematical models for predicting human mobility in the context of infectious disease spread: introducing the impedance model.

PubMed

Sallah, Kankoé; Giorgi, Roch; Bengtsson, Linus; Lu, Xin; Wetter, Erik; Adrien, Paul; Rebaudet, Stanislas; Piarroux, Renaud; Gaudart, Jean

2017-11-22

Mathematical models of human mobility have demonstrated a great potential for infectious disease epidemiology in contexts of data scarcity. While the commonly used gravity model involves parameter tuning and is thus difficult to implement without reference data, the more recent radiation model based on population densities is parameter-free, but biased. In this study we introduce the new impedance model, by analogy with electricity. Previous research has compared models on the basis of a few specific available spatial patterns. In this study, we use a systematic simulation-based approach to assess the performances. Five hundred spatial patterns were generated using various area sizes and location coordinates. Model performances were evaluated based on these patterns. For simulated data, comparison measures were average root mean square error (aRMSE) and bias criteria. Modeling of the 2010 Haiti cholera epidemic with a basic susceptible-infected-recovered (SIR) framework allowed an empirical evaluation through assessing the goodness-of-fit of the observed epidemic curve. The new, parameter-free impedance model outperformed previous models on simulated data according to average aRMSE and bias criteria. The impedance model achieved better performances with heterogeneous population densities and small destination populations. As a proof of concept, the basic compartmental SIR framework was used to confirm the results obtained with the impedance model in predicting the spread of cholera in Haiti in 2010. The proposed new impedance model provides accurate estimations of human mobility, especially when the population distribution is highly heterogeneous. This model can therefore help to achieve more accurate predictions of disease spread in the context of an epidemic.

A Stochastic Simulator of a Blood Product Donation Environment with Demand Spikes and Supply Shocks

PubMed Central

An, Ming-Wen; Reich, Nicholas G.; Crawford, Stephen O.; Brookmeyer, Ron; Louis, Thomas A.; Nelson, Kenrad E.

2011-01-01

The availability of an adequate blood supply is a critical public health need. An influenza epidemic or another crisis affecting population mobility could create a critical donor shortage, which could profoundly impact blood availability. We developed a simulation model for the blood supply environment in the United States to assess the likely impact on blood availability of factors such as an epidemic. We developed a simulator of a multi-state model with transitions among states. Weekly numbers of blood units donated and needed were generated by negative binomial stochastic processes. The simulator allows exploration of the blood system under certain conditions of supply and demand rates, and can be used for planning purposes to prepare for sudden changes in the public's health. The simulator incorporates three donor groups (first-time, sporadic, and regular), immigration and emigration, deferral period, and adjustment factors for recruitment. We illustrate possible uses of the simulator by specifying input values for an -week flu epidemic, resulting in a moderate supply shock and demand spike (for example, from postponed elective surgeries), and different recruitment strategies. The input values are based in part on data from a regional blood center of the American Red Cross during –. Our results from these scenarios suggest that the key to alleviating deficit effects of a system shock may be appropriate timing and duration of recruitment efforts, in turn depending critically on anticipating shocks and rapidly implementing recruitment efforts. PMID:21814550

A stochastic simulator of a blood product donation environment with demand spikes and supply shocks.

PubMed

An, Ming-Wen; Reich, Nicholas G; Crawford, Stephen O; Brookmeyer, Ron; Louis, Thomas A; Nelson, Kenrad E

2011-01-01

The availability of an adequate blood supply is a critical public health need. An influenza epidemic or another crisis affecting population mobility could create a critical donor shortage, which could profoundly impact blood availability. We developed a simulation model for the blood supply environment in the United States to assess the likely impact on blood availability of factors such as an epidemic. We developed a simulator of a multi-state model with transitions among states. Weekly numbers of blood units donated and needed were generated by negative binomial stochastic processes. The simulator allows exploration of the blood system under certain conditions of supply and demand rates, and can be used for planning purposes to prepare for sudden changes in the public's health. The simulator incorporates three donor groups (first-time, sporadic, and regular), immigration and emigration, deferral period, and adjustment factors for recruitment. We illustrate possible uses of the simulator by specifying input values for an 8-week flu epidemic, resulting in a moderate supply shock and demand spike (for example, from postponed elective surgeries), and different recruitment strategies. The input values are based in part on data from a regional blood center of the American Red Cross during 1996-2005. Our results from these scenarios suggest that the key to alleviating deficit effects of a system shock may be appropriate timing and duration of recruitment efforts, in turn depending critically on anticipating shocks and rapidly implementing recruitment efforts.

Epidemic modeling with discrete-space scheduled walkers: extensions and research opportunities

PubMed Central

2009-01-01

Background This exploratory paper outlines an epidemic simulator built on an agent-based, data-driven model of the spread of a disease within an urban environment. An intent of the model is to provide insight into how a disease may reach a tipping point, spreading to an epidemic of uncontrollable proportions. Methods As a complement to analytical methods, simulation is arguably an effective means of gaining a better understanding of system-level disease dynamics within a population and offers greater utility in its modeling capabilities. Our investigation is based on this conjecture, supported by data-driven models that are reasonable, realistic and practical, in an attempt to demonstrate their efficacy in studying system-wide epidemic phenomena. An agent-based model (ABM) offers considerable flexibility in extending the study of the phenomena before, during and after an outbreak or catastrophe. Results An agent-based model was developed based on a paradigm of a 'discrete-space scheduled walker' (DSSW), modeling a medium-sized North American City of 650,000 discrete agents, built upon a conceptual framework of statistical reasoning (law of large numbers, statistical mechanics) as well as a correct-by-construction bias. The model addresses where, who, when and what elements, corresponding to network topography and agent characteristics, behaviours, and interactions upon that topography. The DSSW-ABM has an interface and associated scripts that allow for a variety of what-if scenarios modeling disease spread throughout the population, and for data to be collected and displayed via a web browser. Conclusion This exploratory paper also presents several research opportunities for exploiting data sources of a non-obvious and disparate nature for the purposes of epidemic modeling. There is an increasing amount and variety of data that will continue to contribute to the accuracy of agent-based models and improve their utility in modeling disease spread. The model developed here is well suited to diseases where there is not a predisposition for contraction within the population. One of the advantages of agent-based modeling is the ability to set up a rare event and develop policy as to how one may mitigate damages arising from it. PMID:19922684

Epidemic modeling with discrete-space scheduled walkers: extensions and research opportunities.

PubMed

Borkowski, Maciej; Podaima, Blake W; McLeod, Robert D

2009-11-18

This exploratory paper outlines an epidemic simulator built on an agent-based, data-driven model of the spread of a disease within an urban environment. An intent of the model is to provide insight into how a disease may reach a tipping point, spreading to an epidemic of uncontrollable proportions. As a complement to analytical methods, simulation is arguably an effective means of gaining a better understanding of system-level disease dynamics within a population and offers greater utility in its modeling capabilities. Our investigation is based on this conjecture, supported by data-driven models that are reasonable, realistic and practical, in an attempt to demonstrate their efficacy in studying system-wide epidemic phenomena. An agent-based model (ABM) offers considerable flexibility in extending the study of the phenomena before, during and after an outbreak or catastrophe. An agent-based model was developed based on a paradigm of a 'discrete-space scheduled walker' (DSSW), modeling a medium-sized North American City of 650,000 discrete agents, built upon a conceptual framework of statistical reasoning (law of large numbers, statistical mechanics) as well as a correct-by-construction bias. The model addresses where, who, when and what elements, corresponding to network topography and agent characteristics, behaviours, and interactions upon that topography. The DSSW-ABM has an interface and associated scripts that allow for a variety of what-if scenarios modeling disease spread throughout the population, and for data to be collected and displayed via a web browser. This exploratory paper also presents several research opportunities for exploiting data sources of a non-obvious and disparate nature for the purposes of epidemic modeling. There is an increasing amount and variety of data that will continue to contribute to the accuracy of agent-based models and improve their utility in modeling disease spread. The model developed here is well suited to diseases where there is not a predisposition for contraction within the population. One of the advantages of agent-based modeling is the ability to set up a rare event and develop policy as to how one may mitigate damages arising from it.

Computer simulation of white pine blister rust epidemics

Treesearch

Geral I. McDonald; Raymond J. Hoff; William R. Wykoff

1981-01-01

A simulation of white pine blister rust is described in both word and mathematical models. The objective of this first generation simulation was to organize and analyze the available epidemiological knowledge to produce a foundation for integrated management of this destructive rust of 5-needle pines. Verification procedures and additional research needs are also...

Agent-based modeling of the spread of the 1918-1919 flu in three Canadian fur trading communities.

PubMed

O'Neil, Caroline A; Sattenspiel, Lisa

2010-01-01

Previous attempts to study the 1918-1919 flu in three small communities in central Manitoba have used both three-community population-based and single-community agent-based models. These studies identified critical factors influencing epidemic spread, but they also left important questions unanswered. The objective of this project was to design a more realistic agent-based model that would overcome limitations of earlier models and provide new insights into these outstanding questions. The new model extends the previous agent-based model to three communities so that results can be compared to those from the population-based model. Sensitivity testing was conducted, and the new model was used to investigate the influence of seasonal settlement and mobility patterns, the geographic heterogeneity of the observed 1918-1919 epidemic in Manitoba, and other questions addressed previously. Results confirm outcomes from the population-based model that suggest that (a) social organization and mobility strongly influence the timing and severity of epidemics and (b) the impact of the epidemic would have been greater if it had arrived in the summer rather than the winter. New insights from the model suggest that the observed heterogeneity among communities in epidemic impact was not unusual and would have been the expected outcome given settlement structure and levels of interaction among communities. Application of an agent-based computer simulation has helped to better explain observed patterns of spread of the 1918-1919 flu epidemic in central Manitoba. Contrasts between agent-based and population-based models illustrate the advantages of agent-based models for the study of small populations. © 2010 Wiley-Liss, Inc.

Inference of Epidemiological Dynamics Based on Simulated Phylogenies Using Birth-Death and Coalescent Models

PubMed Central

Boskova, Veronika; Bonhoeffer, Sebastian; Stadler, Tanja

2014-01-01

Quantifying epidemiological dynamics is crucial for understanding and forecasting the spread of an epidemic. The coalescent and the birth-death model are used interchangeably to infer epidemiological parameters from the genealogical relationships of the pathogen population under study, which in turn are inferred from the pathogen genetic sequencing data. To compare the performance of these widely applied models, we performed a simulation study. We simulated phylogenetic trees under the constant rate birth-death model and the coalescent model with a deterministic exponentially growing infected population. For each tree, we re-estimated the epidemiological parameters using both a birth-death and a coalescent based method, implemented as an MCMC procedure in BEAST v2.0. In our analyses that estimate the growth rate of an epidemic based on simulated birth-death trees, the point estimates such as the maximum a posteriori/maximum likelihood estimates are not very different. However, the estimates of uncertainty are very different. The birth-death model had a higher coverage than the coalescent model, i.e. contained the true value in the highest posterior density (HPD) interval more often (2–13% vs. 31–75% error). The coverage of the coalescent decreases with decreasing basic reproductive ratio and increasing sampling probability of infecteds. We hypothesize that the biases in the coalescent are due to the assumption of deterministic rather than stochastic population size changes. Both methods performed reasonably well when analyzing trees simulated under the coalescent. The methods can also identify other key epidemiological parameters as long as one of the parameters is fixed to its true value. In summary, when using genetic data to estimate epidemic dynamics, our results suggest that the birth-death method will be less sensitive to population fluctuations of early outbreaks than the coalescent method that assumes a deterministic exponentially growing infected population. PMID:25375100

Nonlinear model of epidemic spreading in a complex social network.

PubMed

Kosiński, Robert A; Grabowski, A

2007-10-01

The epidemic spreading in a human society is a complex process, which can be described on the basis of a nonlinear mathematical model. In such an approach the complex and hierarchical structure of social network (which has implications for the spreading of pathogens and can be treated as a complex network), can be taken into account. In our model each individual has one of the four permitted states: susceptible, infected, infective, unsusceptible or dead. This refers to the SEIR model used in epidemiology. The state of an individual changes in time, depending on the previous state and the interactions with other individuals. The description of the interpersonal contacts is based on the experimental observations of the social relations in the community. It includes spatial localization of the individuals and hierarchical structure of interpersonal interactions. Numerical simulations were performed for different types of epidemics, giving the progress of a spreading process and typical relationships (e.g. range of epidemic in time, the epidemic curve). The spreading process has a complex and spatially chaotic character. The time dependence of the number of infective individuals shows the nonlinear character of the spreading process. We investigate the influence of the preventive vaccinations on the spreading process. In particular, for a critical value of preventively vaccinated individuals the percolation threshold is observed and the epidemic is suppressed.

Volterra-type Lyapunov functions for fractional-order epidemic systems

NASA Astrophysics Data System (ADS)

Vargas-De-León, Cruz

2015-07-01

In this paper we prove an elementary lemma which estimates fractional derivatives of Volterra-type Lyapunov functions in the sense Caputo when α ∈ (0, 1) . Moreover, by using this result, we study the uniform asymptotic stability of some Caputo-type epidemic systems with a pair of fractional-order differential equations. These epidemic systems are the Susceptible-Infected-Susceptible (SIS), Susceptible-Infected-Recovered (SIR) and Susceptible-Infected-Recovered-Susceptible (SIRS) models and Ross-Macdonald model for vector-borne diseases. We show that the unique endemic equilibrium is uniformly asymptotically stable if the basic reproductive number is greater than one. We illustrate our theoretical results with numerical simulations using the Adams-Bashforth-Moulton scheme implemented in the fde12 Matlab function.

Modeling the effects of social impact on epidemic spreading in complex networks

NASA Astrophysics Data System (ADS)

Ni, Shunjiang; Weng, Wenguo; Zhang, Hui

2011-11-01

We investigate by mean-field analysis and extensive simulations the effects of social impact on epidemic spreading in various typical networks with two types of nodes: active nodes and passive nodes, of which the behavior patterns are modeled according to the social impact theory. In this study, nodes are not only the media to spread the virus, but also disseminate their opinions on the virus-whether there is a need for certain self-protection measures to be taken to reduce the risk of being infected. Our results indicate that the interaction between epidemic spreading and opinion dynamics can have significant influences on the spreading of infectious diseases and related applications, such as the implementation of prevention and control measures against the infectious diseases.

Epidemic spreading on random surfer networks with optimal interaction radius

NASA Astrophysics Data System (ADS)

Feng, Yun; Ding, Li; Hu, Ping

2018-03-01

In this paper, the optimal control problem of epidemic spreading on random surfer heterogeneous networks is considered. An epidemic spreading model is established according to the classification of individual's initial interaction radii. Then, a control strategy is proposed based on adjusting individual's interaction radii. The global stability of the disease free and endemic equilibrium of the model is investigated. We prove that an optimal solution exists for the optimal control problem and the explicit form of which is presented. Numerical simulations are conducted to verify the correctness of the theoretical results. It is proved that the optimal control strategy is effective to minimize the density of infected individuals and the cost associated with the adjustment of interaction radii.

HCV prevalence can predict HIV epidemic potential among people who inject drugs: mathematical modeling analysis.

PubMed

Akbarzadeh, Vajiheh; Mumtaz, Ghina R; Awad, Susanne F; Weiss, Helen A; Abu-Raddad, Laith J

2016-12-03

Hepatitis C virus (HCV) and HIV are both transmitted through percutaneous exposures among people who inject drugs (PWID). Ecological analyses on global epidemiological data have identified a positive association between HCV and HIV prevalence among PWID. Our objective was to demonstrate how HCV prevalence can be used to predict HIV epidemic potential among PWID. Two population-level models were constructed to simulate the evolution of HCV and HIV epidemics among PWID. The models described HCV and HIV parenteral transmission, and were solved both deterministically and stochastically. The modeling results provided a good fit to the epidemiological data describing the ecological HCV and HIV association among PWID. HCV was estimated to be eight times more transmissible per shared injection than HIV. A threshold HCV prevalence of 29.0% (95% uncertainty interval (UI): 20.7-39.8) and 46.5% (95% UI: 37.6-56.6) were identified for a sustainable HIV epidemic (HIV prevalence >1%) and concentrated HIV epidemic (HIV prevalence >5%), respectively. The association between HCV and HIV was further described with six dynamical regimes depicting the overlapping epidemiology of the two infections, and was quantified using defined and estimated measures of association. Modeling predictions across a wide range of HCV prevalence indicated overall acceptable precision in predicting HIV prevalence at endemic equilibrium. Modeling predictions were found to be robust with respect to stochasticity and behavioral and biological parameter uncertainty. In an illustrative application of the methodology, the modeling predictions of endemic HIV prevalence in Iran agreed with the scale and time course of the HIV epidemic in this country. Our results show that HCV prevalence can be used as a proxy biomarker of HIV epidemic potential among PWID, and that the scale and evolution of HIV epidemic expansion can be predicted with sufficient precision to inform HIV policy, programming, and resource allocation.

Bayesian inference for an emerging arboreal epidemic in the presence of control

PubMed Central

Parry, Matthew; Gibson, Gavin J.; Parnell, Stephen; Gottwald, Tim R.; Irey, Michael S.; Gast, Timothy C.; Gilligan, Christopher A.

2014-01-01

The spread of Huanglongbing through citrus groves is used as a case study for modeling an emerging epidemic in the presence of a control. Specifically, the spread of the disease is modeled as a susceptible-exposed-infectious-detected-removed epidemic, where the exposure and infectious times are not observed, detection times are censored, removal times are known, and the disease is spreading through a heterogeneous host population with trees of different age and susceptibility. We show that it is possible to characterize the disease transmission process under these conditions. Two innovations in our work are (i) accounting for control measures via time dependence of the infectious process and (ii) including seasonal and host age effects in the model of the latent period. By estimating parameters in different subregions of a large commercially cultivated orchard, we establish a temporal pattern of invasion, host age dependence of the dispersal parameters, and a close to linear relationship between primary and secondary infectious rates. The model can be used to simulate Huanglongbing epidemics to assess economic costs and potential benefits of putative control scenarios. PMID:24711393

Forecasting peaks of seasonal influenza epidemics.

PubMed

Nsoesie, Elaine; Mararthe, Madhav; Brownstein, John

2013-06-21

We present a framework for near real-time forecast of influenza epidemics using a simulation optimization approach. The method combines an individual-based model and a simple root finding optimization method for parameter estimation and forecasting. In this study, retrospective forecasts were generated for seasonal influenza epidemics using web-based estimates of influenza activity from Google Flu Trends for 2004-2005, 2007-2008 and 2012-2013 flu seasons. In some cases, the peak could be forecasted 5-6 weeks ahead. This study adds to existing resources for influenza forecasting and the proposed method can be used in conjunction with other approaches in an ensemble framework.

Characterizing the reproduction number of epidemics with early subexponential growth dynamics

PubMed Central

Viboud, Cécile; Simonsen, Lone; Moghadas, Seyed M.

2016-01-01

Early estimates of the transmission potential of emerging and re-emerging infections are increasingly used to inform public health authorities on the level of risk posed by outbreaks. Existing methods to estimate the reproduction number generally assume exponential growth in case incidence in the first few disease generations, before susceptible depletion sets in. In reality, outbreaks can display subexponential (i.e. polynomial) growth in the first few disease generations, owing to clustering in contact patterns, spatial effects, inhomogeneous mixing, reactive behaviour changes or other mechanisms. Here, we introduce the generalized growth model to characterize the early growth profile of outbreaks and estimate the effective reproduction number, with no need for explicit assumptions about the shape of epidemic growth. We demonstrate this phenomenological approach using analytical results and simulations from mechanistic models, and provide validation against a range of empirical disease datasets. Our results suggest that subexponential growth in the early phase of an epidemic is the rule rather the exception. Mechanistic simulations show that slight modifications to the classical susceptible–infectious–removed model result in subexponential growth, and in turn a rapid decline in the reproduction number within three to five disease generations. For empirical outbreaks, the generalized-growth model consistently outperforms the exponential model for a variety of directly and indirectly transmitted diseases datasets (pandemic influenza, measles, smallpox, bubonic plague, cholera, foot-and-mouth disease, HIV/AIDS and Ebola) with model estimates supporting subexponential growth dynamics. The rapid decline in effective reproduction number predicted by analytical results and observed in real and synthetic datasets within three to five disease generations contrasts with the expectation of invariant reproduction number in epidemics obeying exponential growth. The generalized-growth concept also provides us a compelling argument for the unexpected extinction of certain emerging disease outbreaks during the early ascending phase. Overall, our approach promotes a more reliable and data-driven characterization of the early epidemic phase, which is important for accurate estimation of the reproduction number and prediction of disease impact. PMID:27707909

On extinction time of a generalized endemic chain-binomial model.

PubMed

Aydogmus, Ozgur

2016-09-01

We considered a chain-binomial epidemic model not conferring immunity after infection. Mean field dynamics of the model has been analyzed and conditions for the existence of a stable endemic equilibrium are determined. The behavior of the chain-binomial process is probabilistically linked to the mean field equation. As a result of this link, we were able to show that the mean extinction time of the epidemic increases at least exponentially as the population size grows. We also present simulation results for the process to validate our analytical findings. Copyright © 2016 Elsevier Inc. All rights reserved.

Estimating a Markovian Epidemic Model Using Household Serial Interval Data from the Early Phase of an Epidemic

PubMed Central

Black, Andrew J.; Ross, Joshua V.

2013-01-01

The clinical serial interval of an infectious disease is the time between date of symptom onset in an index case and the date of symptom onset in one of its secondary cases. It is a quantity which is commonly collected during a pandemic and is of fundamental importance to public health policy and mathematical modelling. In this paper we present a novel method for calculating the serial interval distribution for a Markovian model of household transmission dynamics. This allows the use of Bayesian MCMC methods, with explicit evaluation of the likelihood, to fit to serial interval data and infer parameters of the underlying model. We use simulated and real data to verify the accuracy of our methodology and illustrate the importance of accounting for household size. The output of our approach can be used to produce posterior distributions of population level epidemic characteristics. PMID:24023679

Modelling HIV/AIDS epidemics in sub-Saharan Africa using seroprevalence data from antenatal clinics.

PubMed Central

Salomon, J. A.; Murray, C. J.

2001-01-01

OBJECTIVE: To improve the methodological basis for modelling the HIV/AIDS epidemics in adults in sub-Saharan Africa, with examples from Botswana, Central African Republic, Ethiopia, and Zimbabwe. Understanding the magnitude and trajectory of the HIV/AIDS epidemic is essential for planning and evaluating control strategies. METHODS: Previous mathematical models were developed to estimate epidemic trends based on sentinel surveillance data from pregnant women. In this project, we have extended these models in order to take full advantage of the available data. We developed a maximum likelihood approach for the estimation of model parameters and used numerical simulation methods to compute uncertainty intervals around the estimates. FINDINGS: In the four countries analysed, there were an estimated half a million new adult HIV infections in 1999 (range: 260 to 960 thousand), 4.7 million prevalent infections (range: 3.0 to 6.6 million), and 370 thousand adult deaths from AIDS (range: 266 to 492 thousand). CONCLUSION: While this project addresses some of the limitations of previous modelling efforts, an important research agenda remains, including the need to clarify the relationship between sentinel data from pregnant women and the epidemiology of HIV and AIDS in the general population. PMID:11477962

Efficient mitigation strategies for epidemics in rural regions.

PubMed

Scoglio, Caterina; Schumm, Walter; Schumm, Phillip; Easton, Todd; Roy Chowdhury, Sohini; Sydney, Ali; Youssef, Mina

2010-07-13

Containing an epidemic at its origin is the most desirable mitigation. Epidemics have often originated in rural areas, with rural communities among the first affected. Disease dynamics in rural regions have received limited attention, and results of general studies cannot be directly applied since population densities and human mobility factors are very different in rural regions from those in cities. We create a network model of a rural community in Kansas, USA, by collecting data on the contact patterns and computing rates of contact among a sampled population. We model the impact of different mitigation strategies detecting closely connected groups of people and frequently visited locations. Within those groups and locations, we compare the effectiveness of random and targeted vaccinations using a Susceptible-Exposed-Infected-Recovered compartmental model on the contact network. Our simulations show that the targeted vaccinations of only 10% of the sampled population reduced the size of the epidemic by 34.5%. Additionally, if 10% of the population visiting one of the most popular locations is randomly vaccinated, the epidemic size is reduced by 19%. Our results suggest a new implementation of a highly effective strategy for targeted vaccinations through the use of popular locations in rural communities.

Modeling workplace contact networks: The effects of organizational structure, architecture, and reporting errors on epidemic predictions.

PubMed

Potter, Gail E; Smieszek, Timo; Sailer, Kerstin

2015-09-01

Face-to-face social contacts are potentially important transmission routes for acute respiratory infections, and understanding the contact network can improve our ability to predict, contain, and control epidemics. Although workplaces are important settings for infectious disease transmission, few studies have collected workplace contact data and estimated workplace contact networks. We use contact diaries, architectural distance measures, and institutional structures to estimate social contact networks within a Swiss research institute. Some contact reports were inconsistent, indicating reporting errors. We adjust for this with a latent variable model, jointly estimating the true (unobserved) network of contacts and duration-specific reporting probabilities. We find that contact probability decreases with distance, and that research group membership, role, and shared projects are strongly predictive of contact patterns. Estimated reporting probabilities were low only for 0-5 min contacts. Adjusting for reporting error changed the estimate of the duration distribution, but did not change the estimates of covariate effects and had little effect on epidemic predictions. Our epidemic simulation study indicates that inclusion of network structure based on architectural and organizational structure data can improve the accuracy of epidemic forecasting models.

Modeling workplace contact networks: The effects of organizational structure, architecture, and reporting errors on epidemic predictions

PubMed Central

Potter, Gail E.; Smieszek, Timo; Sailer, Kerstin

2015-01-01

Face-to-face social contacts are potentially important transmission routes for acute respiratory infections, and understanding the contact network can improve our ability to predict, contain, and control epidemics. Although workplaces are important settings for infectious disease transmission, few studies have collected workplace contact data and estimated workplace contact networks. We use contact diaries, architectural distance measures, and institutional structures to estimate social contact networks within a Swiss research institute. Some contact reports were inconsistent, indicating reporting errors. We adjust for this with a latent variable model, jointly estimating the true (unobserved) network of contacts and duration-specific reporting probabilities. We find that contact probability decreases with distance, and that research group membership, role, and shared projects are strongly predictive of contact patterns. Estimated reporting probabilities were low only for 0–5 min contacts. Adjusting for reporting error changed the estimate of the duration distribution, but did not change the estimates of covariate effects and had little effect on epidemic predictions. Our epidemic simulation study indicates that inclusion of network structure based on architectural and organizational structure data can improve the accuracy of epidemic forecasting models. PMID:26634122

Global dynamics of a network-based SIQRS epidemic model with demographics and vaccination

NASA Astrophysics Data System (ADS)

Huang, Shouying; Chen, Fengde; Chen, Lijuan

2017-02-01

This paper investigates a new SIQRS epidemic model with demographics and vaccination on complex heterogeneous networks. We analytically derive the basic reproduction number R0, which determines not only the existence of endemic equilibrium but also the global dynamics of the model. The permanence of the disease and the globally asymptotical stability of disease-free equilibrium are proved in detail. By using a monotone iterative technique, we show that the unique endemic equilibrium is globally attractive under certain conditions. Our results really improve and enrich the results in Li et al (2014) [14]. Interestingly, the basic reproduction number R0 bears no relation to the degree-dependent birth, but our simulations indicate that the degree-dependent birth does affect the epidemic dynamics. Furthermore, we find that quarantine plays a more active role than vaccination in controlling the disease.

Dynamics of epidemic spreading model with drug-resistant variation on scale-free networks

NASA Astrophysics Data System (ADS)

Wan, Chen; Li, Tao; Zhang, Wu; Dong, Jing

2018-03-01

Considering the influence of the virus' drug-resistant variation, a novel SIVRS (susceptible-infected-variant-recovered-susceptible) epidemic spreading model with variation characteristic on scale-free networks is proposed in this paper. By using the mean-field theory, the spreading dynamics of the model is analyzed in detail. Then, the basic reproductive number R0 and equilibriums are derived. Studies show that the existence of disease-free equilibrium is determined by the basic reproductive number R0. The relationships between the basic reproductive number R0, the variation characteristic and the topology of the underlying networks are studied in detail. Furthermore, our studies prove the global stability of the disease-free equilibrium, the permanence of epidemic and the global attractivity of endemic equilibrium. Numerical simulations are performed to confirm the analytical results.

Epidemic Wave Dynamics Attributable to Urban Community Structure: A Theoretical Characterization of Disease Transmission in a Large Network

PubMed Central

Eggo, Rosalind M; Lenczner, Michael

2015-01-01

Background Multiple waves of transmission during infectious disease epidemics represent a major public health challenge, but the ecological and behavioral drivers of epidemic resurgence are poorly understood. In theory, community structure—aggregation into highly intraconnected and loosely interconnected social groups—within human populations may lead to punctuated outbreaks as diseases progress from one community to the next. However, this explanation has been largely overlooked in favor of temporal shifts in environmental conditions and human behavior and because of the difficulties associated with estimating large-scale contact patterns. Objective The aim was to characterize naturally arising patterns of human contact that are capable of producing simulated epidemics with multiple wave structures. Methods We used an extensive dataset of proximal physical contacts between users of a public Wi-Fi Internet system to evaluate the epidemiological implications of an empirical urban contact network. We characterized the modularity (community structure) of the network and then estimated epidemic dynamics under a percolation-based model of infectious disease spread on the network. We classified simulated epidemics as multiwave using a novel metric and we identified network structures that were critical to the network’s ability to produce multiwave epidemics. Results We identified robust community structure in a large, empirical urban contact network from which multiwave epidemics may emerge naturally. This pattern was fueled by a special kind of insularity in which locally popular individuals were not the ones forging contacts with more distant social groups. Conclusions Our results suggest that ordinary contact patterns can produce multiwave epidemics at the scale of a single urban area without the temporal shifts that are usually assumed to be responsible. Understanding the role of community structure in epidemic dynamics allows officials to anticipate epidemic resurgence without having to forecast future changes in hosts, pathogens, or the environment. PMID:26156032

Comparison of an Agent-based Model of Disease Propagation with the Generalised SIR Epidemic Model

DTIC Science & Technology

2009-08-01

has become a practical method for conducting Epidemiological Modelling. In the agent- based approach the whole township can be modelled as a system of...SIR system was initially developed based on a very simplified model of social interaction. For instance an assumption of uniform population mixing was...simulating the progress of a disease within a host and of transmission between hosts is based upon Transportation Analysis and Simulation System

Modeling the effect of transient populations on epidemics in Washington DC.

PubMed

Parikh, Nidhi; Youssef, Mina; Swarup, Samarth; Eubank, Stephen

2013-11-06

Large numbers of transients visit big cities, where they come into contact with many people at crowded areas. However, epidemiological studies have not paid much attention to the role of this subpopulation in disease spread. We evaluate the effect of transients on epidemics by extending a synthetic population model for the Washington DC metro area to include leisure and business travelers. A synthetic population is obtained by combining multiple data sources to build a detailed minute-by-minute simulation of population interaction resulting in a contact network. We simulate an influenza-like illness over the contact network to evaluate the effects of transients on the number of infected residents. We find that there are significantly more infections when transients are considered. Since much population mixing happens at major tourism locations, we evaluate two targeted interventions: closing museums and promoting healthy behavior (such as the use of hand sanitizers, covering coughs, etc.) at museums. Surprisingly, closing museums has no beneficial effect. However, promoting healthy behavior at the museums can both reduce and delay the epidemic peak. We analytically derive the reproductive number and perform stability analysis using an ODE-based model.

Modeling the effect of transient populations on epidemics in Washington DC

NASA Astrophysics Data System (ADS)

Parikh, Nidhi; Youssef, Mina; Swarup, Samarth; Eubank, Stephen

2013-11-01

Large numbers of transients visit big cities, where they come into contact with many people at crowded areas. However, epidemiological studies have not paid much attention to the role of this subpopulation in disease spread. We evaluate the effect of transients on epidemics by extending a synthetic population model for the Washington DC metro area to include leisure and business travelers. A synthetic population is obtained by combining multiple data sources to build a detailed minute-by-minute simulation of population interaction resulting in a contact network. We simulate an influenza-like illness over the contact network to evaluate the effects of transients on the number of infected residents. We find that there are significantly more infections when transients are considered. Since much population mixing happens at major tourism locations, we evaluate two targeted interventions: closing museums and promoting healthy behavior (such as the use of hand sanitizers, covering coughs, etc.) at museums. Surprisingly, closing museums has no beneficial effect. However, promoting healthy behavior at the museums can both reduce and delay the epidemic peak. We analytically derive the reproductive number and perform stability analysis using an ODE-based model.

Effects of human dynamics on epidemic spreading in Côte d'Ivoire

NASA Astrophysics Data System (ADS)

Li, Ruiqi; Wang, Wenxu; Di, Zengru

2017-02-01

Understanding and predicting outbreaks of contagious diseases are crucial to the development of society and public health, especially for underdeveloped countries. However, challenging problems are encountered because of complex epidemic spreading dynamics influenced by spatial structure and human dynamics (including both human mobility and human interaction intensity). We propose a systematical model to depict nationwide epidemic spreading in Côte d'Ivoire, which integrates multiple factors, such as human mobility, human interaction intensity, and demographic features. We provide insights to aid in modeling and predicting the epidemic spreading process by data-driven simulation and theoretical analysis, which is otherwise beyond the scope of local evaluation and geometrical views. We show that the requirement that the average local basic reproductive number to be greater than unity is not necessary for outbreaks of epidemics. The observed spreading phenomenon can be roughly explained as a heterogeneous diffusion-reaction process by redefining mobility distance according to the human mobility volume between nodes, which is beyond the geometrical viewpoint. However, the heterogeneity of human dynamics still poses challenges to precise prediction.

The impact of vaccine failure rate on epidemic dynamics in responsive networks.

PubMed

Liang, Yu-Hao; Juang, Jonq

2015-04-01

An SIS model based on the microscopic Markov-chain approximation is considered in this paper. It is assumed that the individual vaccination behavior depends on the contact awareness, local and global information of an epidemic. To better simulate the real situation, the vaccine failure rate is also taken into consideration. Our main conclusions are given in the following. First, we show that if the vaccine failure rate α is zero, then the epidemic eventually dies out regardless of what the network structure is or how large the effective spreading rate and the immunization response rates of an epidemic are. Second, we show that for any positive α, there exists a positive epidemic threshold depending on an adjusted network structure, which is only determined by the structure of the original network, the positive vaccine failure rate and the immunization response rate for contact awareness. Moreover, the epidemic threshold increases with respect to the strength of the immunization response rate for contact awareness. Finally, if the vaccine failure rate and the immunization response rate for contact awareness are positive, then there exists a critical vaccine failure rate αc > 0 so that the disease free equilibrium (DFE) is stable (resp., unstable) if α < αc (resp., α > αc). Numerical simulations to see the effectiveness of our theoretical results are also provided.

Discrete stochastic analogs of Erlang epidemic models.

PubMed

Getz, Wayne M; Dougherty, Eric R

2018-12-01

Erlang differential equation models of epidemic processes provide more realistic disease-class transition dynamics from susceptible (S) to exposed (E) to infectious (I) and removed (R) categories than the ubiquitous SEIR model. The latter is itself is at one end of the spectrum of Erlang SE[Formula: see text]I[Formula: see text]R models with [Formula: see text] concatenated E compartments and [Formula: see text] concatenated I compartments. Discrete-time models, however, are computationally much simpler to simulate and fit to epidemic outbreak data than continuous-time differential equations, and are also much more readily extended to include demographic and other types of stochasticity. Here we formulate discrete-time deterministic analogs of the Erlang models, and their stochastic extension, based on a time-to-go distributional principle. Depending on which distributions are used (e.g. discretized Erlang, Gamma, Beta, or Uniform distributions), we demonstrate that our formulation represents both a discretization of Erlang epidemic models and generalizations thereof. We consider the challenges of fitting SE[Formula: see text]I[Formula: see text]R models and our discrete-time analog to data (the recent outbreak of Ebola in Liberia). We demonstrate that the latter performs much better than the former; although confining fits to strict SEIR formulations reduces the numerical challenges, but sacrifices best-fit likelihood scores by at least 7%.

HIV competition dynamics over sexual networks: first comer advantage conserves founder effects.

PubMed

Ferdinandy, Bence; Mones, Enys; Vicsek, Tamás; Müller, Viktor

2015-02-01

Outside Africa, the global phylogeography of HIV is characterized by compartmentalized local epidemics that are typically dominated by a single subtype, which indicates strong founder effects. We hypothesized that the competition of viral strains at the epidemic level may involve an advantage of the resident strain that was the first to colonize a population. Such an effect would slow down the invasion of new strains, and thus also the diversification of the epidemic. We developed a stochastic modelling framework to simulate HIV epidemics over dynamic contact networks. We simulated epidemics in which the second strain was introduced into a population where the first strain had established a steady-state epidemic, and assessed whether, and on what time scale, the second strain was able to spread in the population. Simulations were parameterized based on empirical data; we tested scenarios with varying levels of overall prevalence. The spread of the second strain occurred on a much slower time scale compared with the initial expansion of the first strain. With strains of equal transmission efficiency, the second strain was unable to invade on a time scale relevant for the history of the HIV pandemic. To become dominant over a time scale of decades, the second strain needed considerable (>25%) advantage in transmission efficiency over the resident strain. The inhibition effect was weaker if the second strain was introduced while the first strain was still in its growth phase. We also tested how possible mechanisms of interference (inhibition of superinfection, depletion of highly connected hubs in the network, one-time acute peak of infectiousness) contribute to the inhibition effect. Our simulations confirmed a strong first comer advantage in the competition dynamics of HIV at the population level, which may explain the global phylogeography of the virus and may influence the future evolution of the pandemic.

Dynamics of history-dependent epidemics in temporal networks

NASA Astrophysics Data System (ADS)

Sunny, Albert; Kotnis, Bhushan; Kuri, Joy

2015-08-01

The structural properties of temporal networks often influence the dynamical processes that occur on these networks, e.g., bursty interaction patterns have been shown to slow down epidemics. In this paper, we investigate the effect of link lifetimes on the spread of history-dependent epidemics. We formulate an analytically tractable activity-driven temporal network model that explicitly incorporates link lifetimes. For Markovian link lifetimes, we use mean-field analysis for computing the epidemic threshold, while the effect of non-Markovian link lifetimes is studied using simulations. Furthermore, we also study the effect of negative correlation between the number of links spawned by an individual and the lifetimes of those links. Such negative correlations may arise due to the finite cognitive capacity of the individuals. Our investigations reveal that heavy-tailed link lifetimes slow down the epidemic, while negative correlations can reduce epidemic prevalence. We believe that our results help shed light on the role of link lifetimes in modulating diffusion processes on temporal networks.

Forecasted impacts of a sofosbuvir-based national hepatitis C treatment programme on Egypt’s hepatocellular cancer epidemic: simulation of alternatives

PubMed Central

Ma, Wenkang; Soliman, Amr S; Anwar, Wagida A; Hablas, Ahmed; El Din, Tamer B; Ramadan, Mohamed; Seifeldin, Ibrahim A; Wilson, Mark L

2018-01-01

Background Egypt is experiencing a hepatocellular cancer (HCC) epidemic due to widespread hepatitis C virus (HCV) transmission. The use of sofosbuvir-related therapies producing improved treatment success has permitted an updated, nationwide, HCV treatment programme with expanded coverage. This study simulated the multidecade impacts of the new treatment programme on hepatitis and HCC. Methods A Markov model of HCV infection and treatment analysed the HCV-related HCC epidemic between 2009 and 2050, using parameters based on peer-reviewed studies and expert opinion. Comparing the ‘new’ and ‘old’ scenarios, and with the old treatment programme being replaced or not by the new programme in 2015, the annual number, prevalence and incidence of HCC were simulated for representative Egypt populations including HCV-infected patients aged 15–59 years in 2008, healthy people aged 5–59 years in 2008 and 5-year-old children cohorts entering the population each year beginning in 2009. Averted HCC cases were calculated, and sensitivity analyses were performed. Results Compared with the old scenario, the estimated number, prevalence and incidence of future HCC cases in the new scenario would peak earlier and at lower levels in 2025 (~29 000), 2023 (~28/100 000) and 2022 (~14/100 000), respectively. The new treatment programme is estimated to avert ~956 000 HCC cases between 2015 and 2050. Discussion By reducing cancer cases and shortening the peak epidemic period, the new programme should substantially diminish the HCC epidemic across Egypt. Our timeline forecast for Egypt’s HCC epidemic, and evaluation of various disease and programme components, should be useful to other countries that are developing policies to address HCV-related liver cancer prevention. PMID:29707244

Forecasted impacts of a sofosbuvir-based national hepatitis C treatment programme on Egypt's hepatocellular cancer epidemic: simulation of alternatives.

PubMed

Ma, Wenkang; Soliman, Amr S; Anwar, Wagida A; Hablas, Ahmed; El Din, Tamer B; Ramadan, Mohamed; Seifeldin, Ibrahim A; Wilson, Mark L

2018-01-01

Egypt is experiencing a hepatocellular cancer (HCC) epidemic due to widespread hepatitis C virus (HCV) transmission. The use of sofosbuvir-related therapies producing improved treatment success has permitted an updated, nationwide, HCV treatment programme with expanded coverage. This study simulated the multidecade impacts of the new treatment programme on hepatitis and HCC. A Markov model of HCV infection and treatment analysed the HCV-related HCC epidemic between 2009 and 2050, using parameters based on peer-reviewed studies and expert opinion. Comparing the 'new' and 'old' scenarios, and with the old treatment programme being replaced or not by the new programme in 2015, the annual number, prevalence and incidence of HCC were simulated for representative Egypt populations including HCV-infected patients aged 15-59 years in 2008, healthy people aged 5-59 years in 2008 and 5-year-old children cohorts entering the population each year beginning in 2009. Averted HCC cases were calculated, and sensitivity analyses were performed. Compared with the old scenario, the estimated number, prevalence and incidence of future HCC cases in the new scenario would peak earlier and at lower levels in 2025 (~29 000), 2023 (~28/100 000) and 2022 (~14/100 000), respectively. The new treatment programme is estimated to avert ~956 000 HCC cases between 2015 and 2050. By reducing cancer cases and shortening the peak epidemic period, the new programme should substantially diminish the HCC epidemic across Egypt. Our timeline forecast for Egypt's HCC epidemic, and evaluation of various disease and programme components, should be useful to other countries that are developing policies to address HCV-related liver cancer prevention.

Epidemic spreading on random surfer networks with infected avoidance strategy

NASA Astrophysics Data System (ADS)

Feng, Yun; Ding, Li; Huang, Yun-Han; Guan, Zhi-Hong

2016-12-01

In this paper, we study epidemic spreading on random surfer networks with infected avoidance (IA) strategy. In particular, we consider that susceptible individuals’ moving direction angles are affected by the current location information received from infected individuals through a directed information network. The model is mainly analyzed by discrete-time numerical simulations. The results indicate that the IA strategy can restrain epidemic spreading effectively. However, when long-distance jumps of individuals exist, the IA strategy’s effectiveness on restraining epidemic spreading is heavily reduced. Finally, it is found that the influence of the noises from information transferring process on epidemic spreading is indistinctive. Project supported in part by the National Natural Science Foundation of China (Grant Nos. 61403284, 61272114, 61673303, and 61672112) and the Marine Renewable Energy Special Fund Project of the State Oceanic Administration of China (Grant No. GHME2013JS01).

Individual-based approach to epidemic processes on arbitrary dynamic contact networks

NASA Astrophysics Data System (ADS)

Rocha, Luis E. C.; Masuda, Naoki

2016-08-01

The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We develop an individual-based approximation for the susceptible-infected-recovered epidemic model applicable to arbitrary dynamic networks. Our framework provides, at the individual-level, the probability flow over time associated with the infection dynamics. This computationally efficient framework discards the correlation between the states of different nodes, yet provides accurate results in approximating direct numerical simulations. It naturally captures the temporal heterogeneities and correlations of contact sequences, fundamental ingredients regulating the timing and size of an epidemic outbreak, and the number of secondary infections. The high accuracy of our approximation further allows us to detect the index individual of an epidemic outbreak in real-life network data.

Modeling vaccination in a heterogeneous metapopulation system

NASA Astrophysics Data System (ADS)

Lachiany, Menachem

2016-09-01

We present here a multicity SIS epidemic model with vaccination. The model describes the dynamics of heterogeneous metapopulations that contain imperfectly vaccinated individuals. The effect of vaccination on heterogeneous multicity models has not been previously studied. We show that under very generic conditions, the epidemic threshold does not depend on the diffusion coefficient of the vaccinated individuals, but it does depend on the diffusion coefficient of the infected population. We then show, using a novel methodology, that the reproduction number is determined by the homogeneous model parameters and by the maximal number of neighbors a city can have, when the diffusion coefficient of the infected population is low. Finally, we present numerical simulations to support the analytical results.

Comparing large-scale computational approaches to epidemic modeling: agent-based versus structured metapopulation models.

PubMed

Ajelli, Marco; Gonçalves, Bruno; Balcan, Duygu; Colizza, Vittoria; Hu, Hao; Ramasco, José J; Merler, Stefano; Vespignani, Alessandro

2010-06-29

In recent years large-scale computational models for the realistic simulation of epidemic outbreaks have been used with increased frequency. Methodologies adapt to the scale of interest and range from very detailed agent-based models to spatially-structured metapopulation models. One major issue thus concerns to what extent the geotemporal spreading pattern found by different modeling approaches may differ and depend on the different approximations and assumptions used. We provide for the first time a side-by-side comparison of the results obtained with a stochastic agent-based model and a structured metapopulation stochastic model for the progression of a baseline pandemic event in Italy, a large and geographically heterogeneous European country. The agent-based model is based on the explicit representation of the Italian population through highly detailed data on the socio-demographic structure. The metapopulation simulations use the GLobal Epidemic and Mobility (GLEaM) model, based on high-resolution census data worldwide, and integrating airline travel flow data with short-range human mobility patterns at the global scale. The model also considers age structure data for Italy. GLEaM and the agent-based models are synchronized in their initial conditions by using the same disease parameterization, and by defining the same importation of infected cases from international travels. The results obtained show that both models provide epidemic patterns that are in very good agreement at the granularity levels accessible by both approaches, with differences in peak timing on the order of a few days. The relative difference of the epidemic size depends on the basic reproductive ratio, R0, and on the fact that the metapopulation model consistently yields a larger incidence than the agent-based model, as expected due to the differences in the structure in the intra-population contact pattern of the approaches. The age breakdown analysis shows that similar attack rates are obtained for the younger age classes. The good agreement between the two modeling approaches is very important for defining the tradeoff between data availability and the information provided by the models. The results we present define the possibility of hybrid models combining the agent-based and the metapopulation approaches according to the available data and computational resources.

Spread of epidemic disease on networks

NASA Astrophysics Data System (ADS)

Newman, M. E.

2002-07-01

The study of social networks, and in particular the spread of disease on networks, has attracted considerable recent attention in the physics community. In this paper, we show that a large class of standard epidemiological models, the so-called susceptible/infective/removed (SIR) models can be solved exactly on a wide variety of networks. In addition to the standard but unrealistic case of fixed infectiveness time and fixed and uncorrelated probability of transmission between all pairs of individuals, we solve cases in which times and probabilities are nonuniform and correlated. We also consider one simple case of an epidemic in a structured population, that of a sexually transmitted disease in a population divided into men and women. We confirm the correctness of our exact solutions with numerical simulations of SIR epidemics on networks.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks.

PubMed

Jenness, Samuel M; Goodreau, Steven M; Morris, Martina

2018-04-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel , designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel , designed to facilitate the exploration of novel research questions for advanced modelers.

EpiModel: An R Package for Mathematical Modeling of Infectious Disease over Networks

PubMed Central

Jenness, Samuel M.; Goodreau, Steven M.; Morris, Martina

2018-01-01

Package EpiModel provides tools for building, simulating, and analyzing mathematical models for the population dynamics of infectious disease transmission in R. Several classes of models are included, but the unique contribution of this software package is a general stochastic framework for modeling the spread of epidemics on networks. EpiModel integrates recent advances in statistical methods for network analysis (temporal exponential random graph models) that allow the epidemic modeling to be grounded in empirical data on contacts that can spread infection. This article provides an overview of both the modeling tools built into EpiModel, designed to facilitate learning for students new to modeling, and the application programming interface for extending package EpiModel, designed to facilitate the exploration of novel research questions for advanced modelers. PMID:29731699

Epidemiological modelling for the assessment of bovine tuberculosis surveillance in the dairy farm network in Emilia-Romagna (Italy).

PubMed

Rossi, Gianluigi; De Leo, Giulio A; Pongolini, Stefano; Natalini, Silvano; Vincenzi, Simone; Bolzoni, Luca

2015-06-01

Assessing the performance of a surveillance system for infectious diseases of domestic animals is a challenging task for health authorities. Therefore, it is important to assess what strategy is the most effective in identifying the onset of an epidemic and in minimizing the number of infected farms. The aim of the present work was to evaluate the performance of the bovine tuberculosis (bTB) surveillance system in the network of dairy farms in the Emilia-Romagna (ER) Region, Italy. A bTB-free Region since 2007, ER implements an integrated surveillance strategy based on three components, namely routine on-farm tuberculin skin-testing performed every 3 years, tuberculin skin-testing of cattle exchanged between farms, and post-mortem inspection at slaughterhouses. We assessed the effectiveness of surveillance by means of a stochastic network model of both within-farm and between-farm bTB dynamics calibrated on data available for ER dairy farms. Epidemic dynamics were simulated for five scenarios: the current ER surveillance system, a no surveillance scenario that we used as the benchmark to characterize epidemic dynamics, three additional scenarios in which one of the surveillance components was removed at a time so as to outline its significance in detecting the infection. For each scenario we ran Monte Carlo simulations of bTB epidemics following the random introduction of an infected individual in the network. System performances were assessed through the comparative analysis of a number of statistics, including the time required for epidemic detection and the total number of infected farms during the epidemic. Our analysis showed that slaughterhouse inspection is the most effective surveillance component in reducing the time for disease detection, while routine surveillance in reducing the number of multi-farms epidemics. On the other hand, testing exchanged cattle improved the performance of the surveillance system only marginally. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

Approximate Bayesian computation for spatial SEIR(S) epidemic models.

PubMed

Brown, Grant D; Porter, Aaron T; Oleson, Jacob J; Hinman, Jessica A

2018-02-01

Approximate Bayesia n Computation (ABC) provides an attractive approach to estimation in complex Bayesian inferential problems for which evaluation of the kernel of the posterior distribution is impossible or computationally expensive. These highly parallelizable techniques have been successfully applied to many fields, particularly in cases where more traditional approaches such as Markov chain Monte Carlo (MCMC) are impractical. In this work, we demonstrate the application of approximate Bayesian inference to spatially heterogeneous Susceptible-Exposed-Infectious-Removed (SEIR) stochastic epidemic models. These models have a tractable posterior distribution, however MCMC techniques nevertheless become computationally infeasible for moderately sized problems. We discuss the practical implementation of these techniques via the open source ABSEIR package for R. The performance of ABC relative to traditional MCMC methods in a small problem is explored under simulation, as well as in the spatially heterogeneous context of the 2014 epidemic of Chikungunya in the Americas. Copyright © 2017 Elsevier Ltd. All rights reserved.

The Stochastic Multi-strain Dengue Model: Analysis of the Dynamics

NASA Astrophysics Data System (ADS)

Aguiar, Maíra; Stollenwerk, Nico; Kooi, Bob W.

2011-09-01

Dengue dynamics is well known to be particularly complex with large fluctuations of disease incidences. An epidemic multi-strain model motivated by dengue fever epidemiology shows deterministic chaos in wide parameter regions. The addition of seasonal forcing, mimicking the vectorial dynamics, and a low import of infected individuals, which is realistic in the dynamics of infectious diseases epidemics show complex dynamics and qualitatively a good agreement between empirical DHF monitoring data and the obtained model simulation. The addition of noise can explain the fluctuations observed in the empirical data and for large enough population size, the stochastic system can be well described by the deterministic skeleton.

Epidemic spreading and immunization strategy in multiplex networks

NASA Astrophysics Data System (ADS)

Alvarez Zuzek, Lucila G.; Buono, Camila; Braunstein, Lidia A.

2015-09-01

A more connected world has brought major consequences such as facilitate the spread of diseases all over the world to quickly become epidemics, reason why researchers are concentrated in modeling the propagation of epidemics and outbreaks in multilayer networks. In this networks all nodes interact in different layers with different type of links. However, in many scenarios such as in the society, a multiplex network framework is not completely suitable since not all individuals participate in all layers. In this paper, we use a partially overlapped, multiplex network where only a fraction of the individuals are shared by the layers. We develop a mitigation strategy for stopping a disease propagation, considering the Susceptible-Infected- Recover model, in a system consisted by two layers. We consider a random immunization in one of the layers and study the effect of the overlapping fraction in both, the propagation of the disease and the immunization strategy. Using branching theory, we study this scenario theoretically and via simulations and find a lower epidemic threshold than in the case without strategy.

Long-range epidemic spreading in a random environment.

PubMed

Juhász, Róbert; Kovács, István A; Iglói, Ferenc

2015-03-01

Modeling long-range epidemic spreading in a random environment, we consider a quenched, disordered, d-dimensional contact process with infection rates decaying with distance as 1/rd+σ. We study the dynamical behavior of the model at and below the epidemic threshold by a variant of the strong-disorder renormalization-group method and by Monte Carlo simulations in one and two spatial dimensions. Starting from a single infected site, the average survival probability is found to decay as P(t)∼t-d/z up to multiplicative logarithmic corrections. Below the epidemic threshold, a Griffiths phase emerges, where the dynamical exponent z varies continuously with the control parameter and tends to zc=d+σ as the threshold is approached. At the threshold, the spatial extension of the infected cluster (in surviving trials) is found to grow as R(t)∼t1/zc with a multiplicative logarithmic correction and the average number of infected sites in surviving trials is found to increase as Ns(t)∼(lnt)χ with χ=2 in one dimension.

An object simulation model for modeling hypothetical disease epidemics – EpiFlex

PubMed Central

Hanley, Brian

2006-01-01

Background EpiFlex is a flexible, easy to use computer model for a single computer, intended to be operated by one user who need not be an expert. Its purpose is to study in-silico the epidemic behavior of a wide variety of diseases, both known and theoretical, by simulating their spread at the level of individuals contracting and infecting others. To understand the system fully, this paper must be read together in conjunction with study of the software and its results. EpiFlex is evaluated using results from modeling influenza A epidemics and comparing them with a variety of field data sources and other types of modeling. EpiFlex is an object-oriented Monte Carlo system, allocating entities to correspond to individuals, disease vectors, diseases, and the locations that hosts may inhabit. EpiFlex defines eight different contact types available for a disease. Contacts occur inside locations within the model. Populations are composed of demographic groups, each of which has a cycle of movement between locations. Within locations, superspreading is defined by skewing of contact distributions. Results EpiFlex indicates three phenomena of interest for public health: (1) R0 is variable, and the smaller the population, the larger the infected fraction within that population will be; (2) significant compression/synchronization between cities by a factor of roughly 2 occurs between the early incubation phase of a multi-city epidemic and the major manifestation phase; (3) if better true morbidity data were available, more asymptomatic hosts would be seen to spread disease than we currently believe is the case for influenza. These results suggest that field research to study such phenomena, while expensive, should be worthwhile. Conclusion Since EpiFlex shows all stages of disease progression, detailed insight into the progress of epidemics is possible. EpiFlex shows the characteristic multimodality and apparently random variation characteristic of real world data, but does so as an emergent property of a carefully constructed model of disease dynamics and is not simply a stochastic system. EpiFlex can provide a better understanding of infectious diseases and strategies for response. PMID:16928271

Dimensionality reduction in epidemic spreading models

NASA Astrophysics Data System (ADS)

Frasca, M.; Rizzo, A.; Gallo, L.; Fortuna, L.; Porfiri, M.

2015-09-01

Complex dynamical systems often exhibit collective dynamics that are well described by a reduced set of key variables in a low-dimensional space. Such a low-dimensional description offers a privileged perspective to understand the system behavior across temporal and spatial scales. In this work, we propose a data-driven approach to establish low-dimensional representations of large epidemic datasets by using a dimensionality reduction algorithm based on isometric features mapping (ISOMAP). We demonstrate our approach on synthetic data for epidemic spreading in a population of mobile individuals. We find that ISOMAP is successful in embedding high-dimensional data into a low-dimensional manifold, whose topological features are associated with the epidemic outbreak. Across a range of simulation parameters and model instances, we observe that epidemic outbreaks are embedded into a family of closed curves in a three-dimensional space, in which neighboring points pertain to instants that are close in time. The orientation of each curve is unique to a specific outbreak, and the coordinates correlate with the number of infected individuals. A low-dimensional description of epidemic spreading is expected to improve our understanding of the role of individual response on the outbreak dynamics, inform the selection of meaningful global observables, and, possibly, aid in the design of control and quarantine procedures.

The Role of Node Heterogeneity in the Coupled Spreading of Epidemics and Awareness.

PubMed

Guo, Quantong; Lei, Yanjun; Xia, Chengyi; Guo, Lu; Jiang, Xin; Zheng, Zhiming

2016-01-01

Exploring the interplay between information spreading and epidemic spreading is a topic that has been receiving increasing attention. As an efficient means of depicting the spreading of information, which manifests as a cascade phenomenon, awareness cascading is utilized to investigate this coupled transmission. Because in reality, different individuals facing the same epidemic will exhibit distinct behaviors according to their own experiences and attributes, it is important for us to consider the heterogeneity of individuals. Consequently, we propose a heterogeneous spreading model. To describe the heterogeneity, two of the most important but radically different methods for this purpose, the degree and k-core measures, are studied in this paper through three models based on different assumptions. Adopting a Markov chain approach, we succeed in predicting the epidemic threshold trend. Furthermore, we find that when the k-core measure is used to classify individuals, the spreading process is robust to these models, meaning that regardless of the model used, the spreading process is nearly identical at the macroscopic level. In addition, the k-core measure leads to a much larger final epidemic size than the degree measure. These results are cross-checked through numerous simulations, not only of a synthetic network but also of a real multiplex network. The presented findings provide a better understanding of k-core individuals and reveal the importance of considering network structure when investigating various dynamic processes.

The Role of Node Heterogeneity in the Coupled Spreading of Epidemics and Awareness

PubMed Central

2016-01-01

Exploring the interplay between information spreading and epidemic spreading is a topic that has been receiving increasing attention. As an efficient means of depicting the spreading of information, which manifests as a cascade phenomenon, awareness cascading is utilized to investigate this coupled transmission. Because in reality, different individuals facing the same epidemic will exhibit distinct behaviors according to their own experiences and attributes, it is important for us to consider the heterogeneity of individuals. Consequently, we propose a heterogeneous spreading model. To describe the heterogeneity, two of the most important but radically different methods for this purpose, the degree and k-core measures, are studied in this paper through three models based on different assumptions. Adopting a Markov chain approach, we succeed in predicting the epidemic threshold trend. Furthermore, we find that when the k-core measure is used to classify individuals, the spreading process is robust to these models, meaning that regardless of the model used, the spreading process is nearly identical at the macroscopic level. In addition, the k-core measure leads to a much larger final epidemic size than the degree measure. These results are cross-checked through numerous simulations, not only of a synthetic network but also of a real multiplex network. The presented findings provide a better understanding of k-core individuals and reveal the importance of considering network structure when investigating various dynamic processes. PMID:27517715

Modeling the 2014 Ebola Virus Epidemic - Agent-Based Simulations, Temporal Analysis and Future Predictions for Liberia and Sierra Leone.

PubMed

Siettos, Constantinos; Anastassopoulou, Cleo; Russo, Lucia; Grigoras, Christos; Mylonakis, Eleftherios

2015-03-09

We developed an agent-based model to investigate the epidemic dynamics of Ebola virus disease (EVD) in Liberia and Sierra Leone from May 27 to December 21, 2014. The dynamics of the agent-based simulator evolve on small-world transmission networks of sizes equal to the population of each country, with adjustable densities to account for the effects of public health intervention policies and individual behavioral responses to the evolving epidemic. Based on time series of the official case counts from the World Health Organization (WHO), we provide estimates for key epidemiological variables by employing the so-called Equation-Free approach. The underlying transmission networks were characterized by rather random structures in the two countries with densities decreasing by ~19% from the early (May 27-early August) to the last period (mid October-December 21). Our estimates for the values of key epidemiological variables, such as the mean time to death, recovery and the case fatality rate, are very close to the ones reported by the WHO Ebola response team during the early period of the epidemic (until September 14) that were calculated based on clinical data. Specifically, regarding the effective reproductive number Re, our analysis suggests that until mid October, Re was above 2.3 in both countries; from mid October to December 21, Re dropped well below unity in Liberia, indicating a saturation of the epidemic, while in Sierra Leone it was around 1.9, indicating an ongoing epidemic. Accordingly, a ten-week projection from December 21 estimated that the epidemic will fade out in Liberia in early March; in contrast, our results flashed a note of caution for Sierra Leone since the cumulative number of cases could reach as high as 18,000, and the number of deaths might exceed 5,000, by early March 2015. However, by processing the reported data of the very last period (December 21, 2014-January 18, 2015), we obtained more optimistic estimates indicative of a remission of the epidemic in Sierra Leone, as reflected by the derived Re (~0.82, 95% CI: 0.81-0.83).

Phylogenetic Tools for Generalized HIV-1 Epidemics: Findings from the PANGEA-HIV Methods Comparison

PubMed Central

Ratmann, Oliver; Hodcroft, Emma B.; Pickles, Michael; Cori, Anne; Hall, Matthew; Lycett, Samantha; Colijn, Caroline; Dearlove, Bethany; Didelot, Xavier; Frost, Simon; Hossain, A.S. Md Mukarram; Joy, Jeffrey B.; Kendall, Michelle; Kühnert, Denise; Leventhal, Gabriel E.; Liang, Richard; Plazzotta, Giacomo; Poon, Art F.Y.; Rasmussen, David A.; Stadler, Tanja; Volz, Erik; Weis, Caroline; Leigh Brown, Andrew J.; Fraser, Christophe

2017-01-01

Viral phylogenetic methods contribute to understanding how HIV spreads in populations, and thereby help guide the design of prevention interventions. So far, most analyses have been applied to well-sampled concentrated HIV-1 epidemics in wealthy countries. To direct the use of phylogenetic tools to where the impact of HIV-1 is greatest, the Phylogenetics And Networks for Generalized HIV Epidemics in Africa (PANGEA-HIV) consortium generates full-genome viral sequences from across sub-Saharan Africa. Analyzing these data presents new challenges, since epidemics are principally driven by heterosexual transmission and a smaller fraction of cases is sampled. Here, we show that viral phylogenetic tools can be adapted and used to estimate epidemiological quantities of central importance to HIV-1 prevention in sub-Saharan Africa. We used a community-wide methods comparison exercise on simulated data, where participants were blinded to the true dynamics they were inferring. Two distinct simulations captured generalized HIV-1 epidemics, before and after a large community-level intervention that reduced infection levels. Five research groups participated. Structured coalescent modeling approaches were most successful: phylogenetic estimates of HIV-1 incidence, incidence reductions, and the proportion of transmissions from individuals in their first 3 months of infection correlated with the true values (Pearson correlation > 90%), with small bias. However, on some simulations, true values were markedly outside reported confidence or credibility intervals. The blinded comparison revealed current limits and strengths in using HIV phylogenetics in challenging settings, provided benchmarks for future methods’ development, and supports using the latest generation of phylogenetic tools to advance HIV surveillance and prevention. PMID:28053012

Meteorologically Driven Simulations of Dengue Epidemics in San Juan, PR

PubMed Central

Morin, Cory W.; Monaghan, Andrew J.; Hayden, Mary H.; Barrera, Roberto; Ernst, Kacey

2015-01-01

Meteorological factors influence dengue virus ecology by modulating vector mosquito population dynamics, viral replication, and transmission. Dynamic modeling techniques can be used to examine how interactions among meteorological variables, vectors and the dengue virus influence transmission. We developed a dengue fever simulation model by coupling a dynamic simulation model for Aedes aegypti, the primary mosquito vector for dengue, with a basic epidemiological Susceptible-Exposed-Infectious-Recovered (SEIR) model. Employing a Monte Carlo approach, we simulated dengue transmission during the period of 2010–2013 in San Juan, PR, where dengue fever is endemic. The results of 9600 simulations using varied model parameters were evaluated by statistical comparison (r2) with surveillance data of dengue cases reported to the Centers for Disease Control and Prevention. To identify the most influential parameters associated with dengue virus transmission for each period the top 1% of best-fit model simulations were retained and compared. Using the top simulations, dengue cases were simulated well for 2010 (r2 = 0.90, p = 0.03), 2011 (r2 = 0.83, p = 0.05), and 2012 (r2 = 0.94, p = 0.01); however, simulations were weaker for 2013 (r2 = 0.25, p = 0.25) and the entire four-year period (r2 = 0.44, p = 0.002). Analysis of parameter values from retained simulations revealed that rain dependent container habitats were more prevalent in best-fitting simulations during the wetter 2010 and 2011 years, while human managed (i.e. manually filled) container habitats were more prevalent in best-fitting simulations during the drier 2012 and 2013 years. The simulations further indicate that rainfall strongly modulates the timing of dengue (e.g., epidemics occurred earlier during rainy years) while temperature modulates the annual number of dengue fever cases. Our results suggest that meteorological factors have a time-variable influence on dengue transmission relative to other important environmental and human factors. PMID:26275146

Sudden spreading of infections in an epidemic model with a finite seed fraction

NASA Astrophysics Data System (ADS)

Hasegawa, Takehisa; Nemoto, Koji

2018-03-01

We study a simple case of the susceptible-weakened-infected-removed model in regular random graphs in a situation where an epidemic starts from a finite fraction of initially infected nodes (seeds). Previous studies have shown that, assuming a single seed, this model exhibits a kind of discontinuous transition at a certain value of infection rate. Performing Monte Carlo simulations and evaluating approximate master equations, we find that the present model has two critical infection rates for the case with a finite seed fraction. At the first critical rate the system shows a percolation transition of clusters composed of removed nodes, and at the second critical rate, which is larger than the first one, a giant cluster suddenly grows and the order parameter jumps even though it has been already rising. Numerical evaluation of the master equations shows that such sudden epidemic spreading does occur if the degree of the underlying network is large and the seed fraction is small.

Dynamics of tax evasion through an epidemic-like model

NASA Astrophysics Data System (ADS)

Brum, Rafael M.; Crokidakis, Nuno

In this work, we study a model of tax evasion. We considered a fixed population divided in three compartments, namely honest tax payers, tax evaders and a third class between the mentioned two, which we call susceptibles to become evaders. The transitions among those compartments are ruled by probabilities, similarly to a model of epidemic spreading. These probabilities model social interactions among the individuals, as well as the government’s fiscalization. We simulate the model on fully-connected graphs, as well as on scale-free and random complex networks. For the fully-connected and random graph cases, we observe that the emergence of tax evaders in the population is associated with an active-absorbing nonequilibrium phase transition, that is absent in scale-free networks.

Impact of preventive responses to epidemics in rural regions.

PubMed

Schumm, Phillip; Schumm, Walter; Scoglio, Caterina

2013-01-01

Various epidemics have arisen in rural locations through human-animal interaction, such as the H1N1 outbreak of 2009. Through collaboration with local government officials, we have surveyed a rural county and its communities and collected a dataset characterizing the rural population. From the respondents' answers, we build a social (face-to-face) contact network. With this network, we explore the potential spread of epidemics through a Susceptible-Latent-Infected-Recovered (SLIR) disease model. We simulate an exact model of a stochastic SLIR Poisson process with disease parameters representing a typical influenza-like illness. We test vaccine distribution strategies under limited resources. We examine global and location-based distribution strategies, as a way to reach critical individuals in the rural setting. We demonstrate that locations can be identified through contact metrics for use in vaccination strategies to control contagious diseases.

Effects of behavioral changes in a smallpox attack model.

PubMed

Del Valle, S; Hethcote, H; Hyman, J M; Castillo-Chavez, C

2005-06-01

The impact of individual and community behavioral changes in response to an outbreak of a disease with high mortality is often not appreciated. Response strategies to a smallpox bioterrorist attack have focused on interventions such as isolation of infectives, contact tracing, quarantine of contacts, ring vaccination, and mass vaccination. We formulate and analyze a mathematical model in which some individuals lower their daily contact activity rates once an epidemic has been identified in a community. Transmission parameters are estimated from data and an expression is derived for the effective reproduction number. We use computer simulations to analyze the effects of behavior change alone and in combination with other control measures. We demonstrate that the spread of the disease is highly sensitive to how rapidly people reduce their contact activity rates and to the precautions that the population takes to reduce the transmission of the disease. Even gradual and mild behavioral changes can have a dramatic impact in slowing an epidemic. When behavioral changes are combined with other interventions, the epidemic is shortened and the number of smallpox cases is reduced. We conclude that for simulations of a smallpox outbreak to be useful, they must consider the impact of behavioral changes. This is especially true if the model predictions are being used to guide public health policy.

Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics.

PubMed

Zhang, Liping; Wang, Li; Zheng, Yanling; Wang, Kai; Zhang, Xueliang; Zheng, Yujian

2017-03-04

Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1) model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1)), and the Modified Grey Model using Fourier Series (FGM(1,1)), in addition to a multiplicative seasonal ARIMA(1,0,1)(1,1,0)₄ model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1) model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends.

Multiscale mobility networks and the spatial spreading of infectious diseases.

PubMed

Balcan, Duygu; Colizza, Vittoria; Gonçalves, Bruno; Hu, Hao; Ramasco, José J; Vespignani, Alessandro

2009-12-22

Among the realistic ingredients to be considered in the computational modeling of infectious diseases, human mobility represents a crucial challenge both on the theoretical side and in view of the limited availability of empirical data. To study the interplay between short-scale commuting flows and long-range airline traffic in shaping the spatiotemporal pattern of a global epidemic we (i) analyze mobility data from 29 countries around the world and find a gravity model able to provide a global description of commuting patterns up to 300 kms and (ii) integrate in a worldwide-structured metapopulation epidemic model a timescale-separation technique for evaluating the force of infection due to multiscale mobility processes in the disease dynamics. Commuting flows are found, on average, to be one order of magnitude larger than airline flows. However, their introduction into the worldwide model shows that the large-scale pattern of the simulated epidemic exhibits only small variations with respect to the baseline case where only airline traffic is considered. The presence of short-range mobility increases, however, the synchronization of subpopulations in close proximity and affects the epidemic behavior at the periphery of the airline transportation infrastructure. The present approach outlines the possibility for the definition of layered computational approaches where different modeling assumptions and granularities can be used consistently in a unifying multiscale framework.

GENERAL: Epidemic spreading on networks with vaccination

NASA Astrophysics Data System (ADS)

Shi, Hong-Jing; Duan, Zhi-Sheng; Chen, Guan-Rong; Li, Rong

2009-08-01

In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.

Human mobility in an emerging epidemic: a key aspect for response planning

NASA Astrophysics Data System (ADS)

Poletto, Chiara; Bajardi, Paolo; Colizza, Vittoria; Ramasco, Jose J.; Tizzoni, Michele; Vespignani, Alessandro

2010-03-01

Human mobility and interactions represent key ingredients in the spreading dynamics of an infectious disease. The flows of traveling people form a network characterized by complex features, such as strong topological and traffic heterogeneities, that unfolds at different temporal and spatial scales, from short ranges to the global scale. Computational models can be developed that integrate detailed network structures based on demographic and mobility data, in order to simulate the spatial evolution of an epidemic. Focusing on the recent A(H1N1) influenza pandemic as a paradigmatic example, these approaches allow the assessment of the interplay between individual mobility and epidemic dynamics, quantifying the effects of travel restrictions in delaying the epidemic spread and the role of mobility as an additional source of information for the understanding of the early outbreak.

Worm epidemics in wireless ad hoc networks

NASA Astrophysics Data System (ADS)

Nekovee, Maziar

2007-06-01

A dramatic increase in the number of computing devices with wireless communication capability has resulted in the emergence of a new class of computer worms which specifically target such devices. The most striking feature of these worms is that they do not require Internet connectivity for their propagation but can spread directly from device to device using a short-range radio communication technology, such as WiFi or Bluetooth. In this paper, we develop a new model for epidemic spreading of these worms and investigate their spreading in wireless ad hoc networks via extensive Monte Carlo simulations. Our studies show that the threshold behaviour and dynamics of worm epidemics in these networks are greatly affected by a combination of spatial and temporal correlations which characterize these networks, and are significantly different from the previously studied epidemics in the Internet.

Modeling the Effects of Duration and Size of the Control Zones on the Consequences of a Hypothetical African Swine Fever Epidemic in Denmark

PubMed Central

Halasa, Tariq; Bøtner, Anette; Mortensen, Sten; Christensen, Hanne; Wulff, Sisse Birk; Boklund, Anette

2018-01-01

African swine fever (ASF) is a notifiable infectious disease. The disease is endemic in certain regions in Eastern Europe constituting a risk of ASF spread toward Western Europe. Therefore, as part of contingency planning, it is important to continuously explore strategies that can effectively control an epidemic of ASF. A previously published and well documented simulation model for ASF virus spread between herds was used to examine the epidemiologic and economic impacts of the duration and size of the control zones around affected herds. In the current study, scenarios were run, where the duration of the protection and surveillance zones were reduced from 50 and 45 days to 35 and 25 days or to 35 and 25 days, respectively. These scenarios were run with or without enlargement of the surveillance zone around detected herds from 10 to 15 km. The scenarios were also run with only clinical or clinical and serological surveillance of herds within the zones. Sensitivity analysis was conducted on influential input parameters in the model. The model predicts that reducing the duration of the protection and surveillance zones has no impact on the epidemiological consequences of the epidemics, while it may result in a substantial reduction in the total economic losses. In addition, the model predicts that increasing the size of the surveillance zone from 10 to 15 km may reduce both the epidemic duration and the total economic losses, in case of large epidemics. The ranking of the control strategies by the total costs of the epidemics was not influenced by changes of input parameters in the sensitivity analyses. PMID:29616228

Extinction times of epidemic outbreaks in networks.

PubMed

Holme, Petter

2013-01-01

In the Susceptible-Infectious-Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold.

Rapid simulation of spatial epidemics: a spectral method.

PubMed

Brand, Samuel P C; Tildesley, Michael J; Keeling, Matthew J

2015-04-07

Spatial structure and hence the spatial position of host populations plays a vital role in the spread of infection. In the majority of situations, it is only possible to predict the spatial spread of infection using simulation models, which can be computationally demanding especially for large population sizes. Here we develop an approximation method that vastly reduces this computational burden. We assume that the transmission rates between individuals or sub-populations are determined by a spatial transmission kernel. This kernel is assumed to be isotropic, such that the transmission rate is simply a function of the distance between susceptible and infectious individuals; as such this provides the ideal mechanism for modelling localised transmission in a spatial environment. We show that the spatial force of infection acting on all susceptibles can be represented as a spatial convolution between the transmission kernel and a spatially extended 'image' of the infection state. This representation allows the rapid calculation of stochastic rates of infection using fast-Fourier transform (FFT) routines, which greatly improves the computational efficiency of spatial simulations. We demonstrate the efficiency and accuracy of this fast spectral rate recalculation (FSR) method with two examples: an idealised scenario simulating an SIR-type epidemic outbreak amongst N habitats distributed across a two-dimensional plane; the spread of infection between US cattle farms, illustrating that the FSR method makes continental-scale outbreak forecasting feasible with desktop processing power. The latter model demonstrates which areas of the US are at consistently high risk for cattle-infections, although predictions of epidemic size are highly dependent on assumptions about the tail of the transmission kernel. Copyright © 2015 Elsevier Ltd. All rights reserved.

Constructing Rigorous and Broad Biosurveillance Networks for Detecting Emerging Zoonotic Outbreaks

PubMed Central

Brown, Mac; Moore, Leslie; McMahon, Benjamin; Powell, Dennis; LaBute, Montiago; Hyman, James M.; Rivas, Ariel; Jankowski, Mark; Berendzen, Joel; Loeppky, Jason; Manore, Carrie; Fair, Jeanne

2015-01-01

Determining optimal surveillance networks for an emerging pathogen is difficult since it is not known beforehand what the characteristics of a pathogen will be or where it will emerge. The resources for surveillance of infectious diseases in animals and wildlife are often limited and mathematical modeling can play a supporting role in examining a wide range of scenarios of pathogen spread. We demonstrate how a hierarchy of mathematical and statistical tools can be used in surveillance planning help guide successful surveillance and mitigation policies for a wide range of zoonotic pathogens. The model forecasts can help clarify the complexities of potential scenarios, and optimize biosurveillance programs for rapidly detecting infectious diseases. Using the highly pathogenic zoonotic H5N1 avian influenza 2006-2007 epidemic in Nigeria as an example, we determined the risk for infection for localized areas in an outbreak and designed biosurveillance stations that are effective for different pathogen strains and a range of possible outbreak locations. We created a general multi-scale, multi-host stochastic SEIR epidemiological network model, with both short and long-range movement, to simulate the spread of an infectious disease through Nigerian human, poultry, backyard duck, and wild bird populations. We chose parameter ranges specific to avian influenza (but not to a particular strain) and used a Latin hypercube sample experimental design to investigate epidemic predictions in a thousand simulations. We ranked the risk of local regions by the number of times they became infected in the ensemble of simulations. These spatial statistics were then complied into a potential risk map of infection. Finally, we validated the results with a known outbreak, using spatial analysis of all the simulation runs to show the progression matched closely with the observed location of the farms infected in the 2006-2007 epidemic. PMID:25946164

Disease spread across multiple scales in a spatial hierarchy: effect of host spatial structure and of inoculum quantity and distribution.

PubMed

Gosme, Marie; Lucas, Philippe

2009-07-01

Spatial patterns of both the host and the disease influence disease spread and crop losses. Therefore, the manipulation of these patterns might help improve control strategies. Considering disease spread across multiple scales in a spatial hierarchy allows one to capture important features of epidemics developing in space without using explicitly spatialized variables. Thus, if the system under study is composed of roots, plants, and planting hills, the effect of host spatial pattern can be studied by varying the number of plants per planting hill. A simulation model based on hierarchy theory was used to simulate the effects of large versus small planting hills, low versus high level of initial infections, and aggregated versus uniform distribution of initial infections. The results showed that aggregating the initially infected plants always resulted in slower epidemics than spreading out the initial infections uniformly. Simulation results also showed that, in most cases, disease epidemics were slower in the case of large host aggregates (100 plants/hill) than with smaller aggregates (25 plants/hill), except when the initially infected plants were both numerous and spread out uniformly. The optimal strategy for disease control depends on several factors, including initial conditions. More importantly, the model offers a framework to account for the interplay between the spatial characteristics of the system, rates of infection, and aggregation of the disease.

Coupling effects on turning points of infectious diseases epidemics in scale-free networks.

PubMed

Kim, Kiseong; Lee, Sangyeon; Lee, Doheon; Lee, Kwang Hyung

2017-05-31

Pandemic is a typical spreading phenomenon that can be observed in the human society and is dependent on the structure of the social network. The Susceptible-Infective-Recovered (SIR) model describes spreading phenomena using two spreading factors; contagiousness (β) and recovery rate (γ). Some network models are trying to reflect the social network, but the real structure is difficult to uncover. We have developed a spreading phenomenon simulator that can input the epidemic parameters and network parameters and performed the experiment of disease propagation. The simulation result was analyzed to construct a new marker VRTP distribution. We also induced the VRTP formula for three of the network mathematical models. We suggest new marker VRTP (value of recovered on turning point) to describe the coupling between the SIR spreading and the Scale-free (SF) network and observe the aspects of the coupling effects with the various of spreading and network parameters. We also derive the analytic formulation of VRTP in the fully mixed model, the configuration model, and the degree-based model respectively in the mathematical function form for the insights on the relationship between experimental simulation and theoretical consideration. We discover the coupling effect between SIR spreading and SF network through devising novel marker VRTP which reflects the shifting effect and relates to entropy.

Bayesian non-parametric inference for stochastic epidemic models using Gaussian Processes.

PubMed

Xu, Xiaoguang; Kypraios, Theodore; O'Neill, Philip D

2016-10-01

This paper considers novel Bayesian non-parametric methods for stochastic epidemic models. Many standard modeling and data analysis methods use underlying assumptions (e.g. concerning the rate at which new cases of disease will occur) which are rarely challenged or tested in practice. To relax these assumptions, we develop a Bayesian non-parametric approach using Gaussian Processes, specifically to estimate the infection process. The methods are illustrated with both simulated and real data sets, the former illustrating that the methods can recover the true infection process quite well in practice, and the latter illustrating that the methods can be successfully applied in different settings. © The Author 2016. Published by Oxford University Press.

Monte Carlo simulation of the transmission of measles: Beyond the mass action principle

NASA Astrophysics Data System (ADS)

Zekri, Nouredine; Clerc, Jean Pierre

2002-04-01

We present a Monte Carlo simulation of the transmission of measles within a population sample during its growing and equilibrium states by introducing two different vaccination schedules of one and two doses. We study the effects of the contact rate per unit time ξ as well as the initial conditions on the persistence of the disease. We found a weak effect of the initial conditions while the disease persists when ξ lies in the range 1/L-10/L (L being the latent period). Further comparison with existing data, prediction of future epidemics and other estimations of the vaccination efficiency are provided. Finally, we compare our approach to the models using the mass action principle in the first and another epidemic region and found the incidence independent of the number of susceptibles after the epidemic peak while it strongly fluctuates in its growing region. This method can be easily applied to other human, animal, and plant diseases and includes more complicated parameters.

Huntington II Simulation Program - MALAR. Student Workbook, Teacher's Guide, and Resource Handbook.

ERIC Educational Resources Information Center

Friedland, James; Frishman, Austin

Described is the computer model "MALAR" which deals with malaria and its eradication. A computer program allows the tenth- to twelfth-grade student to attempt to control a malaria epidemic. This simulation provides a context within which to study the biological, economic, social, political, and ecological aspects of a classic world health problem.…

On case-fatality rate: review and hypothesis.

PubMed

Yoshikura, Hiroshi

2012-07-01

The relationship between log cumulative number of patients (X) and that of deaths (Y) in an epidemic follows the equation logY = klogX - klogN(0), where k is a constant determining the slope and N(0) is the value of X when Y = 1. Diseases with k = 1 are Ebola hemorrhagic fever, avian influenza H5N1, cholera, and hand, foot, and mouth disease; those with k > 1 are the influenza H1N1 2009 pandemic in countries other than Mexico and the SARS epidemic in some countries; and those with k < 1 include the influenza H1N1 2009 pandemic in Mexico. Epidemics with k > 1 can be simulated by postulating two subpopulations (normal population [NP] and vulnerable population [VP]), where the epidemic proceeds at higher speed and at higher mortality in VP than in NP. Epidemics with k < 1 can be simulated by postulating coexisting high virulence virus (HVV) and low virulence virus (LVV), with the former being propagated at slower speed and with a higher mortality rate than the latter. An epidemic with k > 1 was simulated using parameters that are fractions of subpopulations NP or VP from the total population (f) and NP- or VP-specific patient multiplication (M) and mortality (D) rates. An epidemic with k < 1 was simulated using parameters that are fractions of HVV- or LVV-infected human populations (f), and HVV- or LVV-specific M and D.

Protection motivation theory and social distancing behaviour in response to a simulated infectious disease epidemic.

PubMed

Williams, Lynn; Rasmussen, Susan; Kleczkowski, Adam; Maharaj, Savi; Cairns, Nicole

2015-01-01

Epidemics of respiratory infectious disease remain one of the most serious health risks facing the population. Non-pharmaceutical interventions (e.g. hand-washing or wearing face masks) can have a significant impact on the course of an infectious disease epidemic. The current study investigated whether protection motivation theory (PMT) is a useful framework for understanding social distancing behaviour (i.e. the tendency to reduce social contacts) in response to a simulated infectious disease epidemic. There were 230 participants (109 males, 121 females, mean age 32.4 years) from the general population who completed self-report measures assessing the components of PMT. In addition, participants completed a computer game which simulated an infectious disease epidemic in order to provide a measure of social distancing behaviour. The regression analyses revealed that none of the PMT variables were significant predictors of social distancing behaviour during the simulation task. However, fear (β = .218, p < .001), response efficacy (β = .175, p < .01) and self-efficacy (β = .251, p < .001) were all significant predictors of intention to engage in social distancing behaviour. Overall, the PMT variables (and demographic factors) explain 21.2% of the variance in intention. The findings demonstrated that PMT was a useful framework for understanding intention to engage in social distancing behaviour, but not actual behaviour during the simulated epidemic. These findings may reflect an intention-behaviour gap in relation to social distancing behaviour.

Global stability analysis of two-strain epidemic model with bilinear and non-monotone incidence rates

NASA Astrophysics Data System (ADS)

Baba, Isa Abdullahi; Hincal, Evren

2017-05-01

In this article we studied an epidemic model consisting of two strains with different types of incidence rates; bilinear and non-monotone. The model consists of four equilibrium points: disease-free equilibrium, endemic with respect to strain 1, endemic with respect to strain 2, and endemic with respect to both strains. The global stability analysis of the equilibrium points was carried out through the use of Lyapunov functions. Two basic reproduction ratios R 1 0 and R 2 0 are found, and we have shown that if both are less than one, the disease dies out, and if both are greater than one epidemic occurs. Furthermore, epidemics occur with respect to any strain with a basic reproduction ratio greater than one and disease dies out with respect to any strain with a basic reproduction ratio less than one. It was also shown that any strain with highest basic reproduction ratio will automatically outperform the other strain, thereby eliminating it. Numerical simulations were carried out to support the analytic result and to show the effect of the parameter k in the non-monotone incidence rate, which describes the psychological effect of general public towards infection.

Discrete epidemic models with arbitrary stage distributions and applications to disease control.

PubMed

Hernandez-Ceron, Nancy; Feng, Zhilan; Castillo-Chavez, Carlos

2013-10-01

W.O. Kermack and A.G. McKendrick introduced in their fundamental paper, A Contribution to the Mathematical Theory of Epidemics, published in 1927, a deterministic model that captured the qualitative dynamic behavior of single infectious disease outbreaks. A Kermack–McKendrick discrete-time general framework, motivated by the emergence of a multitude of models used to forecast the dynamics of epidemics, is introduced in this manuscript. Results that allow us to measure quantitatively the role of classical and general distributions on disease dynamics are presented. The case of the geometric distribution is used to evaluate the impact of waiting-time distributions on epidemiological processes or public health interventions. In short, the geometric distribution is used to set up the baseline or null epidemiological model used to test the relevance of realistic stage-period distribution on the dynamics of single epidemic outbreaks. A final size relationship involving the control reproduction number, a function of transmission parameters and the means of distributions used to model disease or intervention control measures, is computed. Model results and simulations highlight the inconsistencies in forecasting that emerge from the use of specific parametric distributions. Examples, using the geometric, Poisson and binomial distributions, are used to highlight the impact of the choices made in quantifying the risk posed by single outbreaks and the relative importance of various control measures.

The opportunistic transmission of wireless worms between mobile devices

NASA Astrophysics Data System (ADS)

Rhodes, C. J.; Nekovee, M.

2008-12-01

The ubiquity of portable wireless-enabled computing and communications devices has stimulated the emergence of malicious codes (wireless worms) that are capable of spreading between spatially proximal devices. The potential exists for worms to be opportunistically transmitted between devices as they move around, so human mobility patterns will have an impact on epidemic spread. The scenario we address in this paper is proximity attacks from fleetingly in-contact wireless devices with short-range communication range, such as Bluetooth-enabled smart phones. An individual-based model of mobile devices is introduced and the effect of population characteristics and device behaviour on the outbreak dynamics is investigated. The model uses straight-line motion to achieve population, though it is recognised that this is a highly simplified representation of human mobility patterns. We show that the contact rate can be derived from the underlying mobility model and, through extensive simulation, that mass-action epidemic models remain applicable to worm spreading in the low density regime studied here. The model gives useful analytical expressions against which more refined simulations of worm spread can be developed and tested.

Epidemics and dimensionality in hierarchical networks

NASA Astrophysics Data System (ADS)

Zheng, Da-Fang; Hui, P. M.; Trimper, Steffen; Zheng, Bo

2005-07-01

Epidemiological processes are studied within a recently proposed hierarchical network model using the susceptible-infected-refractory dynamics of an epidemic. Within the network model, a population may be characterized by H independent hierarchies or dimensions, each of which consists of groupings of individuals into layers of subgroups. Detailed numerical simulations reveal that for H>1, global spreading results regardless of the degree of homophily of the individuals forming a social circle. For H=1, a transition from global to local spread occurs as the population becomes decomposed into increasingly homophilous groups. Multiple dimensions in classifying individuals (nodes) thus make a society (computer network) highly susceptible to large-scale outbreaks of infectious diseases (viruses).

The epidemic threshold theorem with social and contact heterogeneity

NASA Astrophysics Data System (ADS)

Hincapié Palacio, Doracelly; Ospina Giraldo, Juan; Gómez Arias, Rubén Darío

2008-03-01

The threshold theorem of an epidemic SIR model was compared when infectious and susceptible individuals have homogeneous mixing and heterogeneous social status and when individuals of random networks have contact heterogeneity. Particularly the effect of vaccination in such models is considered when: individuals or nodes are exposed to impoverished, vaccination and loss of immunity. An equilibrium analysis and local stability of small perturbations about the equilibrium values were implemented using computer algebra. Numerical simulations were executed in order to describe the dynamic of transmission of diseases and changes of the basic reproductive rate. The implications of these results are examined around the threats to the global public health security.

Multi-granularity immunization strategy based on SIRS model in scale-free network

NASA Astrophysics Data System (ADS)

Nian, Fuzhong; Wang, Ke

2015-04-01

In this paper, a new immunization strategy was established to prevent the epidemic spreading based on the principle of "Multi-granularity" and "Pre-warning Mechanism", which send different pre-warning signal with the risk rank of the susceptible node to be infected. The pre-warning means there is a higher risk that the susceptible node is more likely to be infected. The multi-granularity means the susceptible node is linked with multi-infected nodes. In our model, the effect of the different situation of the multi-granularity immunizations is compared and different spreading rates are adopted to describe the epidemic behavior of nodes. In addition the threshold value of epidemic outbreak is investigated, which makes the result more convincing. The theoretical analysis and the simulations indicate that the proposed immunization strategy is effective and it is also economic and feasible.

Phylogenetic Tools for Generalized HIV-1 Epidemics: Findings from the PANGEA-HIV Methods Comparison.

PubMed

Ratmann, Oliver; Hodcroft, Emma B; Pickles, Michael; Cori, Anne; Hall, Matthew; Lycett, Samantha; Colijn, Caroline; Dearlove, Bethany; Didelot, Xavier; Frost, Simon; Hossain, A S Md Mukarram; Joy, Jeffrey B; Kendall, Michelle; Kühnert, Denise; Leventhal, Gabriel E; Liang, Richard; Plazzotta, Giacomo; Poon, Art F Y; Rasmussen, David A; Stadler, Tanja; Volz, Erik; Weis, Caroline; Leigh Brown, Andrew J; Fraser, Christophe

2017-01-01

Viral phylogenetic methods contribute to understanding how HIV spreads in populations, and thereby help guide the design of prevention interventions. So far, most analyses have been applied to well-sampled concentrated HIV-1 epidemics in wealthy countries. To direct the use of phylogenetic tools to where the impact of HIV-1 is greatest, the Phylogenetics And Networks for Generalized HIV Epidemics in Africa (PANGEA-HIV) consortium generates full-genome viral sequences from across sub-Saharan Africa. Analyzing these data presents new challenges, since epidemics are principally driven by heterosexual transmission and a smaller fraction of cases is sampled. Here, we show that viral phylogenetic tools can be adapted and used to estimate epidemiological quantities of central importance to HIV-1 prevention in sub-Saharan Africa. We used a community-wide methods comparison exercise on simulated data, where participants were blinded to the true dynamics they were inferring. Two distinct simulations captured generalized HIV-1 epidemics, before and after a large community-level intervention that reduced infection levels. Five research groups participated. Structured coalescent modeling approaches were most successful: phylogenetic estimates of HIV-1 incidence, incidence reductions, and the proportion of transmissions from individuals in their first 3 months of infection correlated with the true values (Pearson correlation > 90%), with small bias. However, on some simulations, true values were markedly outside reported confidence or credibility intervals. The blinded comparison revealed current limits and strengths in using HIV phylogenetics in challenging settings, provided benchmarks for future methods' development, and supports using the latest generation of phylogenetic tools to advance HIV surveillance and prevention. © The Author 2016. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.

Parameterization of Keeling's network generation algorithm.

PubMed

Badham, Jennifer; Abbass, Hussein; Stocker, Rob

2008-09-01

Simulation is increasingly being used to examine epidemic behaviour and assess potential management options. The utility of the simulations rely on the ability to replicate those aspects of the social structure that are relevant to epidemic transmission. One approach is to generate networks with desired social properties. Recent research by Keeling and his colleagues has generated simulated networks with a range of properties, and examined the impact of these properties on epidemic processes occurring over the network. However, published work has included only limited analysis of the algorithm itself and the way in which the network properties are related to the algorithm parameters. This paper identifies some relationships between the algorithm parameters and selected network properties (mean degree, degree variation, clustering coefficient and assortativity). Our approach enables users of the algorithm to efficiently generate a network with given properties, thereby allowing realistic social networks to be used as the basis of epidemic simulations. Alternatively, the algorithm could be used to generate social networks with a range of property values, enabling analysis of the impact of these properties on epidemic behaviour.

Effect of chemotherapy on malaria transmission among Yanomami Amerindians: simulated consequences of placebo treatment.

PubMed

Freeman, J; Laserson, K F; Petralanda, I; Spielman, A

1999-05-01

To determine whether chemotherapy effectively reduces Plasmodium falciparum malaria transmission in isolated human populations, we followed two abrupt sequential outbreaks of malaria infection among Yanomami Amerindians and modeled the effect of chemotherapy and the consequences if no drug was available. A Macdonald-type mathematical model demonstrated that both outbreaks comprised a single epidemic event linked by an invisible outbreak in vector mosquitoes. The basic reproductive number, R0, from fitted values based on the treated epidemic was 2 during the initial phase of the epidemic, and waned as vector density decreased with the onset of the dry season. In the observed epidemic, 60 (45%) of 132 village residents were affected, and the treated outbreak ended after two months. Although the initial chemotherapy regimen was only marginally effective, the duration of human infectivity was reduced from an expected nine months to two weeks. In the absence of this intervention, the initial R0 value would have been 40, more than 60% of the population would have been infected, and more than 30% would have remained parasitemic until the next rainy season (about six months later). Another outbreak would then have ensued, and malaria probably would have remained endemic in this village. Our simulated placebo treatment permits us to conclude that even partially effective chemotherapeutic interventions, such as those in our study, interrupt serial transmission of P. falciparum among isolated human populations that are exposed to infection seasonally.

Critical behavior in a stochastic model of vector mediated epidemics

NASA Astrophysics Data System (ADS)

Alfinito, E.; Beccaria, M.; Macorini, G.

2016-06-01

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

Critical behavior in a stochastic model of vector mediated epidemics.

PubMed

Alfinito, E; Beccaria, M; Macorini, G

2016-06-06

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation.

Epidemic spreading in annealed directed networks: susceptible-infected-susceptible model and contact process.

PubMed

Kwon, Sungchul; Kim, Yup

2013-01-01

We investigate epidemic spreading in annealed directed scale-free networks with the in-degree (k) distribution P(in)(k)~k(-γ(in)) and the out-degree (ℓ) distribution, P(out)(ℓ)~ℓ(-γ(out)). The correlation of each node on the networks is controlled by the probability r(0≤r≤1) in two different algorithms, the so-called k and ℓ algorithms. For r=1, the k algorithm gives =, whereas the ℓ algorithm gives =<ℓ(2)>. For r=0, =<ℓ> for both algorithms. As the prototype of epidemic spreading, the susceptible-infected-susceptible model and contact process on the networks are analyzed using the heterogeneous mean-field theory and Monte Carlo simulations. The directedness of links and the correlation of the network are found to play important roles in the spreading, so that critical behaviors of both models are distinct from those on undirected scale-free networks.

Efficient Control of Epidemics Spreading on Networks: Balance between Treatment and Recovery

PubMed Central

Oleś, Katarzyna; Gudowska-Nowak, Ewa; Kleczkowski, Adam

2013-01-01

We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models. PMID:23750205

Efficient control of epidemics spreading on networks: balance between treatment and recovery.

PubMed

Oleś, Katarzyna; Gudowska-Nowak, Ewa; Kleczkowski, Adam

2013-01-01

We analyse two models describing disease transmission and control on regular and small-world networks. We use simulations to find a control strategy that minimizes the total cost of an outbreak, thus balancing the costs of disease against that of the preventive treatment. The models are similar in their epidemiological part, but differ in how the removed/recovered individuals are treated. The differences in models affect choice of the strategy only for very cheap treatment and slow spreading disease. However for the combinations of parameters that are important from the epidemiological perspective (high infectiousness and expensive treatment) the models give similar results. Moreover, even where the choice of the strategy is different, the total cost spent on controlling the epidemic is very similar for both models.

Disease Extinction Versus Persistence in Discrete-Time Epidemic Models.

PubMed

van den Driessche, P; Yakubu, Abdul-Aziz

2018-04-12

We focus on discrete-time infectious disease models in populations that are governed by constant, geometric, Beverton-Holt or Ricker demographic equations, and give a method for computing the basic reproduction number, [Formula: see text]. When [Formula: see text] and the demographic population dynamics are asymptotically constant or under geometric growth (non-oscillatory), we prove global asymptotic stability of the disease-free equilibrium of the disease models. Under the same demographic assumption, when [Formula: see text], we prove uniform persistence of the disease. We apply our theoretical results to specific discrete-time epidemic models that are formulated for SEIR infections, cholera in humans and anthrax in animals. Our simulations show that a unique endemic equilibrium of each of the three specific disease models is asymptotically stable whenever [Formula: see text].

Effective degree Markov-chain approach for discrete-time epidemic processes on uncorrelated networks.

PubMed

Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue

2014-11-01

Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011)PLEEE81539-375510.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011)JMBLAJ0303-681210.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.

Bayesian structured additive regression modeling of epidemic data: application to cholera

PubMed Central

2012-01-01

Background A significant interest in spatial epidemiology lies in identifying associated risk factors which enhances the risk of infection. Most studies, however, make no, or limited use of the spatial structure of the data, as well as possible nonlinear effects of the risk factors. Methods We develop a Bayesian Structured Additive Regression model for cholera epidemic data. Model estimation and inference is based on fully Bayesian approach via Markov Chain Monte Carlo (MCMC) simulations. The model is applied to cholera epidemic data in the Kumasi Metropolis, Ghana. Proximity to refuse dumps, density of refuse dumps, and proximity to potential cholera reservoirs were modeled as continuous functions; presence of slum settlers and population density were modeled as fixed effects, whereas spatial references to the communities were modeled as structured and unstructured spatial effects. Results We observe that the risk of cholera is associated with slum settlements and high population density. The risk of cholera is equal and lower for communities with fewer refuse dumps, but variable and higher for communities with more refuse dumps. The risk is also lower for communities distant from refuse dumps and potential cholera reservoirs. The results also indicate distinct spatial variation in the risk of cholera infection. Conclusion The study highlights the usefulness of Bayesian semi-parametric regression model analyzing public health data. These findings could serve as novel information to help health planners and policy makers in making effective decisions to control or prevent cholera epidemics. PMID:22866662

Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics.

PubMed

Lambert, Amaury; Alexander, Helen K; Stadler, Tanja

2014-07-07

The reconstruction of phylogenetic trees based on viral genetic sequence data sequentially sampled from an epidemic provides estimates of the past transmission dynamics, by fitting epidemiological models to these trees. To our knowledge, none of the epidemiological models currently used in phylogenetics can account for recovery rates and sampling rates dependent on the time elapsed since transmission, i.e. age of infection. Here we introduce an epidemiological model where infectives leave the epidemic, by either recovery or sampling, after some random time which may follow an arbitrary distribution. We derive an expression for the likelihood of the phylogenetic tree of sampled infectives under our general epidemiological model. The analytic concept developed in this paper will facilitate inference of past epidemiological dynamics and provide an analytical framework for performing very efficient simulations of phylogenetic trees under our model. The main idea of our analytic study is that the non-Markovian epidemiological model giving rise to phylogenetic trees growing vertically as time goes by can be represented by a Markovian "coalescent point process" growing horizontally by the sequential addition of pairs of coalescence and sampling times. As examples, we discuss two special cases of our general model, described in terms of influenza and HIV epidemics. Though phrased in epidemiological terms, our framework can also be used for instance to fit macroevolutionary models to phylogenies of extant and extinct species, accounting for general species lifetime distributions. Copyright © 2014 Elsevier Ltd. All rights reserved.

Acute HIV infection transmission among people who inject drugs in a mature epidemic setting.

PubMed

Escudero, Daniel J; Lurie, Mark N; Mayer, Kenneth H; Weinreb, Caleb; King, Maximilian; Galea, Sandro; Friedman, Samuel R; Marshall, Brandon D L

2016-10-23

Estimates for the contribution of transmission arising from acute HIV infections (AHIs) to overall HIV incidence vary significantly. Furthermore, little is known about AHI-attributable transmission among people who inject drugs (PWID), including the extent to which interventions targeting chronic infections (e.g. HAART as prevention) are limited by AHI transmission. Thus, we estimated the proportion of transmission events attributable to AHI within the mature HIV epidemic among PWID in New York City (NYC). Modeling study. We constructed an interactive sexual and injecting transmission network using an agent-based model simulating the HIV epidemic in NYC between 1996 and 2012. Using stochastic microsimulations, we cataloged transmission from PWID based on the disease stage of index agents to determine the proportion of infections transmitted during AHI (in primary analyses, assumed to last 3 months). Our calibrated model approximated the epidemiological features of the mature HIV epidemic in NYC between 1996 and 2012. Annual HIV incidence among PWID dropped from approximately 1.8% in 1996 to 0.7% in 2012. Over the 16-year period, AHI accounted for 4.9% (10th/90th percentile: 0.1-12.3%) of incident HIV cases among PWID. The annualized contribution of AHI increased over this period from 3.6% in 1996 to 5.9% in 2012. Our results suggest that, in mature epidemics such as NYC, between 3% and 6% of transmission events are attributable to AHI among PWID. Current HIV treatment as prevention strategies are unlikely to be substantially affected by AHI-attributable transmission among PWID populations in mature epidemic settings.

Mathematical modelling of vector-borne diseases and insecticide resistance evolution.

PubMed

Gabriel Kuniyoshi, Maria Laura; Pio Dos Santos, Fernando Luiz

2017-01-01

Vector-borne diseases are important public health issues and, consequently, in silico models that simulate them can be useful. The susceptible-infected-recovered (SIR) model simulates the population dynamics of an epidemic and can be easily adapted to vector-borne diseases, whereas the Hardy-Weinberg model simulates allele frequencies and can be used to study insecticide resistance evolution. The aim of the present study is to develop a coupled system that unifies both models, therefore enabling the analysis of the effects of vector population genetics on the population dynamics of an epidemic. Our model consists of an ordinary differential equation system. We considered the populations of susceptible, infected and recovered humans, as well as susceptible and infected vectors. Concerning these vectors, we considered a pair of alleles, with complete dominance interaction that determined the rate of mortality induced by insecticides. Thus, we were able to separate the vectors according to the genotype. We performed three numerical simulations of the model. In simulation one, both alleles conferred the same mortality rate values, therefore there was no resistant strain. In simulations two and three, the recessive and dominant alleles, respectively, conferred a lower mortality. Our numerical results show that the genetic composition of the vector population affects the dynamics of human diseases. We found that the absolute number of vectors and the proportion of infected vectors are smaller when there is no resistant strain, whilst the ratio of infected people is larger in the presence of insecticide-resistant vectors. The dynamics observed for infected humans in all simulations has a very similar shape to real epidemiological data. The population genetics of vectors can affect epidemiological dynamics, and the presence of insecticide-resistant strains can increase the number of infected people. Based on the present results, the model is a basis for development of other models and for investigating population dynamics.

Coevolution of Epidemics, Social Networks, and Individual Behavior: A Case Study

NASA Astrophysics Data System (ADS)

Chen, Jiangzhuo; Marathe, Achla; Marathe, Madhav

This research shows how a limited supply of antivirals can be distributed optimally between the hospitals and the market so that the attack rate is minimized and enough revenue is generated to recover the cost of the antivirals. Results using an individual based model find that prevalence elastic demand behavior delays the epidemic and change in the social contact network induced by isolation reduces the peak of the epidemic significantly. A microeconomic analysis methodology combining behavioral economics and agent-based simulation is a major contribution of this work. In this paper we apply this methodology to analyze the fairness of the stockpile distribution, and the response of human behavior to disease prevalence level and its interaction with the market.

Epidemic extinction paths in complex networks

NASA Astrophysics Data System (ADS)

Hindes, Jason; Schwartz, Ira B.

2017-05-01

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic susceptible-infected-susceptible model, we predict the distribution of large fluctuations, the most probable or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.

Epidemic extinction paths in complex networks.

PubMed

Hindes, Jason; Schwartz, Ira B

2017-05-01

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic susceptible-infected-susceptible model, we predict the distribution of large fluctuations, the most probable or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.

Simulation models examining the effect of Brugian filariasis on dengue epidemics.

PubMed

Vaughan, Jefferson A; Focks, Dana A; Turell, Michael J

2009-01-01

Concurrent ingestion of microfilariae (mf) and arboviruses by mosquitoes can enhance the transmission of virus compared with when virus is ingested alone. We studied the effect of mf enhancement on the extrinsic incubation period (EIP) of dengue 1 virus within Aedes aegypti mosquitoes by feeding mosquitoes on blood that either contained virus plus Brugia malayi mf or virus only. Mosquitoes were sampled over time to determine viral dissemination rates. Co-ingestion of mf and virus reduced viral EIP by over half. We used the computer simulation program, DENSiM, to compare the predicted patterns of dengue incidence that would result from such a shortened EIP versus the EIP derived from the control (i.e., virus only) group of mosquitoes. Results indicated that, over the 14-year simulation period, mf-induced acceleration of the EIP would generate more frequent (but not necessarily more severe) epidemics. Potential interactions between arboviruses and hematozoans deserve closer scrutiny.

Modeling a SI epidemic with stochastic transmission: hyperbolic incidence rate.

PubMed

Christen, Alejandra; Maulén-Yañez, M Angélica; González-Olivares, Eduardo; Curé, Michel

2018-03-01

In this paper a stochastic susceptible-infectious (SI) epidemic model is analysed, which is based on the model proposed by Roberts and Saha (Appl Math Lett 12: 37-41, 1999), considering a hyperbolic type nonlinear incidence rate. Assuming the proportion of infected population varies with time, our new model is described by an ordinary differential equation, which is analogous to the equation that describes the double Allee effect. The limit of the solution of this equation (deterministic model) is found when time tends to infinity. Then, the asymptotic behaviour of a stochastic fluctuation due to the environmental variation in the coefficient of disease transmission is studied. Thus a stochastic differential equation (SDE) is obtained and the existence of a unique solution is proved. Moreover, the SDE is analysed through the associated Fokker-Planck equation to obtain the invariant measure when the proportion of the infected population reaches steady state. An explicit expression for invariant measure is found and we study some of its properties. The long time behaviour of deterministic and stochastic models are compared by simulations. According to our knowledge this incidence rate has not been previously used for this type of epidemic models.

Further results on the macroeconomic effects of AIDS: the dualistic, labor-surplus economy.

PubMed

Cuddington, J T

1993-09-01

Analyses by Cuddington in 1993 and forthcoming work from Cuddington and Hancock model the macroeconomic effects of the AIDS epidemic using a modified Solow growth model. This single-sector framework rests upon the assumption that labor and capital are always efficiently allocated throughout the economy with neither market failures nor policy-induced distortions resulting in resource misallocation. Economies in low-income developing countries in sub-Saharan Africa, however, are not operating at capacity. Impact models based upon the potential growth path of economies will therefore significantly overstate the effect of an AIDS epidemic. The author thus incorporates the presence of underemployment and dual labor markets to redress the limitations of these earlier impact models. The dual-economy simulations of the economic impact of AIDS using Tanzanian data suggest that the macroeconomic consequences of the epidemic are of the same order of magnitude as those obtained using a single-sector, full-employment model: gross domestic product (GDP) is 15-25% smaller by 2010 than it would have been without AIDS, and per capita GDP is 0-10% smaller. Output lost from AIDS in the dual-economy framework is approximately the same as the output gain achievable through policies designed to increase labor market flexibility. Findings suggest that serious economic reform in economies fraught with AIDS may lessen the negative economic effects of the epidemic.

Time Prediction Models for Echinococcosis Based on Gray System Theory and Epidemic Dynamics

PubMed Central

Zhang, Liping; Wang, Li; Zheng, Yanling; Wang, Kai; Zhang, Xueliang; Zheng, Yujian

2017-01-01

Echinococcosis, which can seriously harm human health and animal husbandry production, has become an endemic in the Xinjiang Uygur Autonomous Region of China. In order to explore an effective human Echinococcosis forecasting model in Xinjiang, three grey models, namely, the traditional grey GM(1,1) model, the Grey-Periodic Extensional Combinatorial Model (PECGM(1,1)), and the Modified Grey Model using Fourier Series (FGM(1,1)), in addition to a multiplicative seasonal ARIMA(1,0,1)(1,1,0)4 model, are applied in this study for short-term predictions. The accuracy of the different grey models is also investigated. The simulation results show that the FGM(1,1) model has a higher performance ability, not only for model fitting, but also for forecasting. Furthermore, considering the stability and the modeling precision in the long run, a dynamic epidemic prediction model based on the transmission mechanism of Echinococcosis is also established for long-term predictions. Results demonstrate that the dynamic epidemic prediction model is capable of identifying the future tendency. The number of human Echinococcosis cases will increase steadily over the next 25 years, reaching a peak of about 1250 cases, before eventually witnessing a slow decline, until it finally ends. PMID:28273856

Analysis of novel stochastic switched SILI epidemic models with continuous and impulsive control

NASA Astrophysics Data System (ADS)

Gao, Shujing; Zhong, Deming; Zhang, Yan

2018-04-01

In this paper, we establish two new stochastic switched epidemic models with continuous and impulsive control. The stochastic perturbations are considered for the natural death rate in each equation of the models. Firstly, a stochastic switched SILI model with continuous control schemes is investigated. By using Lyapunov-Razumikhin method, the sufficient conditions for extinction in mean are established. Our result shows that the disease could be die out theoretically if threshold value R is less than one, regardless of whether the disease-free solutions of the corresponding subsystems are stable or unstable. Then, a stochastic switched SILI model with continuous control schemes and pulse vaccination is studied. The threshold value R is derived. The global attractivity of the model is also obtained. At last, numerical simulations are carried out to support our results.

Epidemic patch models applied to pandemic influenza: contact matrix, stochasticity, robustness of predictions.

PubMed

Lunelli, Antonella; Pugliese, Andrea; Rizzo, Caterina

2009-07-01

Due to the recent emergence of H5N1 virus, the modelling of pandemic influenza has become a relevant issue. Here we present an SEIR model formulated to simulate a possible outbreak in Italy, analysing its structure and, more generally, the effect of including specific details into a model. These details regard population heterogeneities, such as age and spatial distribution, as well as stochasticity, that regulates the epidemic dynamics when the number of infectives is low. We discuss and motivate the specific modelling choices made when building the model and investigate how the model details influence the predicted dynamics. Our analysis may help in deciding which elements of complexity are worth including in the design of a deterministic model for pandemic influenza, in a balance between, on the one hand, keeping the model computationally efficient and the number of parameters low and, on the other hand, maintaining the necessary realistic features.

Integrating remote sensing, GIS and dynamic models for landscape-level simulation of forest insect disturbance

USDA-ARS?s Scientific Manuscript database

Cellular automata (CA) is a powerful tool in modeling the evolution of macroscopic scale phenomena as it couples time, space, and variable together while remaining in a simplified form. However, such application has remained challenging in landscape-level chronic forest insect epidemics due to the h...

Stability analysis of the Euler discretization for SIR epidemic model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Suryanto, Agus

2014-06-19

In this paper we consider a discrete SIR epidemic model obtained by the Euler method. For that discrete model, existence of disease free equilibrium and endemic equilibrium is established. Sufficient conditions on the local asymptotical stability of both disease free equilibrium and endemic equilibrium are also derived. It is found that the local asymptotical stability of the existing equilibrium is achieved only for a small time step size h. If h is further increased and passes the critical value, then both equilibriums will lose their stability. Our numerical simulations show that a complex dynamical behavior such as bifurcation or chaosmore » phenomenon will appear for relatively large h. Both analytical and numerical results show that the discrete SIR model has a richer dynamical behavior than its continuous counterpart.« less

The Impact of Resources for Clinical Surveillance on the Control of a Hypothetical Foot-and-Mouth Disease Epidemic in Denmark

PubMed Central

Halasa, Tariq; Boklund, Anette

2014-01-01

The objectives of this study were to assess whether current surveillance capacity is sufficient to fulfill EU and Danish regulations to control a hypothetical foot-and-mouth disease (FMD) epidemic in Denmark, and whether enlarging the protection and/or surveillance zones could minimize economic losses. The stochastic spatial simulation model DTU-DADS was further developed to simulate clinical surveillance of herds within the protection and surveillance zones and used to model spread of FMD between herds. A queuing system was included in the model, and based on daily surveillance capacity, which was 450 herds per day, it was decided whether herds appointed for surveillance would be surveyed on the current day or added to the queue. The model was run with a basic scenario representing the EU and Danish regulations, which includes a 3 km protection and 10 km surveillance zone around detected herds. In alternative scenarios, the protection zone was enlarged to 5 km, the surveillance zone was enlarged to 15 or 20 km, or a combined enlargement of the protection and surveillance zones was modelled. Sensitivity analysis included changing surveillance capacity to 200, 350 or 600 herds per day, frequency of repeated visits for herds in overlapping surveillance zones from every 14 days to every 7, 21 and 30 days, and the size of the zones combined with a surveillance capacity increased to 600 herds per day. The results showed that the default surveillance capacity is sufficient to survey herds on time. Extra resources for surveillance did not improve the situation, but fewer resources could result in larger epidemics and costs. Enlarging the protection zone was a better strategy than the basic scenario. Despite that enlarging the surveillance zone might result in shorter epidemic duration, and lower number of affected herds, it resulted frequently in larger economic losses. PMID:25014351

Inferring epidemiological parameters from phylogenetic information for the HIV-1 epidemic among MSM

NASA Astrophysics Data System (ADS)

Quax, Rick; van de Vijver, David A. M. C.; Frentz, Dineke; Sloot, Peter M. A.

2013-09-01

The HIV-1 epidemic in Europe is primarily sustained by a dynamic topology of sexual interactions among MSM who have individual immune systems and behavior. This epidemiological process shapes the phylogeny of the virus population. Both fields of epidemic modeling and phylogenetics have a long history, however it remains difficult to use phylogenetic data to infer epidemiological parameters such as the structure of the sexual network and the per-act infectiousness. This is because phylogenetic data is necessarily incomplete and ambiguous. Here we show that the cluster-size distribution indeed contains information about epidemiological parameters using detailed numberical experiments. We simulate the HIV epidemic among MSM many times using the Monte Carlo method with all parameter values and their ranges taken from literature. For each simulation and the corresponding set of parameter values we calculate the likelihood of reproducing an observed cluster-size distribution. The result is an estimated likelihood distribution of all parameters from the phylogenetic data, in particular the structure of the sexual network, the per-act infectiousness, and the risk behavior reduction upon diagnosis. These likelihood distributions encode the knowledge provided by the observed cluster-size distrbution, which we quantify using information theory. Our work suggests that the growing body of genetic data of patients can be exploited to understand the underlying epidemiological process.

Epidemic and economic impacts of delayed detection of foot-and-mouth disease: a case study of a simulated outbreak in California.

PubMed

Carpenter, Tim E; O'Brien, Joshua M; Hagerman, Amy D; McCarl, Bruce A

2011-01-01

The epidemic and economic impacts of Foot-and-mouth disease virus (FMDV) spread and control were examined by using epidemic simulation and economic (epinomic) optimization models. The simulated index herd was a ≥2,000 cow dairy located in California. Simulated disease spread was limited to California; however, economic impact was assessed throughout the United States and included international trade effects. Five index case detection delays were examined, which ranged from 7 to 22 days. The simulated median number of infected premises (IP) ranged from approximately 15 to 745, increasing as the detection delay increased from 7 to 22 days. Similarly, the median number of herds under quarantine increased from approximately 680 to 6,200, whereas animals slaughtered went from approximately 8,700 to 260,400 for detection delays of 7-22 days, respectively. The median economic impact of an FMD outbreak in California was estimated to result in national agriculture welfare losses of $2.3-$69.0 billion as detection delay increased from 7 to 22 days, respectively. If assuming a detection delay of 21 days, it was estimated that, for every additional hr of delay, the impact would be an additional approximately 2,000 animals slaughtered and an additional economic loss of $565 million. These findings underline the critical importance that the United States has an effective early detection system in place before an introduction of FMDV if it hopes to avoid dramatic losses to both livestock and the economy.

Inferring a District-Based Hierarchical Structure of Social Contacts from Census Data

PubMed Central

Yu, Zhiwen; Liu, Jiming; Zhu, Xianjun

2015-01-01

Researchers have recently paid attention to social contact patterns among individuals due to their useful applications in such areas as epidemic evaluation and control, public health decisions, chronic disease research and social network research. Although some studies have estimated social contact patterns from social networks and surveys, few have considered how to infer the hierarchical structure of social contacts directly from census data. In this paper, we focus on inferring an individual’s social contact patterns from detailed census data, and generate various types of social contact patterns such as hierarchical-district-structure-based, cross-district and age-district-based patterns. We evaluate newly generated contact patterns derived from detailed 2011 Hong Kong census data by incorporating them into a model and simulation of the 2009 Hong Kong H1N1 epidemic. We then compare the newly generated social contact patterns with the mixing patterns that are often used in the literature, and draw the following conclusions. First, the generation of social contact patterns based on a hierarchical district structure allows for simulations at different district levels. Second, the newly generated social contact patterns reflect individuals social contacts. Third, the newly generated social contact patterns improve the accuracy of the SEIR-based epidemic model. PMID:25679787

An individual-based approach to SIR epidemics in contact networks.

PubMed

Youssef, Mina; Scoglio, Caterina

2011-08-21

Many approaches have recently been proposed to model the spread of epidemics on networks. For instance, the Susceptible/Infected/Recovered (SIR) compartmental model has successfully been applied to different types of diseases that spread out among humans and animals. When this model is applied on a contact network, the centrality characteristics of the network plays an important role in the spreading process. However, current approaches only consider an aggregate representation of the network structure, which can result in inaccurate analysis. In this paper, we propose a new individual-based SIR approach, which considers the whole description of the network structure. The individual-based approach is built on a continuous time Markov chain, and it is capable of evaluating the state probability for every individual in the network. Through mathematical analysis, we rigorously confirm the existence of an epidemic threshold below which an epidemic does not propagate in the network. We also show that the epidemic threshold is inversely proportional to the maximum eigenvalue of the network. Additionally, we study the role of the whole spectrum of the network, and determine the relationship between the maximum number of infected individuals and the set of eigenvalues and eigenvectors. To validate our approach, we analytically study the deviation with respect to the continuous time Markov chain model, and we show that the new approach is accurate for a large range of infection strength. Furthermore, we compare the new approach with the well-known heterogeneous mean field approach in the literature. Ultimately, we support our theoretical results through extensive numerical evaluations and Monte Carlo simulations. Published by Elsevier Ltd.

Dynamic health policies for controlling the spread of emerging infections: influenza as an example.

PubMed

Yaesoubi, Reza; Cohen, Ted

2011-01-01

The recent appearance and spread of novel infectious pathogens provide motivation for using models as tools to guide public health decision-making. Here we describe a modeling approach for developing dynamic health policies that allow for adaptive decision-making as new data become available during an epidemic. In contrast to static health policies which have generally been selected by comparing the performance of a limited number of pre-determined sequences of interventions within simulation or mathematical models, dynamic health policies produce "real-time" recommendations for the choice of the best current intervention based on the observable state of the epidemic. Using cumulative real-time data for disease spread coupled with current information about resource availability, these policies provide recommendations for interventions that optimally utilize available resources to preserve the overall health of the population. We illustrate the design and implementation of a dynamic health policy for the control of a novel strain of influenza, where we assume that two types of intervention may be available during the epidemic: (1) vaccines and antiviral drugs, and (2) transmission reducing measures, such as social distancing or mask use, that may be turned "on" or "off" repeatedly during the course of epidemic. In this example, the optimal dynamic health policy maximizes the overall population's health during the epidemic by specifying at any point of time, based on observable conditions, (1) the number of individuals to vaccinate if vaccines are available, and (2) whether the transmission-reducing intervention should be either employed or removed.

Real-time dynamic modelling for the design of a cluster-randomized phase 3 Ebola vaccine trial in Sierra Leone.

PubMed

Camacho, A; Eggo, R M; Goeyvaerts, N; Vandebosch, A; Mogg, R; Funk, S; Kucharski, A J; Watson, C H; Vangeneugden, T; Edmunds, W J

2017-01-23

Declining incidence and spatial heterogeneity complicated the design of phase 3 Ebola vaccine trials during the tail of the 2013-16 Ebola virus disease (EVD) epidemic in West Africa. Mathematical models can provide forecasts of expected incidence through time and can account for both vaccine efficacy in participants and effectiveness in populations. Determining expected disease incidence was critical to calculating power and determining trial sample size. In real-time, we fitted, forecasted, and simulated a proposed phase 3 cluster-randomized vaccine trial for a prime-boost EVD vaccine in three candidate regions in Sierra Leone. The aim was to forecast trial feasibility in these areas through time and guide study design planning. EVD incidence was highly variable during the epidemic, especially in the declining phase. Delays in trial start date were expected to greatly reduce the ability to discern an effect, particularly as a trial with an effective vaccine would cause the epidemic to go extinct more quickly in the vaccine arm. Real-time updates of the model allowed decision-makers to determine how trial feasibility changed with time. This analysis was useful for vaccine trial planning because we simulated effectiveness as well as efficacy, which is possible with a dynamic transmission model. It contributed to decisions on choice of trial location and feasibility of the trial. Transmission models should be utilised as early as possible in the design process to provide mechanistic estimates of expected incidence, with which decisions about sample size, location, timing, and feasibility can be determined. Copyright © 2016. Published by Elsevier Ltd.

Real-time characterization of partially observed epidemics using surrogate models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Safta, Cosmin; Ray, Jaideep; Lefantzi, Sophia

We present a statistical method, predicated on the use of surrogate models, for the 'real-time' characterization of partially observed epidemics. Observations consist of counts of symptomatic patients, diagnosed with the disease, that may be available in the early epoch of an ongoing outbreak. Characterization, in this context, refers to estimation of epidemiological parameters that can be used to provide short-term forecasts of the ongoing epidemic, as well as to provide gross information on the dynamics of the etiologic agent in the affected population e.g., the time-dependent infection rate. The characterization problem is formulated as a Bayesian inverse problem, and epidemiologicalmore » parameters are estimated as distributions using a Markov chain Monte Carlo (MCMC) method, thus quantifying the uncertainty in the estimates. In some cases, the inverse problem can be computationally expensive, primarily due to the epidemic simulator used inside the inversion algorithm. We present a method, based on replacing the epidemiological model with computationally inexpensive surrogates, that can reduce the computational time to minutes, without a significant loss of accuracy. The surrogates are created by projecting the output of an epidemiological model on a set of polynomial chaos bases; thereafter, computations involving the surrogate model reduce to evaluations of a polynomial. We find that the epidemic characterizations obtained with the surrogate models is very close to that obtained with the original model. We also find that the number of projections required to construct a surrogate model is O(10)-O(10{sup 2}) less than the number of samples required by the MCMC to construct a stationary posterior distribution; thus, depending upon the epidemiological models in question, it may be possible to omit the offline creation and caching of surrogate models, prior to their use in an inverse problem. The technique is demonstrated on synthetic data as well as observations from the 1918 influenza pandemic collected at Camp Custer, Michigan.« less

Stochasticity in staged models of epidemics: quantifying the dynamics of whooping cough

PubMed Central

Black, Andrew J.; McKane, Alan J.

2010-01-01

Although many stochastic models can accurately capture the qualitative epidemic patterns of many childhood diseases, there is still considerable discussion concerning the basic mechanisms generating these patterns; much of this stems from the use of deterministic models to try to understand stochastic simulations. We argue that a systematic method of analysing models of the spread of childhood diseases is required in order to consistently separate out the effects of demographic stochasticity, external forcing and modelling choices. Such a technique is provided by formulating the models as master equations and using the van Kampen system-size expansion to provide analytical expressions for quantities of interest. We apply this method to the susceptible–exposed–infected–recovered (SEIR) model with distributed exposed and infectious periods and calculate the form that stochastic oscillations take on in terms of the model parameters. With the use of a suitable approximation, we apply the formalism to analyse a model of whooping cough which includes seasonal forcing. This allows us to more accurately interpret the results of simulations and to make a more quantitative assessment of the predictions of the model. We show that the observed dynamics are a result of a macroscopic limit cycle induced by the external forcing and resonant stochastic oscillations about this cycle. PMID:20164086

Impact of an effective multidrug-resistant tuberculosis control programme in the setting of an immature HIV epidemic: system dynamics simulation model.

PubMed

Atun, Rifat A; Lebcir, Reda; Drobniewski, Francis; Coker, Richard J

2005-08-01

This study sought to determine the impact of an effective programme of multidrug resistant tuberculosis control (MDRTB) on a population that is witnessing an explosive HIV epidemic among injecting drug users (IDUs), where the prevalence of MDRTB is already high. A transmission model was constructed that represents the dynamics of the drug-susceptible tuberculosis (DSTB), MDRTB and HIV spread among the adult population of Samara Oblast, Russia: from official notifications of tuberculosis and of HIV infection, estimates of MDRTB derived from surveillance studies, population data from official regional statistics, data on transmission probabilities from peer-reviewed publications and informed estimates, and policy-makers' estimates of IDU populations. Two scenarios of programme effectiveness for MDRTB were modelled and run over a period of 10 years to predict cumulative deaths. In a population of 3.3 million with a high prevalence of MDRTB, an emerging epidemic of HIV among IDUs, and a functioning directly observed therapy-short course (DOTS) programme, the model predicts that under low cure rates for MDRTB the expected cumulative deaths from tuberculosis will reach 6303 deaths including 1900 deaths from MDRTB at 10 years. Under high cure rate for MDRTB 4465 deaths will occur including 134 deaths from MDRTB. At 10 years there is little impact on HIV-infected populations from the MDRTB epidemic, but as the HIV epidemic matures the impact becomes substantial. When the model is extended to 20 years cumulative deaths from MDRTB become very high if cure rates for MDRTB are low and cumulative deaths in the HIV-infected population, likewise, are profoundly affected. In the presence of an immature HIV epidemic failure to actively control MDRTB may result in approximately a third more deaths than if effective treatment is given. As the HIV epidemic matures then the impact of MDRTB grows substantially if MDRTB control strategies are ineffective. The epidemiological starting point for these scenarios is present in many regions within the former Soviet Union and this analysis suggests control of MDRTB should be an urgent priority.

[Mathematical models and epidemiological analysis].

PubMed

Gerasimov, A N

2010-01-01

The limited use of mathematical simulation in epidemiology is due not only to the difficulty of monitoring the epidemic process and identifying its parameters but also to the application of oversimplified models. It is shown that realistic reproduction of actual morbidity dynamics requires taking into account heterogeneity and finiteness of the population and seasonal character of pathogen transmission mechanism.

Contact, Travel, and Transmission: The Impact of Winter Holidays on Influenza Dynamics in the United States

PubMed Central

Ewing, Anne; Lee, Elizabeth C.; Viboud, Cécile

2017-01-01

Abstract Background. The seasonality of influenza is thought to vary according to environmental factors and human behavior. During winter holidays, potential disease-causing contact and travel deviate from typical patterns. We aim to understand these changes on age-specific and spatial influenza transmission. Methods. We characterized the changes to transmission and epidemic trajectories among children and adults in a spatial context before, during, and after the winter holidays among aggregated physician medical claims in the United States from 2001 to 2009 and among synthetic data simulated from a deterministic, age-specific spatial metapopulation model. Results. Winter holidays reduced influenza transmission and delayed the trajectory of influenza season epidemics. The holiday period was marked by a shift in the relative risk of disease from children toward adults. Model results indicated that holidays delayed epidemic peaks and synchronized incidence across locations, and that contact reductions from school closures, rather than age-specific mixing and travel, produced these observed holiday influenza dynamics. Conclusions. Winter holidays delay seasonal influenza epidemic peaks and shift disease risk toward adults because of changes in contact patterns. These findings may inform targeted influenza information and vaccination campaigns during holiday periods. PMID:28031259

The Apollo Structured Vocabulary: an OWL2 ontology of phenomena in infectious disease epidemiology and population biology for use in epidemic simulation.

PubMed

Hogan, William R; Wagner, Michael M; Brochhausen, Mathias; Levander, John; Brown, Shawn T; Millett, Nicholas; DePasse, Jay; Hanna, Josh

2016-08-18

We developed the Apollo Structured Vocabulary (Apollo-SV)-an OWL2 ontology of phenomena in infectious disease epidemiology and population biology-as part of a project whose goal is to increase the use of epidemic simulators in public health practice. Apollo-SV defines a terminology for use in simulator configuration. Apollo-SV is the product of an ontological analysis of the domain of infectious disease epidemiology, with particular attention to the inputs and outputs of nine simulators. Apollo-SV contains 802 classes for representing the inputs and outputs of simulators, of which approximately half are new and half are imported from existing ontologies. The most important Apollo-SV class for users of simulators is infectious disease scenario, which is a representation of an ecosystem at simulator time zero that has at least one infection process (a class) affecting at least one population (also a class). Other important classes represent ecosystem elements (e.g., households), ecosystem processes (e.g., infection acquisition and infectious disease), censuses of ecosystem elements (e.g., censuses of populations), and infectious disease control measures. In the larger project, which created an end-user application that can send the same infectious disease scenario to multiple simulators, Apollo-SV serves as the controlled terminology and strongly influences the design of the message syntax used to represent an infectious disease scenario. As we added simulators for different pathogens (e.g., malaria and dengue), the core classes of Apollo-SV have remained stable, suggesting that our conceptualization of the information required by simulators is sound. Despite adhering to the OBO Foundry principle of orthogonality, we could not reuse Infectious Disease Ontology classes as the basis for infectious disease scenarios. We thus defined new classes in Apollo-SV for host, pathogen, infection, infectious disease, colonization, and infection acquisition. Unlike IDO, our ontological analysis extended to existing mathematical models of key biological phenomena studied by infectious disease epidemiology and population biology. Our ontological analysis as expressed in Apollo-SV was instrumental in developing a simulator-independent representation of infectious disease scenarios that can be run on multiple epidemic simulators. Our experience suggests the importance of extending ontological analysis of a domain to include existing mathematical models of the phenomena studied by the domain. Apollo-SV is freely available at: http://purl.obolibrary.org/obo/apollo_sv.owl .

Spread of information and infection on finite random networks

NASA Astrophysics Data System (ADS)

Isham, Valerie; Kaczmarska, Joanna; Nekovee, Maziar

2011-04-01

The modeling of epidemic-like processes on random networks has received considerable attention in recent years. While these processes are inherently stochastic, most previous work has been focused on deterministic models that ignore important fluctuations that may persist even in the infinite network size limit. In a previous paper, for a class of epidemic and rumor processes, we derived approximate models for the full probability distribution of the final size of the epidemic, as opposed to only mean values. In this paper we examine via direct simulations the adequacy of the approximate model to describe stochastic epidemics and rumors on several random network topologies: homogeneous networks, Erdös-Rényi (ER) random graphs, Barabasi-Albert scale-free networks, and random geometric graphs. We find that the approximate model is reasonably accurate in predicting the probability of spread. However, the position of the threshold and the conditional mean of the final size for processes near the threshold are not well described by the approximate model even in the case of homogeneous networks. We attribute this failure to the presence of other structural properties beyond degree-degree correlations, and in particular clustering, which are present in any finite network but are not incorporated in the approximate model. In order to test this “hypothesis” we perform additional simulations on a set of ER random graphs where degree-degree correlations and clustering are separately and independently introduced using recently proposed algorithms from the literature. Our results show that even strong degree-degree correlations have only weak effects on the position of the threshold and the conditional mean of the final size. On the other hand, the introduction of clustering greatly affects both the position of the threshold and the conditional mean. Similar analysis for the Barabasi-Albert scale-free network confirms the significance of clustering on the dynamics of rumor spread. For this network, though, with its highly skewed degree distribution, the addition of positive correlation had a much stronger effect on the final size distribution than was found for the simple random graph.

Real-time forecasts of dengue epidemics

NASA Astrophysics Data System (ADS)

Yamana, T. K.; Shaman, J. L.

2015-12-01

Dengue is a mosquito-borne viral disease prevalent in the tropics and subtropics, with an estimated 2.5 billion people at risk of transmission. In many areas with endemic dengue, disease transmission is seasonal but prone to high inter-annual variability with occasional severe epidemics. Predicting and preparing for periods of higher than average transmission is a significant public health challenge. Here we present a model of dengue transmission and a framework for optimizing model simulations with real-time observational data of dengue cases and environmental variables in order to generate ensemble-based forecasts of the timing and severity of disease outbreaks. The model-inference system is validated using synthetic data and dengue outbreak records. Retrospective forecasts are generated for a number of locations and the accuracy of these forecasts is quantified.

Behaviors of susceptible-infected epidemics on scale-free networks with identical infectivity

NASA Astrophysics Data System (ADS)

Zhou, Tao; Liu, Jian-Guo; Bai, Wen-Jie; Chen, Guanrong; Wang, Bing-Hong

2006-11-01

In this paper, we propose a susceptible-infected model with identical infectivity, in which, at every time step, each node can only contact a constant number of neighbors. We implemented this model on scale-free networks, and found that the infected population grows in an exponential form with the time scale proportional to the spreading rate. Furthermore, by numerical simulation, we demonstrated that the targeted immunization of the present model is much less efficient than that of the standard susceptible-infected model. Finally, we investigate a fast spreading strategy when only local information is available. Different from the extensively studied path-finding strategy, the strategy preferring small-degree nodes is more efficient than that preferring large-degree nodes. Our results indicate the existence of an essential relationship between network traffic and network epidemic on scale-free networks.

Constructing rigorous and broad biosurveillance networks for detecting emerging zoonotic outbreaks

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, Mac; Moore, Leslie; McMahon, Benjamin

Determining optimal surveillance networks for an emerging pathogen is difficult since it is not known beforehand what the characteristics of a pathogen will be or where it will emerge. The resources for surveillance of infectious diseases in animals and wildlife are often limited and mathematical modeling can play a supporting role in examining a wide range of scenarios of pathogen spread. We demonstrate how a hierarchy of mathematical and statistical tools can be used in surveillance planning help guide successful surveillance and mitigation policies for a wide range of zoonotic pathogens. The model forecasts can help clarify the complexities ofmore » potential scenarios, and optimize biosurveillance programs for rapidly detecting infectious diseases. Using the highly pathogenic zoonotic H5N1 avian influenza 2006-2007 epidemic in Nigeria as an example, we determined the risk for infection for localized areas in an outbreak and designed biosurveillance stations that are effective for different pathogen strains and a range of possible outbreak locations. We created a general multi-scale, multi-host stochastic SEIR epidemiological network model, with both short and long-range movement, to simulate the spread of an infectious disease through Nigerian human, poultry, backyard duck, and wild bird populations. We chose parameter ranges specific to avian influenza (but not to a particular strain) and used a Latin hypercube sample experimental design to investigate epidemic predictions in a thousand simulations. We ranked the risk of local regions by the number of times they became infected in the ensemble of simulations. These spatial statistics were then complied into a potential risk map of infection. Finally, we validated the results with a known outbreak, using spatial analysis of all the simulation runs to show the progression matched closely with the observed location of the farms infected in the 2006-2007 epidemic.« less

Constructing rigorous and broad biosurveillance networks for detecting emerging zoonotic outbreaks

DOE PAGES

Brown, Mac; Moore, Leslie; McMahon, Benjamin; ...

2015-05-06

Determining optimal surveillance networks for an emerging pathogen is difficult since it is not known beforehand what the characteristics of a pathogen will be or where it will emerge. The resources for surveillance of infectious diseases in animals and wildlife are often limited and mathematical modeling can play a supporting role in examining a wide range of scenarios of pathogen spread. We demonstrate how a hierarchy of mathematical and statistical tools can be used in surveillance planning help guide successful surveillance and mitigation policies for a wide range of zoonotic pathogens. The model forecasts can help clarify the complexities ofmore » potential scenarios, and optimize biosurveillance programs for rapidly detecting infectious diseases. Using the highly pathogenic zoonotic H5N1 avian influenza 2006-2007 epidemic in Nigeria as an example, we determined the risk for infection for localized areas in an outbreak and designed biosurveillance stations that are effective for different pathogen strains and a range of possible outbreak locations. We created a general multi-scale, multi-host stochastic SEIR epidemiological network model, with both short and long-range movement, to simulate the spread of an infectious disease through Nigerian human, poultry, backyard duck, and wild bird populations. We chose parameter ranges specific to avian influenza (but not to a particular strain) and used a Latin hypercube sample experimental design to investigate epidemic predictions in a thousand simulations. We ranked the risk of local regions by the number of times they became infected in the ensemble of simulations. These spatial statistics were then complied into a potential risk map of infection. Finally, we validated the results with a known outbreak, using spatial analysis of all the simulation runs to show the progression matched closely with the observed location of the farms infected in the 2006-2007 epidemic.« less

Critical behavior in a stochastic model of vector mediated epidemics

PubMed Central

Alfinito, E.; Beccaria, M.; Macorini, G.

2016-01-01

The extreme vulnerability of humans to new and old pathogens is constantly highlighted by unbound outbreaks of epidemics. This vulnerability is both direct, producing illness in humans (dengue, malaria), and also indirect, affecting its supplies (bird and swine flu, Pierce disease, and olive quick decline syndrome). In most cases, the pathogens responsible for an illness spread through vectors. In general, disease evolution may be an uncontrollable propagation or a transient outbreak with limited diffusion. This depends on the physiological parameters of hosts and vectors (susceptibility to the illness, virulence, chronicity of the disease, lifetime of the vectors, etc.). In this perspective and with these motivations, we analyzed a stochastic lattice model able to capture the critical behavior of such epidemics over a limited time horizon and with a finite amount of resources. The model exhibits a critical line of transition that separates spreading and non-spreading phases. The critical line is studied with new analytical methods and direct simulations. Critical exponents are found to be the same as those of dynamical percolation. PMID:27264105

Dynamics of an epidemic model with quarantine on scale-free networks

NASA Astrophysics Data System (ADS)

Kang, Huiyan; Liu, Kaihui; Fu, Xinchu

2017-12-01

Quarantine strategies are frequently used to control or reduce the transmission risks of epidemic diseases such as SARS, tuberculosis and cholera. In this paper, we formulate a susceptible-exposed-infected-quarantined-recovered model on a scale-free network incorporating the births and deaths of individuals. Considering that the infectivity is related to the degrees of infectious nodes, we introduce quarantined rate as a function of degree into the model, and quantify the basic reproduction number, which is shown to be dependent on some parameters, such as quarantined rate, infectivity and network structures. A theoretical result further indicates the heterogeneity of networks and higher infectivity will raise the disease transmission risk while quarantine measure will contribute to the prevention of epidemic spreading. Meanwhile, the contact assumption between susceptibles and infectives may impact the disease transmission. Furthermore, we prove that the basic reproduction number serves as a threshold value for the global stability of the disease-free and endemic equilibria and the uniform persistence of the disease on the network by constructing appropriate Lyapunov functions. Finally, some numerical simulations are illustrated to perform and complement our analytical results.

An application of Mean Escape Time and metapopulation on forestry catastrophe insurance

NASA Astrophysics Data System (ADS)

Li, Jiangcheng; Zhang, Chunmin; Liu, Jifa; Li, Zhen; Yang, Xuan

2018-04-01

A forestry catastrophe insurance model due to forestry pest infestations and disease epidemics is developed by employing metapopulation dynamics and statistics properties of Mean Escape Time (MET). The probability of outbreak of forestry catastrophe loss and the catastrophe loss payment time with MET are respectively investigated. Forestry loss data in China is used for model simulation. Experimental results are concluded as: (1) The model with analytical results is shown to be a better fit; (2) Within the condition of big area of patches and structure of patches, high system factor, low extinction rate, high multiplicative noises, and additive noises with a high cross-correlated strength range, an outbreak of forestry catastrophe loss or catastrophe loss payment due to forestry pest infestations and disease epidemics could occur; (3) An optimal catastrophe loss payment time MET due to forestry pest infestations and disease epidemics can be identified by taking proper value of multiplicative noises and limits the additive noises on a low range of value, and cross-correlated strength at a high range of value.

Epidemic spreading on activity-driven networks with attractiveness.

PubMed

Pozzana, Iacopo; Sun, Kaiyuan; Perra, Nicola

2017-10-01

We study SIS epidemic spreading processes unfolding on a recent generalization of the activity-driven modeling framework. In this model of time-varying networks, each node is described by two variables: activity and attractiveness. The first describes the propensity to form connections, while the second defines the propensity to attract them. We derive analytically the epidemic threshold considering the time scale driving the evolution of contacts and the contagion as comparable. The solutions are general and hold for any joint distribution of activity and attractiveness. The theoretical picture is confirmed via large-scale numerical simulations performed considering heterogeneous distributions and different correlations between the two variables. We find that heterogeneous distributions of attractiveness alter the contagion process. In particular, in the case of uncorrelated and positive correlations between the two variables, heterogeneous attractiveness facilitates the spreading. On the contrary, negative correlations between activity and attractiveness hamper the spreading. The results presented contribute to the understanding of the dynamical properties of time-varying networks and their effects on contagion phenomena unfolding on their fabric.

Using computer algebra and SMT-solvers to analyze a mathematical model of cholera propagation

NASA Astrophysics Data System (ADS)

Trujillo Arredondo, Mariana

2014-06-01

We analyze a mathematical model for the transmission of cholera. The model is already defined and involves variables such as the pathogen agent, which in this case is the bacterium Vibrio cholera, and the human population. The human population is divided into three classes: susceptible, infectious and removed. Using Computer Algebra, specifically Maple we obtain two equilibrium states: the disease free state and the endemic state. Using Maple it is possible to prove that the disease free state is locally asymptotically stable if and only if R0 < 1. Using Maple it is possible to prove that the endemic equilibrium state is locally stable when it exists, it is to say when R0 > 1. Using the package Red-Log of the Computer algebra system Reduce and the SMT-Solver Z3Py it is possible to obtain numerical conditions for the model. The formula for the basic reproductive number makes a synthesis with all epidemic parameters in the model. Also it is possible to make numerical simulations which are very illustrative about the epidemic patters that are expected to be observed in real situations. We claim that these kinds of software are very useful in the analysis of epidemic models given that the symbolic computation provides algebraic formulas for the basic reproductive number and such algebraic formulas are very useful to derive control measures. For other side, computer algebra software is a powerful tool to make the stability analysis for epidemic models given that the all steps in the stability analysis can be made automatically: finding the equilibrium points, computing the jacobian, computing the characteristic polynomial for the jacobian, and applying the Routh-Hurwitz theorem to the characteristic polynomial. Finally, using SMT-Solvers is possible to make automatically checks of satisfiability, validity and quantifiers elimination being these computations very useful to analyse complicated epidemic models.

Evaluation of Movement Restriction Zone Sizes in Controlling Classical Swine Fever Outbreaks

PubMed Central

Yadav, Shankar; Olynk Widmar, Nicole; Lay, Donald C.; Croney, Candace; Weng, Hsin-Yi

2017-01-01

The objective of this study was to compare the impacts of movement restriction zone sizes of 3, 5, 9, and 11 km with that of 7 km (the recommended zone size in the United States) in controlling a classical swine fever (CSF) outbreak. In addition to zone size, different compliance assumptions and outbreak types (single site and multiple site) were incorporated in the study. Three assumptions of compliance level were simulated: baseline, baseline ± 10%, and baseline ± 15%. The compliance level was held constant across all zone sizes in the baseline simulation. In the baseline ± 10% and baseline ± 15% simulations, the compliance level was increased for 3 and 5 km and decreased for 9 and 11 km from the baseline by the indicated percentages. The compliance level remained constant in all simulations for the 7-km zone size. Four single-site (i.e., with one index premises at the onset of outbreak) and four multiple-site (i.e., with more than one index premises at the onset of outbreak) CSF outbreak scenarios in Indiana were simulated incorporating various zone sizes and compliance assumptions using a stochastic between-premises disease spread model to estimate epidemic duration, percentage of infected, and preemptively culled swine premises. Furthermore, a risk assessment model that incorporated the results from the disease spread model was developed to estimate the number of swine premises under movement restrictions that would experience animal welfare outcomes of overcrowding or feed interruption during a CSF outbreak in Indiana. Compared with the 7-km zone size, the 3-km zone size resulted in a longer median epidemic duration, larger percentages of infected premises, and preemptively culled premises (P’s < 0.001) across all compliance assumptions and outbreak types. With the assumption of a higher compliance level, the 5-km zone size significantly (P < 0.001) reduced the epidemic duration and percentage of swine premises that would experience animal welfare outcomes in both outbreak types, whereas assumption of a lower compliance level for 9- and 11-km zone sizes significantly (P < 0.001) increased the epidemic duration and percentage of swine premises with animal welfare outcomes compared with the 7-km zone size. The magnitude of impact due to a zone size varied across the outbreak types (single site and multiple site). Overall, the 7-km zone size was found to be most effective in controlling CSF outbreaks, whereas the 5-km zone size was comparable to the 7-km zone size in some circumstances. PMID:28119920

Uncertainty Quantification in Simulations of Epidemics Using Polynomial Chaos

PubMed Central

Santonja, F.; Chen-Charpentier, B.

2012-01-01

Mathematical models based on ordinary differential equations are a useful tool to study the processes involved in epidemiology. Many models consider that the parameters are deterministic variables. But in practice, the transmission parameters present large variability and it is not possible to determine them exactly, and it is necessary to introduce randomness. In this paper, we present an application of the polynomial chaos approach to epidemiological mathematical models based on ordinary differential equations with random coefficients. Taking into account the variability of the transmission parameters of the model, this approach allows us to obtain an auxiliary system of differential equations, which is then integrated numerically to obtain the first-and the second-order moments of the output stochastic processes. A sensitivity analysis based on the polynomial chaos approach is also performed to determine which parameters have the greatest influence on the results. As an example, we will apply the approach to an obesity epidemic model. PMID:22927889

Modeling human mobility responses to the large-scale spreading of infectious diseases.

PubMed

Meloni, Sandro; Perra, Nicola; Arenas, Alex; Gómez, Sergio; Moreno, Yamir; Vespignani, Alessandro

2011-01-01

Current modeling of infectious diseases allows for the study of realistic scenarios that include population heterogeneity, social structures, and mobility processes down to the individual level. The advances in the realism of epidemic description call for the explicit modeling of individual behavioral responses to the presence of disease within modeling frameworks. Here we formulate and analyze a metapopulation model that incorporates several scenarios of self-initiated behavioral changes into the mobility patterns of individuals. We find that prevalence-based travel limitations do not alter the epidemic invasion threshold. Strikingly, we observe in both synthetic and data-driven numerical simulations that when travelers decide to avoid locations with high levels of prevalence, this self-initiated behavioral change may enhance disease spreading. Our results point out that the real-time availability of information on the disease and the ensuing behavioral changes in the population may produce a negative impact on disease containment and mitigation.

A dynamic model of the marriage market-Part 2: simulation of marital states and application to empirical data.

PubMed

Matthews, A P; Garenne, M L

2013-09-01

A dynamic, two-sex, age-structured marriage model is presented. Part 1 focused on first marriage only and described a marriage market matching algorithm. In Part 2 the model is extended to include divorce, widowing, and remarriage. The model produces a self-consistent set of marital states distributed by age and sex in a stable population by means of a gender-symmetric numerical method. The model is compared with empirical data for the case of Zambia. Furthermore, a dynamic marriage function for a changing population is demonstrated in simulations of three hypothetical scenarios of elevated mortality in young to middle adulthood. The marriage model has its primary application to simulation of HIV-AIDS epidemics in African countries. Copyright © 2013 Elsevier Inc. All rights reserved.

Climate Change, Population Immunity, and Hyperendemicity in the Transmission Threshold of Dengue

PubMed Central

Oki, Mika; Yamamoto, Taro

2012-01-01

Background It has been suggested that the probability of dengue epidemics could increase because of climate change. The probability of epidemics is most commonly evaluated by the basic reproductive number (R0), and in mosquito-borne diseases, mosquito density (the number of female mosquitoes per person [MPP]) is the critical determinant of the R0 value. In dengue-endemic areas, 4 different serotypes of dengue virus coexist–a state known as hyperendemicity–and a certain proportion of the population is immune to one or more of these serotypes. Nevertheless, these factors are not included in the calculation of R0. We aimed to investigate the effects of temperature change, population immunity, and hyperendemicity on the threshold MPP that triggers an epidemic. Methods and Findings We designed a mathematical model of dengue transmission dynamics. An epidemic was defined as a 10% increase in seroprevalence in a year, and the MPP that triggered an epidemic was defined as the threshold MPP. Simulations were conducted in Singapore based on the recorded temperatures from 1980 to 2009 The threshold MPP was estimated with the effect of (1) temperature only; (2) temperature and fluctuation of population immunity; and (3) temperature, fluctuation of immunity, and hyperendemicity. When only the effect of temperature was considered, the threshold MPP was estimated to be 0.53 in the 1980s and 0.46 in the 2000s, a decrease of 13.2%. When the fluctuation of population immunity and hyperendemicity were considered in the model, the threshold MPP decreased by 38.7%, from 0.93 to 0.57, from the 1980s to the 2000s. Conclusions The threshold MPP was underestimated if population immunity was not considered and overestimated if hyperendemicity was not included in the simulations. In addition to temperature, these factors are particularly important when quantifying the threshold MPP for the purpose of setting goals for vector control in dengue-endemic areas. PMID:23144746

Climate change, population immunity, and hyperendemicity in the transmission threshold of dengue.

PubMed

Oki, Mika; Yamamoto, Taro

2012-01-01

It has been suggested that the probability of dengue epidemics could increase because of climate change. The probability of epidemics is most commonly evaluated by the basic reproductive number (R(0)), and in mosquito-borne diseases, mosquito density (the number of female mosquitoes per person [MPP]) is the critical determinant of the R(0) value. In dengue-endemic areas, 4 different serotypes of dengue virus coexist-a state known as hyperendemicity-and a certain proportion of the population is immune to one or more of these serotypes. Nevertheless, these factors are not included in the calculation of R(0). We aimed to investigate the effects of temperature change, population immunity, and hyperendemicity on the threshold MPP that triggers an epidemic. We designed a mathematical model of dengue transmission dynamics. An epidemic was defined as a 10% increase in seroprevalence in a year, and the MPP that triggered an epidemic was defined as the threshold MPP. Simulations were conducted in Singapore based on the recorded temperatures from 1980 to 2009 The threshold MPP was estimated with the effect of (1) temperature only; (2) temperature and fluctuation of population immunity; and (3) temperature, fluctuation of immunity, and hyperendemicity. When only the effect of temperature was considered, the threshold MPP was estimated to be 0.53 in the 1980s and 0.46 in the 2000s, a decrease of 13.2%. When the fluctuation of population immunity and hyperendemicity were considered in the model, the threshold MPP decreased by 38.7%, from 0.93 to 0.57, from the 1980s to the 2000s. The threshold MPP was underestimated if population immunity was not considered and overestimated if hyperendemicity was not included in the simulations. In addition to temperature, these factors are particularly important when quantifying the threshold MPP for the purpose of setting goals for vector control in dengue-endemic areas.

Time-spatial model on the dynamics of the proliferation of Aedes aegypti

NASA Astrophysics Data System (ADS)

Gouvêa, Maury Meirelles, Jr.

2017-03-01

Some complex physical systems, such as cellular regulation, ecosystems, and societies, can be represented by local interactions between agents. Then, complex behaviors may emerge. A cellular automaton is a discrete dynamic system with these features. Among the several complex systems, epidemic diseases are given special attention by researchers with respect to their dynamics. Understanding the behavior of an epidemic may well benefit a society. For instance, different proliferation scenarios may be produced and a prevention policy set. This paper presents a new simulation method of the time-spatial spread of the Dengue mosquito with a cellular automaton. Thus, it will be possible to create different dissemination scenarios and preventive policies for these in several regions. Simulations were performed with different initial conditions and parameters as a result of which the behavior of the proposed method was characterized.

Small-world network model of propagation of the AIDS epidemic

NASA Astrophysics Data System (ADS)

Shi, Pengliang; Small, Michael

2004-03-01

Sexual contact and intravenus drug-use are the most common modes of transmission of HIV-AIDS. In this paper, homogenerous and heterogeneous models are proposed to model the dynamics in a system contains Small-World clusters. Four high risk groups: intravenus drug-users (D); homosexuals (H); individuals with multiple-sexual partners (M) and prostitutes (P), are classified using two models. Both networks are embedded among a background (low-risk) population using rich-get-richer preferential attachment. When a network is established, an epidemic is simulated in it by seeding randomly. We compare the two epidemic networks in detail and consider the effect of different levels of control policies in both. This study highlights two main conclusions: (i) set high protection coefficient for a massive-linkage-vertex (i.e. protect the highly connected individuals); and, (ii) a quick removal for the infected massive-linkage-veterx from the network is essential (rapidly quarantine infected individuals). While these conclusions may be intuitive, they indicate a necessary change of public policy toward prostitution in some developing countries such as China and India. An active effort to prevent possible infection from super-spreader is recommended.

Reconstructing a spatially heterogeneous epidemic: Characterising the geographic spread of 2009 A/H1N1pdm infection in England

NASA Astrophysics Data System (ADS)

Birrell, Paul J.; Zhang, Xu-Sheng; Pebody, Richard G.; Gay, Nigel J.; de Angelis, Daniela

2016-07-01

Understanding how the geographic distribution of and movements within a population influence the spatial spread of infections is crucial for the design of interventions to curb transmission. Existing knowledge is typically based on results from simulation studies whereas analyses of real data remain sparse. The main difficulty in quantifying the spatial pattern of disease spread is the paucity of available data together with the challenge of incorporating optimally the limited information into models of disease transmission. To address this challenge the role of routine migration on the spatial pattern of infection during the epidemic of 2009 pandemic influenza in England is investigated here through two modelling approaches: parallel-region models, where epidemics in different regions are assumed to occur in isolation with shared characteristics; and meta-region models where inter-region transmission is expressed as a function of the commuter flux between regions. Results highlight that the significantly less computationally demanding parallel-region approach is sufficiently flexible to capture the underlying dynamics. This suggests that inter-region movement is either inaccurately characterized by the available commuting data or insignificant once its initial impact on transmission has subsided.

Modelling Drug Abuse Epidemics in the Presence of Limited Rehabilitation Capacity.

PubMed

Mushanyu, J; Nyabadza, F; Muchatibaya, G; Stewart, A G R

2016-12-01

The abuse of drugs is now an epidemic globally whose control has been mainly through rehabilitation. The demand for drug abuse rehabilitation has not been matched with the available capacity resulting in limited placement of addicts into rehabilitation. In this paper, we model limited rehabilitation through the Hill function incorporated into a system of nonlinear ordinary differential equations. Not every member of the community is equally likely to embark on drug use, risk structure is included to help differentiate those more likely (high risk) to abuse drugs and those less likely (low risk) to abuse drugs. It is shown that the model has multiple equilibria, and using the centre manifold theory, the model exhibits the phenomenon of backward bifurcation whose implications to rehabilitation are discussed. Sensitivity analysis and numerical simulations are performed. The results show that saturation in rehabilitation will in the long run lead to the escalation of drug abuse. This means that limited access to rehabilitation has negative implications in the fight against drug abuse where rehabilitation is the main form of control. This suggests that increased access to rehabilitation is likely to lower the drug abuse epidemic.

Modeling Routes of Chronic Wasting Disease Transmission: Environmental Prion Persistence Promotes Deer Population Decline and Extinction

PubMed Central

Almberg, Emily S.; Cross, Paul C.; Johnson, Christopher J.; Heisey, Dennis M.; Richards, Bryan J.

2011-01-01

Chronic wasting disease (CWD) is a fatal disease of deer, elk, and moose transmitted through direct, animal-to-animal contact, and indirectly, via environmental contamination. Considerable attention has been paid to modeling direct transmission, but despite the fact that CWD prions can remain infectious in the environment for years, relatively little information exists about the potential effects of indirect transmission on CWD dynamics. In the present study, we use simulation models to demonstrate how indirect transmission and the duration of environmental prion persistence may affect epidemics of CWD and populations of North American deer. Existing data from Colorado, Wyoming, and Wisconsin's CWD epidemics were used to define plausible short-term outcomes and associated parameter spaces. Resulting long-term outcomes range from relatively low disease prevalence and limited host-population decline to host-population collapse and extinction. Our models suggest that disease prevalence and the severity of population decline is driven by the duration that prions remain infectious in the environment. Despite relatively low epidemic growth rates, the basic reproductive number, R 0, may be much larger than expected under the direct-transmission paradigm because the infectious period can vastly exceed the host's life span. High prion persistence is expected to lead to an increasing environmental pool of prions during the early phases (i.e. approximately during the first 50 years) of the epidemic. As a consequence, over this period of time, disease dynamics will become more heavily influenced by indirect transmission, which may explain some of the observed regional differences in age and sex-specific disease patterns. This suggests management interventions, such as culling or vaccination, will become increasingly less effective as CWD epidemics progress. PMID:21603638

Modeling routes of chronic wasting disease transmission: Environmental prion persistence promotes deer population decline and extinction

USGS Publications Warehouse

Almberg, Emily S.; Cross, Paul C.; Johnson, Christopher J.; Heisey, Dennis M.; Richards, Bryan J.

2011-01-01

Chronic wasting disease (CWD) is a fatal disease of deer, elk, and moose transmitted through direct, animal-to-animal contact, and indirectly, via environmental contamination. Considerable attention has been paid to modeling direct transmission, but despite the fact that CWD prions can remain infectious in the environment for years, relatively little information exists about the potential effects of indirect transmission on CWD dynamics. In the present study, we use simulation models to demonstrate how indirect transmission and the duration of environmental prion persistence may affect epidemics of CWD and populations of North American deer. Existing data from Colorado, Wyoming, and Wisconsin's CWD epidemics were used to define plausible short-term outcomes and associated parameter spaces. Resulting long-term outcomes range from relatively low disease prevalence and limited host-population decline to host-population collapse and extinction. Our models suggest that disease prevalence and the severity of population decline is driven by the duration that prions remain infectious in the environment. Despite relatively low epidemic growth rates, the basic reproductive number, R0, may be much larger than expected under the direct-transmission paradigm because the infectious period can vastly exceed the host's life span. High prion persistence is expected to lead to an increasing environmental pool of prions during the early phases (i.e. approximately during the first 50 years) of the epidemic. As a consequence, over this period of time, disease dynamics will become more heavily influenced by indirect transmission, which may explain some of the observed regional differences in age and sex-specific disease patterns. This suggests management interventions, such as culling or vaccination, will become increasingly less effective as CWD epidemics progress.

Spatial spreading of infectious disease via local and national mobility networks in South Korea

NASA Astrophysics Data System (ADS)

Kwon, Okyu; Son, Woo-Sik

2017-12-01

We study the spread of infectious disease based on local- and national-scale mobility networks. We construct a local mobility network using data on urban bus services to estimate local-scale movement of people. We also construct a national mobility network from orientation-destination data of vehicular traffic between highway tollgates to evaluate national-scale movement of people. A metapopulation model is used to simulate the spread of epidemics. Thus, the number of infected people is simulated using a susceptible-infectious-recovered (SIR) model within the administrative division, and inter-division spread of infected people is determined through local and national mobility networks. In this paper, we consider two scenarios for epidemic spread. In the first, the infectious disease only spreads through local-scale movement of people, that is, the local mobility network. In the second, it spreads via both local and national mobility networks. For the former, the simulation results show infected people sequentially spread to neighboring divisions. Yet for the latter, we observe a faster spreading pattern to distant divisions. Thus, we confirm the national mobility network enhances synchronization among the incidence profiles of all administrative divisions.

Temporal dynamics of connectivity and epidemic properties of growing networks

NASA Astrophysics Data System (ADS)

Fotouhi, Babak; Shirkoohi, Mehrdad Khani

2016-01-01

Traditional mathematical models of epidemic disease had for decades conventionally considered static structure for contacts. Recently, an upsurge of theoretical inquiry has strived towards rendering the models more realistic by incorporating the temporal aspects of networks of contacts, societal and online, that are of interest in the study of epidemics (and other similar diffusion processes). However, temporal dynamics have predominantly focused on link fluctuations and nodal activities, and less attention has been paid to the growth of the underlying network. Many real networks grow: Online networks are evidently in constant growth, and societal networks can grow due to migration flux and reproduction. The effect of network growth on the epidemic properties of networks is hitherto unknown, mainly due to the predominant focus of the network growth literature on the so-called steady state. This paper takes a step towards alleviating this gap. We analytically study the degree dynamics of a given arbitrary network that is subject to growth. We use the theoretical findings to predict the epidemic properties of the network as a function of time. We observe that the introduction of new individuals into the network can enhance or diminish its resilience against endemic outbreaks and investigate how this regime shift depends upon the connectivity of newcomers and on how they establish connections to existing nodes. Throughout, theoretical findings are corroborated with Monte Carlo simulations over synthetic and real networks. The results shed light on the effects of network growth on the future epidemic properties of networks and offers insights for devising a priori immunization strategies.

Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study

PubMed Central

Katriel, G.; Yaari, R.; Huppert, A.; Roll, U.; Stone, L.

2011-01-01

This paper presents new computational and modelling tools for studying the dynamics of an epidemic in its initial stages that use both available incidence time series and data describing the population's infection network structure. The work is motivated by data collected at the beginning of the H1N1 pandemic outbreak in Israel in the summer of 2009. We formulated a new discrete-time stochastic epidemic SIR (susceptible-infected-recovered) model that explicitly takes into account the disease's specific generation-time distribution and the intrinsic demographic stochasticity inherent to the infection process. Moreover, in contrast with many other modelling approaches, the model allows direct analytical derivation of estimates for the effective reproductive number (Re) and of their credible intervals, by maximum likelihood and Bayesian methods. The basic model can be extended to include age–class structure, and a maximum likelihood methodology allows us to estimate the model's next-generation matrix by combining two types of data: (i) the incidence series of each age group, and (ii) infection network data that provide partial information of ‘who-infected-who’. Unlike other approaches for estimating the next-generation matrix, the method developed here does not require making a priori assumptions about the structure of the next-generation matrix. We show, using a simulation study, that even a relatively small amount of information about the infection network greatly improves the accuracy of estimation of the next-generation matrix. The method is applied in practice to estimate the next-generation matrix from the Israeli H1N1 pandemic data. The tools developed here should be of practical importance for future investigations of epidemics during their initial stages. However, they require the availability of data which represent a random sample of the real epidemic process. We discuss the conditions under which reporting rates may or may not influence our estimated quantities and the effects of bias. PMID:21247949

A chaotic model for the plague epidemic that has occurred in Bombay at the end of the 19th century

NASA Astrophysics Data System (ADS)

Mangiarotti, Sylvain

2015-04-01

The plague epidemic that has occurred in Bombay at the end of the 19th century was detected in 1896. One year before, an Advisory Committee had been appointed by the Secretary of State for India, the Royal Society, and the Lister Institute. This Committee made numerous investigations and gathered a large panel of data including the number of people attacked and died from the plague, records of rat and flea populations, as well as meteorological records of temperature and humidity [1]. The global modeling technique [2] aims to obtain low dimensional models able to simulate the observed cycles from time series. As far as we know, this technique has been tried only to one case of epidemiological analysis (the whooping cough infection) based on a discrete formulation [3]. In the present work, the continuous time formulation of this technique is used to analyze the time evolution of the plague epidemic from this data set. One low dimensional model (three variables) is obtained exhibiting a limit cycle of period-5. A chaotic behavior could be derived from this model by tuning the model parameters. It provides a strong argument for a dynamical behavior that can be approximated by low dimensional deterministic equations. This model also provides an empirical argument for chaos in epidemics. [1] Verjbitski D. T., Bannerman W. B. & Kápadiâ R. T., 1908. Reports on Plague Investigations in India (May,1908), The Journal of Hygiene, 8(2), 161 -308. [2] Mangiarotti S., Coudret R., Drapeau L. & Jarlan L., 2012. Polynomial search and Global modelling: two algorithms for modeling chaos. Physical Review E, 86(4), 046205. [3] Boudjema G. & Cazelles B., 2003. Extraction of nonlinear dynamics from short and noisy time series. Chaos, Solitons and Fractals, 12, 2051-2069.

Discrete-time moment closure models for epidemic spreading in populations of interacting individuals.

PubMed

Frasca, Mattia; Sharkey, Kieran J

2016-06-21

Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies. Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.

Epidemic thresholds for bipartite networks

NASA Astrophysics Data System (ADS)

Hernández, D. G.; Risau-Gusman, S.

2013-11-01

It is well known that sexually transmitted diseases (STD) spread across a network of human sexual contacts. This network is most often bipartite, as most STD are transmitted between men and women. Even though network models in epidemiology have quite a long history now, there are few general results about bipartite networks. One of them is the simple dependence, predicted using the mean field approximation, between the epidemic threshold and the average and variance of the degree distribution of the network. Here we show that going beyond this approximation can lead to qualitatively different results that are supported by numerical simulations. One of the new features, that can be relevant for applications, is the existence of a critical value for the infectivity of each population, below which no epidemics can arise, regardless of the value of the infectivity of the other population.

Evaluating Temporal Factors in Combined Interventions of Workforce Shift and School Closure for Mitigating the Spread of Influenza

PubMed Central

Zhang, Tianyou; Fu, Xiuju; Ma, Stefan; Xiao, Gaoxi; Wong, Limsoon; Kwoh, Chee Keong; Lees, Michael; Lee, Gary Kee Khoon; Hung, Terence

2012-01-01

Background It is believed that combined interventions may be more effective than individual interventions in mitigating epidemic. However there is a lack of quantitative studies on performance of the combination of individual interventions under different temporal settings. Methodology/Principal Findings To better understand the problem, we develop an individual-based simulation model running on top of contact networks based on real-life contact data in Singapore. We model and evaluate the spread of influenza epidemic with intervention strategies of workforce shift and its combination with school closure, and examine the impacts of temporal factors, namely the trigger threshold and the duration of an intervention. By comparing simulation results for intervention scenarios with different temporal factors, we find that combined interventions do not always outperform individual interventions and are more effective only when the duration is longer than 6 weeks or school closure is triggered at the 5% threshold; combined interventions may be more effective if school closure starts first when the duration is less than 4 weeks or workforce shift starts first when the duration is longer than 4 weeks. Conclusions/Significance We therefore conclude that identifying the appropriate timing configuration is crucial for achieving optimal or near optimal performance in mitigating the spread of influenza epidemic. The results of this study are useful to policy makers in deliberating and planning individual and combined interventions. PMID:22403634

Bursts of Vertex Activation and Epidemics in Evolving Networks

PubMed Central

Rocha, Luis E. C.; Blondel, Vincent D.

2013-01-01

The dynamic nature of contact patterns creates diverse temporal structures. In particular, empirical studies have shown that contact patterns follow heterogeneous inter-event time intervals, meaning that periods of high activity are followed by long periods of inactivity. To investigate the impact of these heterogeneities in the spread of infection from a theoretical perspective, we propose a stochastic model to generate temporal networks where vertices make instantaneous contacts following heterogeneous inter-event intervals, and may leave and enter the system. We study how these properties affect the prevalence of an infection and estimate , the number of secondary infections of an infectious individual in a completely susceptible population, by modeling simulated infections (SI and SIR) that co-evolve with the network structure. We find that heterogeneous contact patterns cause earlier and larger epidemics in the SIR model in comparison to homogeneous scenarios for a vast range of parameter values, while smaller epidemics may happen in some combinations of parameters. In the case of SI and heterogeneous patterns, the epidemics develop faster in the earlier stages followed by a slowdown in the asymptotic limit. For increasing vertex turnover rates, heterogeneous patterns generally cause higher prevalence in comparison to homogeneous scenarios with the same average inter-event interval. We find that is generally higher for heterogeneous patterns, except for sufficiently large infection duration and transmission probability. PMID:23555211

Stage-structured infection transmission and a spatial epidemic: a model for Lyme disease.

PubMed

Caraco, Thomas; Glavanakov, Stephan; Chen, Gang; Flaherty, Joseph E; Ohsumi, Toshiro K; Szymanski, Boleslaw K

2002-09-01

A greater understanding of the rate at which emerging disease advances spatially has both ecological and applied significance. Analyzing the spread of vector-borne disease can be relatively complex when the vector's acquisition of a pathogen and subsequent transmission to a host occur in different life stages. A contemporary example is Lyme disease. A long-lived tick vector acquires infection during the larval blood meal and transmits it as a nymph. We present a reaction-diffusion model for the ecological dynamics governing the velocity of the current epidemic's spread. We find that the equilibrium density of infectious tick nymphs (hence the risk of human disease) can depend on density-independent survival interacting with biotic effects on the tick's stage structure. The local risk of infection reaches a maximum at an intermediate level of adult tick mortality and at an intermediate rate of juvenile tick attacks on mammalian hosts. If the juvenile tick attack rate is low, an increase generates both a greater density of infectious nymphs and an increased spatial velocity. However, if the juvenile attack rate is relatively high, nymph density may decline while the epidemic's velocity still increases. Velocities of simulated two-dimensional epidemics correlate with the model pathogen's basic reproductive number (R0), but calculating R0 involves parameters of both host infection dynamics and the vector's stage-structured dynamics.

Stability analysis and application of a mathematical cholera model.

PubMed

Liao, Shu; Wang, Jin

2011-07-01

In this paper, we conduct a dynamical analysis of the deterministic cholera model proposed in [9]. We study the stability of both the disease-free and endemic equilibria so as to explore the complex epidemic and endemic dynamics of the disease. We demonstrate a real-world application of this model by investigating the recent cholera outbreak in Zimbabwe. Meanwhile, we present numerical simulation results to verify the analytical predictions.

Forecasting Epidemics Through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model.

PubMed

Smirnova, Alexandra; deCamp, Linda; Chowell, Gerardo

2017-05-02

Deterministic and stochastic methods relying on early case incidence data for forecasting epidemic outbreaks have received increasing attention during the last few years. In mathematical terms, epidemic forecasting is an ill-posed problem due to instability of parameter identification and limited available data. While previous studies have largely estimated the time-dependent transmission rate by assuming specific functional forms (e.g., exponential decay) that depend on a few parameters, here we introduce a novel approach for the reconstruction of nonparametric time-dependent transmission rates by projecting onto a finite subspace spanned by Legendre polynomials. This approach enables us to effectively forecast future incidence cases, the clear advantage over recovering the transmission rate at finitely many grid points within the interval where the data are currently available. In our approach, we compare three regularization algorithms: variational (Tikhonov's) regularization, truncated singular value decomposition (TSVD), and modified TSVD in order to determine the stabilizing strategy that is most effective in terms of reliability of forecasting from limited data. We illustrate our methodology using simulated data as well as case incidence data for various epidemics including the 1918 influenza pandemic in San Francisco and the 2014-2015 Ebola epidemic in West Africa.

Optimal control analysis of Ebola disease with control strategies of quarantine and vaccination.

PubMed

Ahmad, Muhammad Dure; Usman, Muhammad; Khan, Adnan; Imran, Mudassar

2016-07-13

The 2014 Ebola epidemic is the largest in history, affecting multiple countries in West Africa. Some isolated cases were also observed in other regions of the world. In this paper, we introduce a deterministic SEIR type model with additional hospitalization, quarantine and vaccination components in order to understand the disease dynamics. Optimal control strategies, both in the case of hospitalization (with and without quarantine) and vaccination are used to predict the possible future outcome in terms of resource utilization for disease control and the effectiveness of vaccination on sick populations. Further, with the help of uncertainty and sensitivity analysis we also have identified the most sensitive parameters which effectively contribute to change the disease dynamics. We have performed mathematical analysis with numerical simulations and optimal control strategies on Ebola virus models. We used dynamical system tools with numerical simulations and optimal control strategies on our Ebola virus models. The original model, which allowed transmission of Ebola virus via human contact, was extended to include imperfect vaccination and quarantine. After the qualitative analysis of all three forms of Ebola model, numerical techniques, using MATLAB as a platform, were formulated and analyzed in detail. Our simulation results support the claims made in the qualitative section. Our model incorporates an important component of individuals with high risk level with exposure to disease, such as front line health care workers, family members of EVD patients and Individuals involved in burial of deceased EVD patients, rather than the general population in the affected areas. Our analysis suggests that in order for R 0 (i.e., the basic reproduction number) to be less than one, which is the basic requirement for the disease elimination, the transmission rate of isolated individuals should be less than one-fourth of that for non-isolated ones. Our analysis also predicts, we need high levels of medication and hospitalization at the beginning of an epidemic. Further, optimal control analysis of the model suggests the control strategies that may be adopted by public health authorities in order to reduce the impact of epidemics like Ebola.

Model for disease dynamics of a waterborne pathogen on a random network.

PubMed

Li, Meili; Ma, Junling; van den Driessche, P

2015-10-01

A network epidemic SIWR model for cholera and other diseases that can be transmitted via the environment is developed and analyzed. The person-to-person contacts are modeled by a random contact network, and the contagious environment is modeled by an external node that connects to every individual. The model is adapted from the Miller network SIR model, and in the homogeneous mixing limit becomes the Tien and Earn deterministic cholera model without births and deaths. The dynamics of our model shows excellent agreement with stochastic simulations. The basic reproduction number [Formula: see text] is computed, and on a Poisson network shown to be the sum of the basic reproduction numbers of the person-to-person and person-to-water-to-person transmission pathways. However, on other networks, [Formula: see text] depends nonlinearly on the transmission along the two pathways. Type reproduction numbers are computed and quantify measures to control the disease. Equations giving the final epidemic size are obtained.

Social networks and spreading of epidemics

NASA Astrophysics Data System (ADS)

Trimper, Steffen; Zheng, Dafang; Brandau, Marian

2004-05-01

Epidemiological processes are studied within a recently proposed social network model using the susceptible-infected-refractory dynamics (SIR) of an epidemic. Within the network model, a population of individuals may be characterized by H independent hierarchies or dimensions, each of which consists of groupings of individuals into layers of subgroups. Detailed numerical simulations reveals that for H > 1, the global spreading results regardless of the degree of homophily α of the individuals forming a social circle. For H = 1, a transition from a global to a local spread occurs as the population becomes decomposed into increasingly homophilous groups. Multiple dimensions in classifying individuals (nodes) thus make a society (computer network) highly susceptible to large scale outbreaks of infectious diseases (viruses). The SIR-model can be extended by the inclusion of waiting times resulting in modified distribution function of the recovered.

A comparison between two simulation models for spread of foot-and-mouth disease.

PubMed

Halasa, Tariq; Boklund, Anette; Stockmarr, Anders; Enøe, Claes; Christiansen, Lasse E

2014-01-01

Two widely used simulation models of foot-and-mouth disease (FMD) were used in order to compare the models' predictions in term of disease spread, consequence, and the ranking of the applied control strategies, and to discuss the effect of the way disease spread is modeled on the predicted outcomes of each model. The DTU-DADS (version 0.100), and ISP (version 2.001.11) were used to simulate a hypothetical spread of FMD in Denmark. Actual herd type, movements, and location data in the period 1st October 2006 and 30th September 2007 was used. The models simulated the spread of FMD using 3 different control scenarios: 1) A basic scenario representing EU and Danish control strategies, 2) pre-emptive depopulation of susceptible herds within a 500 meters radius around the detected herds, and 3) suppressive vaccination of susceptible herds within a 1,000 meters radius around the detected herds. Depopulation and vaccination started 14 days following the detection of the first infected herd. Five thousand index herds were selected randomly, of which there were 1,000 cattle herds located in high density cattle areas and 1,000 in low density cattle areas, 1,000 swine herds located in high density swine areas and 1,000 in low density swine areas, and 1,000 sheep herds. Generally, DTU-DADS predicted larger, longer duration and costlier epidemics than ISP, except when epidemics started in cattle herds located in high density cattle areas. ISP supported suppressive vaccination rather than pre-emptive depopulation, while DTU-DADS was indifferent to the alternative control strategies. Nonetheless, the absolute differences between control strategies were small making the choice of control strategy during an outbreak to be most likely based on practical reasons.

Deciphering Dynamics of Recent Epidemic Spread and Outbreak in West Africa: The Case of Ebola Virus

NASA Astrophysics Data System (ADS)

Upadhyay, Ranjit Kumar; Roy, Parimita

Recently, the 2014 Ebola virus (EBOV) outbreak in West Africa was the largest outbreak to date. In this paper, an attempt has been made for modeling the virus dynamics using an SEIR model to better understand and characterize the transmission trajectories of the Ebola outbreak. We compare the simulated results with the most recent reported data of Ebola infected cases in the three most affected countries Guinea, Liberia and Sierra Leone. The epidemic model exhibits two equilibria, namely, the disease-free and unique endemic equilibria. Existence and local stability of these equilibria are explored. Using central manifold theory, it is established that the transcritical bifurcation occurs when basic reproduction number passes through unity. The proposed Ebola epidemic model provides an estimate to the potential number of future cases. The model indicates that the disease will decline after peaking if multisectorial and multinational efforts to control the spread of infection are maintained. Possible implication of the results for disease eradication and its control are discussed which suggests that proper control strategies like: (i) transmission precautions, (ii) isolation and care of infectious Ebola patients, (iii) safe burial, (iv) contact tracing with follow-up and quarantine, and (v) early diagnosis are needed to stop the recurrent outbreak.

Effects of Pre-industrial Agricultural Expansion and Epidemics on the Climate and the Carbon Cycle

NASA Astrophysics Data System (ADS)

Pongratz, J.; Raddatz, T.; Reick, C.; Claussen, M.

2008-12-01

To assess the effects of anthropogenic land cover change on the pre-industrial climate and carbon cycle we apply a new, detailed reconstruction of land cover for the last millennium in a general circulation model. A transient simulation including the marine and terrestrial carbon cycle suggests that the agricultural expansion increased the atmospheric CO2 concentration by about 3.5 ppm between AD 800 and the late pre- industrial period. Taking into account land cover change prior to the last millennium, up to 5 ppm of the Holocene CO2 increase may be attributed to changes in vegetation and soil carbon as a consequence of agricultural activity. This value is smaller but of similar magnitude than the estimates by Ruddiman (2007). In contrast to his study the ocean is simulated to be a sink rather than a source of carbon at least during the last millennium, leaving much of the observed pre-industrial CO2 increase unexplained. On a regional scale, epidemics have the potential to change land cover by allowing natural vegetation to regrow on abandoned agricultural areas. While the land cover reconstruction indicates only small absolute changes in agricultural areas after European conquest of the Americas, it indicates forest regrowth on about 0.18 million km2 in Europe as a consequence of the medieval Black Death. For this event, simulations of radiative forcing show that the energy balance is significantly altered by the changes in surface albedo. This suggests that local to regional climate may be modified by the biogeophysical effects of vegetation changes induced by epidemics. First results, however, indicate that the amount of carbon taken up by the regrowing vegetation may not suffice to counterbalance the emissions of expanding agriculture in the other parts of the world. The effect on atmospheric CO2 concentrations may thus be small. Ensemble simulations are planned to compare the effects of epidemics on atmospheric CO2 with natural variability.

Dynamics of eco-epidemiological model with harvesting

NASA Astrophysics Data System (ADS)

Purnomo, Anna Silvia; Darti, Isnani; Suryanto, Agus

2017-12-01

In this paper, we study an eco-epidemiology model which is derived from S I epidemic model with bilinear incidence rate and modified Leslie Gower predator-prey model with harvesting on susceptible prey. Existence condition and stability of all equilibrium points are discussed for the proposed model. Furthermore, we show that the model exhibits a Hopf bifurcation around interior equilibrium point which is driven by the rate of infection. Our numerical simulations using some different value of parameters confirm our analytical analysis.

Contact, Travel, and Transmission: The Impact of Winter Holidays on Influenza Dynamics in the United States.

PubMed

Ewing, Anne; Lee, Elizabeth C; Viboud, Cécile; Bansal, Shweta

2017-03-01

The seasonality of influenza is thought to vary according to environmental factors and human behavior. During winter holidays, potential disease-causing contact and travel deviate from typical patterns. We aim to understand these changes on age-specific and spatial influenza transmission. We characterized the changes to transmission and epidemic trajectories among children and adults in a spatial context before, during, and after the winter holidays among aggregated physician medical claims in the United States from 2001 to 2009 and among synthetic data simulated from a deterministic, age-specific spatial metapopulation model. Winter holidays reduced influenza transmission and delayed the trajectory of influenza season epidemics. The holiday period was marked by a shift in the relative risk of disease from children toward adults. Model results indicated that holidays delayed epidemic peaks and synchronized incidence across locations, and that contact reductions from school closures, rather than age-specific mixing and travel, produced these observed holiday influenza dynamics. Winter holidays delay seasonal influenza epidemic peaks and shift disease risk toward adults because of changes in contact patterns. These findings may inform targeted influenza information and vaccination campaigns during holiday periods. © The Author 2016. Published by Oxford University Press for the Infectious Diseases Society of America. All rights reserved. For permissions, e-mail: journals.permissions@oup.com.

Public health interventions for epidemics: implications for multiple infection waves.

PubMed

Wessel, Lindsay; Hua, Yi; Wu, Jianhong; Moghadas, Seyed M

2011-02-25

Epidemics with multiple infection waves have been documented for some human diseases, most notably during past influenza pandemics. While pathogen evolution, co-infection, and behavioural changes have been proposed as possible mechanisms for the occurrence of subsequent outbreaks, the effect of public health interventions remains undetermined. We develop mean-field and stochastic epidemiological models for disease transmission, and perform simulations to show how control measures, such as drug treatment and isolation of ill individuals, can influence the epidemic profile and generate sequences of infection waves with different characteristics. We demonstrate the impact of parameters representing the effectiveness and adverse consequences of intervention measures, such as treatment and emergence of drug resistance, on the spread of a pathogen in the population. If pathogen resistant strains evolve under drug pressure, multiple outbreaks are possible with variability in their characteristics, magnitude, and timing. In this context, the level of drug use and isolation capacity play an important role in the occurrence of subsequent outbreaks. Our simulations for influenza infection as a case study indicate that the intensive use of these interventions during the early stages of the epidemic could delay the spread of disease, but it may also result in later infection waves with possibly larger magnitudes. The findings highlight the importance of intervention parameters in the process of public health decision-making, and in evaluating control measures when facing substantial uncertainty regarding the epidemiological characteristics of an emerging infectious pathogen. Critical factors that influence population health including evolutionary responses of the pathogen under the pressure of different intervention measures during an epidemic should be considered for the design of effective strategies that address short-term targets compatible with long-term disease outcomes.

Persistence and extinction for a class of stochastic SIS epidemic models with nonlinear incidence rate

NASA Astrophysics Data System (ADS)

Teng, Zhidong; Wang, Lei

2016-06-01

In this paper, a class of stochastic SIS epidemic models with nonlinear incidence rate is investigated. It is shown that the extinction and persistence of the disease in probability are determined by a threshold value R˜0. That is, if R˜0 < 1 and an additional condition holds then disease dies out, and if R˜0 > 1 then disease is weak permanent with probability one. To obtain the permanence in the mean of the disease, a new quantity R̂0 is introduced, and it is proved that if R̂0 > 1 the disease is permanent in the mean with probability one. Furthermore, the numerical simulations are presented to illustrate some open problems given in Remarks 1-3 and 5 of this paper.

Chimera states in multi-strain epidemic models with temporary immunity

NASA Astrophysics Data System (ADS)

Bauer, Larissa; Bassett, Jason; Hövel, Philipp; Kyrychko, Yuliya N.; Blyuss, Konstantin B.

2017-11-01

We investigate a time-delayed epidemic model for multi-strain diseases with temporary immunity. In the absence of cross-immunity between strains, dynamics of each individual strain exhibit emergence and annihilation of limit cycles due to a Hopf bifurcation of the endemic equilibrium, and a saddle-node bifurcation of limit cycles depending on the time delay associated with duration of temporary immunity. Effects of all-to-all and non-local coupling topologies are systematically investigated by means of numerical simulations, and they suggest that cross-immunity is able to induce a diverse range of complex dynamical behaviors and synchronization patterns, including discrete traveling waves, solitary states, and amplitude chimeras. Interestingly, chimera states are observed for narrower cross-immunity kernels, which can have profound implications for understanding the dynamics of multi-strain diseases.

Modeling US Adult Obesity Trends: A System Dynamics Model for Estimating Energy Imbalance Gap

PubMed Central

Rahmandad, Hazhir; Huang, Terry T.-K.; Bures, Regina M.; Glass, Thomas A.

2014-01-01

Objectives. We present a system dynamics model that quantifies the energy imbalance gap responsible for the US adult obesity epidemic among gender and racial subpopulations. Methods. We divided the adult population into gender–race/ethnicity subpopulations and body mass index (BMI) classes. We defined transition rates between classes as a function of metabolic dynamics of individuals within each class. We estimated energy intake in each BMI class within the past 4 decades as a multiplication of the equilibrium energy intake of individuals in that class. Through calibration, we estimated the energy gap multiplier for each gender–race–BMI group by matching simulated BMI distributions for each subpopulation against national data with maximum likelihood estimation. Results. No subpopulation showed a negative or zero energy gap, suggesting that the obesity epidemic continues to worsen, albeit at a slower rate. In the past decade the epidemic has slowed for non-Hispanic Whites, is starting to slow for non-Hispanic Blacks, but continues to accelerate among Mexican Americans. Conclusions. The differential energy balance gap across subpopulations and over time suggests that interventions should be tailored to subpopulations’ needs. PMID:24832405

Epidemic dynamics on a risk-based evolving social network

NASA Astrophysics Data System (ADS)

Antwi, Shadrack; Shaw, Leah

2013-03-01

Social network models have been used to study how behavior affects the dynamics of an infection in a population. Motivated by HIV, we consider how a trade-off between benefits and risks of sexual connections determine network structure and disease prevalence. We define a stochastic network model with formation and breaking of links as changes in sexual contacts. Each node has an intrinsic benefit its neighbors derive from connecting to it. Nodes' infection status is not apparent to others, but nodes with more connections (higher degree) are assumed more likely to be infected. The probability to form and break links is determined by a payoff computed from the benefit and degree-dependent risk. The disease is represented by a SI (susceptible-infected) model. We study network and epidemic evolution via Monte Carlo simulation and analytically predict the behavior with a heterogeneous mean field approach. The dependence of network connectivity and infection threshold on parameters is determined, and steady state degree distribution and epidemic levels are obtained. We also study a situation where system-wide infection levels alter perception of risk and cause nodes to adjust their behavior. This is a case of an adaptive network, where node status feeds back to change network geometry.

Stability analysis of an HIV/AIDS epidemic model with treatment

NASA Astrophysics Data System (ADS)

Cai, Liming; Li, Xuezhi; Ghosh, Mini; Guo, Baozhu

2009-07-01

An HIV/AIDS epidemic model with treatment is investigated. The model allows for some infected individuals to move from the symptomatic phase to the asymptomatic phase by all sorts of treatment methods. We first establish the ODE treatment model with two infective stages. Mathematical analyses establish that the global dynamics of the spread of the HIV infectious disease are completely determined by the basic reproduction number [real]0. If [real]0<=1, the disease-free equilibrium is globally stable, whereas the unique infected equilibrium is globally asymptotically stable if [real]0>1. Then, we introduce a discrete time delay to the model to describe the time from the start of treatment in the symptomatic stage until treatment effects become visible. The effect of the time delay on the stability of the endemically infected equilibrium is investigated. Moreover, the delay model exhibits Hopf bifurcations by using the delay as a bifurcation parameter. Finally, numerical simulations are presented to illustrate the results.

Evaluation of the risk of classical swine fever (CSF) spread from backyard pigs to other domestic pigs by using the spatial stochastic disease spread model Be-FAST: the example of Bulgaria.

PubMed

Martínez-López, Beatriz; Ivorra, Benjamin; Ramos, Angel Manuel; Fernández-Carrión, Eduardo; Alexandrov, Tsviatko; Sánchez-Vizcaíno, José Manuel

2013-07-26

The study presented here is one of the very first aimed at exploring the potential spread of classical swine fever (CSF) from backyard pigs to other domestic pigs. Specifically, we used a spatial stochastic spread model, called Be-FAST, to evaluate the potential spread of CSF virus (CSFV) in Bulgaria, which holds a large number of backyards (96% of the total number of pig farms) and is one of the very few countries for which backyard pigs and farm counts are available. The model revealed that, despite backyard pigs being very likely to become infected, infections from backyard pigs to other domestic pigs were rare. In general, the magnitude and duration of the CSF simulated epidemics were small, with a median [95% PI] number of infected farms per epidemic of 1 [1,4] and a median [95% PI] duration of the epidemic of 44 [17,101] days. CSFV transmission occurs primarily (81.16%) due to indirect contacts (i.e. vehicles, people and local spread) whereas detection of infected premises was mainly (69%) associated with the observation of clinical signs on farm rather than with implementation of tracing or zoning. Methods and results of this study may support the implementation of risk-based strategies more cost-effectively to prevent, control and, ultimately, eradicate CSF from Bulgaria. The model may also be easily adapted to other countries in which the backyard system is predominant. It can also be used to simulate other similar diseases such as African swine fever. Copyright © 2013 Elsevier B.V. All rights reserved.

Dynamics analysis of epidemic and information spreading in overlay networks.

PubMed

Liu, Guirong; Liu, Zhimei; Jin, Zhen

2018-05-07

We establish an SIS-UAU model to present the dynamics of epidemic and information spreading in overlay networks. The overlay network is represented by two layers: one where the dynamics of the epidemic evolves and another where the information spreads. We theoretically derive the explicit formulas for the basic reproduction number of awareness R 0 a by analyzing the self-consistent equation and the basic reproduction number of disease R 0 d by using the next generation matrix. The formula of R 0 d shows that the effect of awareness can reduce the basic reproduction number of disease. In particular, when awareness does not affect epidemic spreading, R 0 d is shown to match the existing theoretical results. Furthermore, we demonstrate that the disease-free equilibrium is globally asymptotically stable if R 0 d <1; and the endemic equilibrium is globally asymptotically stable if R 0 d >1. Finally, numerical simulations show that information plays a vital role in preventing and controlling disease and effectively reduces the final disease scale. Copyright © 2018 Elsevier Ltd. All rights reserved.

Optimal information dissemination strategy to promote preventive behaviors in multilayer epidemic networks.

PubMed

Shakeri, Heman; Sahneh, Faryad Darabi; Scoglio, Caterina; Poggi-Corradini, Pietro; Preciado, Victor M

2015-06-01

Launching a prevention campaign to contain the spread of infection requires substantial financial investments; therefore, a trade-off exists between suppressing the epidemic and containing costs. Information exchange among individuals can occur as physical contacts (e.g., word of mouth, gatherings), which provide inherent possibilities of disease transmission, and non-physical contacts (e.g., email, social networks), through which information can be transmitted but the infection cannot be transmitted. Contact network (CN) incorporates physical contacts, and the information dissemination network (IDN) represents non-physical contacts, thereby generating a multilayer network structure. Inherent differences between these two layers cause alerting through CN to be more effective but more expensive than IDN. The constraint for an epidemic to die out derived from a nonlinear Perron-Frobenius problem that was transformed into a semi-definite matrix inequality and served as a constraint for a convex optimization problem. This method guarantees a dying-out epidemic by choosing the best nodes for adopting preventive behaviors with minimum monetary resources. Various numerical simulations with network models and a real-world social network validate our method.

A Comparison between Two Simulation Models for Spread of Foot-and-Mouth Disease

PubMed Central

Halasa, Tariq; Boklund, Anette; Stockmarr, Anders; Enøe, Claes; Christiansen, Lasse E.

2014-01-01

Two widely used simulation models of foot-and-mouth disease (FMD) were used in order to compare the models’ predictions in term of disease spread, consequence, and the ranking of the applied control strategies, and to discuss the effect of the way disease spread is modeled on the predicted outcomes of each model. The DTU-DADS (version 0.100), and ISP (version 2.001.11) were used to simulate a hypothetical spread of FMD in Denmark. Actual herd type, movements, and location data in the period 1st October 2006 and 30th September 2007 was used. The models simulated the spread of FMD using 3 different control scenarios: 1) A basic scenario representing EU and Danish control strategies, 2) pre-emptive depopulation of susceptible herds within a 500 meters radius around the detected herds, and 3) suppressive vaccination of susceptible herds within a 1,000 meters radius around the detected herds. Depopulation and vaccination started 14 days following the detection of the first infected herd. Five thousand index herds were selected randomly, of which there were 1,000 cattle herds located in high density cattle areas and 1,000 in low density cattle areas, 1,000 swine herds located in high density swine areas and 1,000 in low density swine areas, and 1,000 sheep herds. Generally, DTU-DADS predicted larger, longer duration and costlier epidemics than ISP, except when epidemics started in cattle herds located in high density cattle areas. ISP supported suppressive vaccination rather than pre-emptive depopulation, while DTU-DADS was indifferent to the alternative control strategies. Nonetheless, the absolute differences between control strategies were small making the choice of control strategy during an outbreak to be most likely based on practical reasons. PMID:24667525

Simulation of an epidemic model with vector transmission

NASA Astrophysics Data System (ADS)

Dickman, Adriana G.; Dickman, Ronald

2015-03-01

We study a lattice model for vector-mediated transmission of a disease in a population consisting of two species, A and B, which contract the disease from one another. Individuals of species A are sedentary, while those of species B (the vector) diffuse in space. Examples of such diseases are malaria, dengue fever, and Pierce's disease in vineyards. The model exhibits a phase transition between an absorbing (infection free) phase and an active one as parameters such as infection rates and vector density are varied. We study the static and dynamic critical behavior of the model using initial spreading, initial decay, and quasistationary simulations. Simulations are checked against mean-field analysis. Although phase transitions to an absorbing state fall generically in the directed percolation universality class, this appears not to be the case for the present model.

Computational modeling and statistical analyses on individual contact rate and exposure to disease in complex and confined transportation hubs

NASA Astrophysics Data System (ADS)

Wang, W. L.; Tsui, K. L.; Lo, S. M.; Liu, S. B.

2018-01-01

Crowded transportation hubs such as metro stations are thought as ideal places for the development and spread of epidemics. However, for the special features of complex spatial layout, confined environment with a large number of highly mobile individuals, it is difficult to quantify human contacts in such environments, wherein disease spreading dynamics were less explored in the previous studies. Due to the heterogeneity and dynamic nature of human interactions, increasing studies proved the importance of contact distance and length of contact in transmission probabilities. In this study, we show how detailed information on contact and exposure patterns can be obtained by statistical analyses on microscopic crowd simulation data. To be specific, a pedestrian simulation model-CityFlow was employed to reproduce individuals' movements in a metro station based on site survey data, values and distributions of individual contact rate and exposure in different simulation cases were obtained and analyzed. It is interesting that Weibull distribution fitted the histogram values of individual-based exposure in each case very well. Moreover, we found both individual contact rate and exposure had linear relationship with the average crowd densities of the environments. The results obtained in this paper can provide reference to epidemic study in complex and confined transportation hubs and refine the existing disease spreading models.

The IDEA model: A single equation approach to the Ebola forecasting challenge.

PubMed

Tuite, Ashleigh R; Fisman, David N

2018-03-01

Mathematical modeling is increasingly accepted as a tool that can inform disease control policy in the face of emerging infectious diseases, such as the 2014-2015 West African Ebola epidemic, but little is known about the relative performance of alternate forecasting approaches. The RAPIDD Ebola Forecasting Challenge (REFC) tested the ability of eight mathematical models to generate useful forecasts in the face of simulated Ebola outbreaks. We used a simple, phenomenological single-equation model (the "IDEA" model), which relies only on case counts, in the REFC. Model fits were performed using a maximum likelihood approach. We found that the model performed reasonably well relative to other more complex approaches, with performance metrics ranked on average 4th or 5th among participating models. IDEA appeared better suited to long- than short-term forecasts, and could be fit using nothing but reported case counts. Several limitations were identified, including difficulty in identifying epidemic peak (even retrospectively), unrealistically precise confidence intervals, and difficulty interpolating daily case counts when using a model scaled to epidemic generation time. More realistic confidence intervals were generated when case counts were assumed to follow a negative binomial, rather than Poisson, distribution. Nonetheless, IDEA represents a simple phenomenological model, easily implemented in widely available software packages that could be used by frontline public health personnel to generate forecasts with accuracy that approximates that which is achieved using more complex methodologies. Copyright © 2016 The Author(s). Published by Elsevier B.V. All rights reserved.

Spreading dynamics on complex networks: a general stochastic approach.

PubMed

Noël, Pierre-André; Allard, Antoine; Hébert-Dufresne, Laurent; Marceau, Vincent; Dubé, Louis J

2014-12-01

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.

Simulation of between-farm transmission of porcine reproductive and respiratory syndrome virus in Ontario, Canada using the North American Animal Disease Spread Model.

PubMed

Thakur, Krishna K; Revie, Crawford W; Hurnik, Daniel; Poljak, Zvonimir; Sanchez, Javier

2015-03-01

Porcine reproductive and respiratory syndrome (PRRS), a viral disease of swine, has major economic impacts on the swine industry. The North American Animal Disease Spread Model (NAADSM) is a spatial, stochastic, farm level state-transition modeling framework originally developed to simulate highly contagious and foreign livestock diseases. The objectives of this study were to develop a model to simulate between-farm spread of a homologous strain of PRRS virus in Ontario swine farms via direct (animal movement) and indirect (sharing of trucks between farms) contacts using the NAADSM and to compare the patterns and extent of outbreak under different simulated conditions. A total of 2552 swine farms in Ontario province were allocated to each census division of Ontario and geo-locations of the farms were randomly generated within the agriculture land of each Census Division. Contact rates among different production types were obtained using pig movement information from four regions in Canada. A total of 24 scenarios were developed involving various direct (movement of infected animals) and indirect (pig transportation trucks) contact parameters in combination with alternating the production type of the farm in which the infection was seeded. Outbreaks were simulated for one year with 1000 replications. The median number of farms infected, proportion of farms with multiple outbreaks and time to reach the peak epidemic were used to compare the size, progression and extent of outbreaks. Scenarios involving spread only by direct contact between farms resulted in outbreaks where the median percentage of infected farms ranged from 31.5 to 37% of all farms. In scenarios with both direct and indirect contact, the median percentage of infected farms increased to a range from 41.6 to 48.6%. Furthermore, scenarios with both direct and indirect contact resulted in a 44% increase in median epidemic size when compared to the direct contact scenarios. Incorporation of both animal movements and the sharing of trucks within the model indicated that the effect of direct and indirect contact may be nonlinear on outbreak progression. The increase of 44% in epidemic size when indirect contact, via sharing of trucks, was incorporated into the model highlights the importance of proper biosecurity measures in preventing transmission of the PRRS virus. Simulation of between-farm spread of the PRRS virus in swine farms has highlighted the relative importance of direct and indirect contact and provides important insights regarding the possible patterns and extent of spread of the PRRS virus in a completely susceptible population with herd demographics similar to those found in Ontario, Canada. Copyright © 2015 Elsevier B.V. All rights reserved.

Distributed micro-releases of bioterror pathogens : threat characterizations and epidemiology from uncertain patient observables.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolf, Michael M.; Marzouk, Youssef M.; Adams, Brian M.

2008-10-01

Terrorist attacks using an aerosolized pathogen preparation have gained credibility as a national security concern since the anthrax attacks of 2001. The ability to characterize the parameters of such attacks, i.e., to estimate the number of people infected, the time of infection, the average dose received, and the rate of disease spread in contemporary American society (for contagious diseases), is important when planning a medical response. For non-contagious diseases, we address the characterization problem by formulating a Bayesian inverse problem predicated on a short time-series of diagnosed patients exhibiting symptoms. To keep the approach relevant for response planning, we limitmore » ourselves to 3.5 days of data. In computational tests performed for anthrax, we usually find these observation windows sufficient, especially if the outbreak model employed in the inverse problem is accurate. For contagious diseases, we formulated a Bayesian inversion technique to infer both pathogenic transmissibility and the social network from outbreak observations, ensuring that the two determinants of spreading are identified separately. We tested this technique on data collected from a 1967 smallpox epidemic in Abakaliki, Nigeria. We inferred, probabilistically, different transmissibilities in the structured Abakaliki population, the social network, and the chain of transmission. Finally, we developed an individual-based epidemic model to realistically simulate the spread of a rare (or eradicated) disease in a modern society. This model incorporates the mixing patterns observed in an (American) urban setting and accepts, as model input, pathogenic transmissibilities estimated from historical outbreaks that may have occurred in socio-economic environments with little resemblance to contemporary society. Techniques were also developed to simulate disease spread on static and sampled network reductions of the dynamic social networks originally in the individual-based model, yielding faster, though approximate, network-based epidemic models. These reduced-order models are useful in scenario analysis for medical response planning, as well as in computationally intensive inverse problems.« less

History, Epidemic Evolution, and Model Burn-In for a Network of Annual Invasion: Soybean Rust.

PubMed

Sanatkar, M R; Scoglio, C; Natarajan, B; Isard, S A; Garrett, K A

2015-07-01

Ecological history may be an important driver of epidemics and disease emergence. We evaluated the role of history and two related concepts, the evolution of epidemics and the burn-in period required for fitting a model to epidemic observations, for the U.S. soybean rust epidemic (caused by Phakopsora pachyrhizi). This disease allows evaluation of replicate epidemics because the pathogen reinvades the United States each year. We used a new maximum likelihood estimation approach for fitting the network model based on observed U.S. epidemics. We evaluated the model burn-in period by comparing model fit based on each combination of other years of observation. When the miss error rates were weighted by 0.9 and false alarm error rates by 0.1, the mean error rate did decline, for most years, as more years were used to construct models. Models based on observations in years closer in time to the season being estimated gave lower miss error rates for later epidemic years. The weighted mean error rate was lower in backcasting than in forecasting, reflecting how the epidemic had evolved. Ongoing epidemic evolution, and potential model failure, can occur because of changes in climate, host resistance and spatial patterns, or pathogen evolution.

a Discrete Mathematical Model to Simulate Malware Spreading

NASA Astrophysics Data System (ADS)

Del Rey, A. Martin; Sánchez, G. Rodriguez

2012-10-01

With the advent and worldwide development of Internet, the study and control of malware spreading has become very important. In this sense, some mathematical models to simulate malware propagation have been proposed in the scientific literature, and usually they are based on differential equations exploiting the similarities with mathematical epidemiology. The great majority of these models study the behavior of a particular type of malware called computer worms; indeed, to the best of our knowledge, no model has been proposed to simulate the spreading of a computer virus (the traditional type of malware which differs from computer worms in several aspects). In this sense, the purpose of this work is to introduce a new mathematical model not based on continuous mathematics tools but on discrete ones, to analyze and study the epidemic behavior of computer virus. Specifically, cellular automata are used in order to design such model.

The need for data science in epidemic modelling. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Danon, Leon; Brooks-Pollock, Ellen

2016-09-01

In their review, Chowell et al. consider the ability of mathematical models to predict early epidemic growth [1]. In particular, they question the central prediction of classical differential equation models that the number of cases grows exponentially during the early stages of an epidemic. Using examples including HIV and Ebola, they argue that classical models fail to capture key qualitative features of early growth and describe a selection of models that do capture non-exponential epidemic growth. An implication of this failure is that predictions may be inaccurate and unusable, highlighting the need for care when embarking upon modelling using classical methodology. There remains a lack of understanding of the mechanisms driving many observed epidemic patterns; we argue that data science should form a fundamental component of epidemic modelling, providing a rigorous methodology for data-driven approaches, rather than trying to enforce established frameworks. The need for refinement of classical models provides a strong argument for the use of data science, to identify qualitative characteristics and pinpoint the mechanisms responsible for the observed epidemic patterns.

A generic model to simulate air-borne diseases as a function of crop architecture.

PubMed

Casadebaig, Pierre; Quesnel, Gauthier; Langlais, Michel; Faivre, Robert

2012-01-01

In a context of pesticide use reduction, alternatives to chemical-based crop protection strategies are needed to control diseases. Crop and plant architectures can be viewed as levers to control disease outbreaks by affecting microclimate within the canopy or pathogen transmission between plants. Modeling and simulation is a key approach to help analyze the behaviour of such systems where direct observations are difficult and tedious. Modeling permits the joining of concepts from ecophysiology and epidemiology to define structures and functions generic enough to describe a wide range of epidemiological dynamics. Additionally, this conception should minimize computing time by both limiting the complexity and setting an efficient software implementation. In this paper, our aim was to present a model that suited these constraints so it could first be used as a research and teaching tool to promote discussions about epidemic management in cropping systems. The system was modelled as a combination of individual hosts (population of plants or organs) and infectious agents (pathogens) whose contacts are restricted through a network of connections. The system dynamics were described at an individual scale. Additional attention was given to the identification of generic properties of host-pathogen systems to widen the model's applicability domain. Two specific pathosystems with contrasted crop architectures were considered: ascochyta blight on pea (homogeneously layered canopy) and potato late blight (lattice of individualized plants). The model behavior was assessed by simulation and sensitivity analysis and these results were discussed against the model ability to discriminate between the defined types of epidemics. Crop traits related to disease avoidance resulting in a low exposure, a slow dispersal or a de-synchronization of plant and pathogen cycles were shown to strongly impact the disease severity at the crop scale.

A stochastic agent-based model of pathogen propagation in dynamic multi-relational social networks

PubMed Central

Khan, Bilal; Dombrowski, Kirk; Saad, Mohamed

2015-01-01

We describe a general framework for modeling and stochastic simulation of epidemics in realistic dynamic social networks, which incorporates heterogeneity in the types of individuals, types of interconnecting risk-bearing relationships, and types of pathogens transmitted across them. Dynamism is supported through arrival and departure processes, continuous restructuring of risk relationships, and changes to pathogen infectiousness, as mandated by natural history; dynamism is regulated through constraints on the local agency of individual nodes and their risk behaviors, while simulation trajectories are validated using system-wide metrics. To illustrate its utility, we present a case study that applies the proposed framework towards a simulation of HIV in artificial networks of intravenous drug users (IDUs) modeled using data collected in the Social Factors for HIV Risk survey. PMID:25859056

Non-Markovian Infection Spread Dramatically Alters the Susceptible-Infected-Susceptible Epidemic Threshold in Networks

NASA Astrophysics Data System (ADS)

Van Mieghem, P.; van de Bovenkamp, R.

2013-03-01

Most studies on susceptible-infected-susceptible epidemics in networks implicitly assume Markovian behavior: the time to infect a direct neighbor is exponentially distributed. Much effort so far has been devoted to characterize and precisely compute the epidemic threshold in susceptible-infected-susceptible Markovian epidemics on networks. Here, we report the rather dramatic effect of a nonexponential infection time (while still assuming an exponential curing time) on the epidemic threshold by considering Weibullean infection times with the same mean, but different power exponent α. For three basic classes of graphs, the Erdős-Rényi random graph, scale-free graphs and lattices, the average steady-state fraction of infected nodes is simulated from which the epidemic threshold is deduced. For all graph classes, the epidemic threshold significantly increases with the power exponents α. Hence, real epidemics that violate the exponential or Markovian assumption can behave seriously differently than anticipated based on Markov theory.

Suppressing epidemics on networks by exploiting observer nodes.

PubMed

Takaguchi, Taro; Hasegawa, Takehisa; Yoshida, Yuichi

2014-07-01

To control infection spreading on networks, we investigate the effect of observer nodes that recognize infection in a neighboring node and make the rest of the neighbor nodes immune. We numerically show that random placement of observer nodes works better on networks with clustering than on locally treelike networks, implying that our model is promising for realistic social networks. The efficiency of several heuristic schemes for observer placement is also examined for synthetic and empirical networks. In parallel with numerical simulations of epidemic dynamics, we also show that the effect of observer placement can be assessed by the size of the largest connected component of networks remaining after removing observer nodes and links between their neighboring nodes.

Suppressing epidemics on networks by exploiting observer nodes

NASA Astrophysics Data System (ADS)

Takaguchi, Taro; Hasegawa, Takehisa; Yoshida, Yuichi

2014-07-01

To control infection spreading on networks, we investigate the effect of observer nodes that recognize infection in a neighboring node and make the rest of the neighbor nodes immune. We numerically show that random placement of observer nodes works better on networks with clustering than on locally treelike networks, implying that our model is promising for realistic social networks. The efficiency of several heuristic schemes for observer placement is also examined for synthetic and empirical networks. In parallel with numerical simulations of epidemic dynamics, we also show that the effect of observer placement can be assessed by the size of the largest connected component of networks remaining after removing observer nodes and links between their neighboring nodes.

Dynamic properties of epidemic spreading on finite size complex networks

NASA Astrophysics Data System (ADS)

Li, Ying; Liu, Yang; Shan, Xiu-Ming; Ren, Yong; Jiao, Jian; Qiu, Ben

2005-11-01

The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS (susceptible-infected-susceptible) model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.

Anticipation of Local Epidemics Management

NASA Astrophysics Data System (ADS)

Krivy, Ivan

2008-10-01

Local epidemics are systems where temporary elements (infected ones) are distributed over a hexagonal or rectangular network of permanent elements (humans). Their relation of being neighbors is considered to be constant. The systems of this type can occur in rest homes, institutes of social care, nursery schools, summer camps, prisons, etc. The process of the infection propagation depends on the neighborhood relation and on the actual distance of the neighbors. It is influenced by delays during the transitive affecting the people and by random effects, the size of which can be diminished by the intervention of health care service. The anticipation of the health care intervention effects was supported by simulation models implemented by means of the object-oriented programming.

Modeling the spread and control of foot-and-mouth disease in Pennsylvania following its discovery and options for control

PubMed Central

Tildesley, Michael J.; Smith, Gary; Keeling, Matt J.

2013-01-01

In this paper, we simulate outbreaks of foot-and-mouth disease in the Commonwealth of Pennsylvania, USA – after the introduction of a state-wide movement ban – as they might unfold in the presence of mitigation strategies. We have adapted a model previously used to investigate FMD control policies in the UK to examine the potential for disease spread given an infection seeded in each county in Pennsylvania. The results are highly dependent upon the county of introduction and the spatial scale of transmission. Should the transmission kernel be identical to that for the UK, the epidemic impact is limited to fewer than 20 premises, regardless of the county of introduction. However, for wider kernels where infection can spread further, outbreaks seeded in or near the county with highest density of premises and animals result in large epidemics (>150 premises). Ring culling and vaccination reduce epidemic size, with the optimal radius of the rings being dependent upon the county of introduction. Should the kernel width exceed a given county-dependent threshold, ring culling is unable to control the epidemic. We find that a vaccinate-to-live policy is generally preferred to ring culling (in terms of reducing the overall number of premises culled), indicating that well-targeted control can dramatically reduce the risk of large scale outbreaks of foot-and-mouth disease occurring in Pennsylvania. PMID:22169708

Eigen values in epidemic and other bio-inspired models

NASA Astrophysics Data System (ADS)

Supriatna, A. K.; Anggriani, N.; Carnia, E.; Raihan, A.

2017-08-01

Eigen values and the largest eigen value have special roles in many applications. In this paper we will discuss its role in determining the epidemic threshold in which we can determine if an epidemic will decease or blow out eventually. Some examples and their consequences to controling the epidemic are also discusses. Beside the application in epidemic model, the paper also discusses other example of appication in bio-inspired model, such as the backcross breeding for two age classes of local and exotic goats. Here we give some elaborative examples on the use of previous backcross breeding model. Some future direction on the exploration of the relationship between these eigenvalues to different epidemic models and other bio-inspired models are also presented.

Epidemics in adaptive networks with community structure

NASA Astrophysics Data System (ADS)

Shaw, Leah; Tunc, Ilker

2010-03-01

Models for epidemic spread on static social networks do not account for changes in individuals' social interactions. Recent studies of adaptive networks have modeled avoidance behavior, as non-infected individuals try to avoid contact with infectives. Such models have not generally included realistic social structure. Here we study epidemic spread on an adaptive network with community structure. We model the effect of heterogeneous communities on infection levels and epidemic extinction. We also show how an epidemic can alter the community structure.

A cellular automata model of SARS epidemic spreading

NASA Astrophysics Data System (ADS)

Xu, Tian; Zhang, Peipei; Su, Beibei; Jiang, Yumai; He, Da-Ren

2004-03-01

We suggest a cellular automata model for a simulation on the process of SARS spreading in Beijing. Suppose a number of people are located in a two-dimensional lattice, in which a certain portion belongs to immune and others belong to acceptive. In every time step each of the acceptive people may become ill with a certain probability if one of his 8 neighbors is a SARS patient. At same time all the people have another possibility to change their positions. Each patient will recover or die after different number of days. A recovered patient becomes immune. The numerical simulation by this model leads to the results, which are in a good agreement with the practical statistical data.

Statistics of Epidemics in Networks by Passing Messages

NASA Astrophysics Data System (ADS)

Shrestha, Munik Kumar

Epidemic processes are common out-of-equilibrium phenomena of broad interdisciplinary interest. In this thesis, we show how message-passing approach can be a helpful tool for simulating epidemic models in disordered medium like networks, and in particular for estimating the probability that a given node will become infectious at a particular time. The sort of dynamics we consider are stochastic, where randomness can arise from the stochastic events or from the randomness of network structures. As in belief propagation, variables or messages in message-passing approach are defined on the directed edges of a network. However, unlike belief propagation, where the posterior distributions are updated according to Bayes' rule, in message-passing approach we write differential equations for the messages over time. It takes correlations between neighboring nodes into account while preventing causal signals from backtracking to their immediate source, and thus avoids "echo chamber effects" where a pair of adjacent nodes each amplify the probability that the other is infectious. In our first results, we develop a message-passing approach to threshold models of behavior popular in sociology. These are models, first proposed by Granovetter, where individuals have to hear about a trend or behavior from some number of neighbors before adopting it themselves. In thermodynamic limit of large random networks, we provide an exact analytic scheme while calculating the time dependence of the probabilities and thus learning about the whole dynamics of bootstrap percolation, which is a simple model known in statistical physics for exhibiting discontinuous phase transition. As an application, we apply a similar model to financial networks, studying when bankruptcies spread due to the sudden devaluation of shared assets in overlapping portfolios. We predict that although diversification may be good for individual institutions, it can create dangerous systemic effects, and as a result financial contagion gets worse with too much diversification. We also predict that financial system exhibits "robust yet fragile" behavior, with regions of the parameter space where contagion is rare but catastrophic whenever it occurs. In further results, we develop a message-passing approach to recurrent state epidemics like susceptible-infectious-susceptible and susceptible-infectious-recovered-susceptible where nodes can return to previously inhabited states and multiple waves of infection can pass through the population. Given that message-passing has been applied exclusively to models with one-way state changes like susceptible-infectious and susceptible-infectious-recovered, we develop message-passing for recurrent epidemics based on a new class of differential equations and demonstrate that our approach is simple and efficiently approximates results obtained from Monte Carlo simulation, and that the accuracy of message-passing is often superior to the pair approximation (which also takes second-order correlations into account).

Combining Participatory Influenza Surveillance with Modeling and Forecasting: Three Alternative Approaches.

PubMed

Brownstein, John S; Chu, Shuyu; Marathe, Achla; Marathe, Madhav V; Nguyen, Andre T; Paolotti, Daniela; Perra, Nicola; Perrotta, Daniela; Santillana, Mauricio; Swarup, Samarth; Tizzoni, Michele; Vespignani, Alessandro; Vullikanti, Anil Kumar S; Wilson, Mandy L; Zhang, Qian

2017-11-01

Influenza outbreaks affect millions of people every year and its surveillance is usually carried out in developed countries through a network of sentinel doctors who report the weekly number of Influenza-like Illness cases observed among the visited patients. Monitoring and forecasting the evolution of these outbreaks supports decision makers in designing effective interventions and allocating resources to mitigate their impact. Describe the existing participatory surveillance approaches that have been used for modeling and forecasting of the seasonal influenza epidemic, and how they can help strengthen real-time epidemic science and provide a more rigorous understanding of epidemic conditions. We describe three different participatory surveillance systems, WISDM (Widely Internet Sourced Distributed Monitoring), Influenzanet and Flu Near You (FNY), and show how modeling and simulation can be or has been combined with participatory disease surveillance to: i) measure the non-response bias in a participatory surveillance sample using WISDM; and ii) nowcast and forecast influenza activity in different parts of the world (using Influenzanet and Flu Near You). WISDM-based results measure the participatory and sample bias for three epidemic metrics i.e. attack rate, peak infection rate, and time-to-peak, and find the participatory bias to be the largest component of the total bias. The Influenzanet platform shows that digital participatory surveillance data combined with a realistic data-driven epidemiological model can provide both short-term and long-term forecasts of epidemic intensities, and the ground truth data lie within the 95 percent confidence intervals for most weeks. The statistical accuracy of the ensemble forecasts increase as the season progresses. The Flu Near You platform shows that participatory surveillance data provide accurate short-term flu activity forecasts and influenza activity predictions. The correlation of the HealthMap Flu Trends estimates with the observed CDC ILI rates is 0.99 for 2013-2015. Additional data sources lead to an error reduction of about 40% when compared to the estimates of the model that only incorporates CDC historical information. While the advantages of participatory surveillance, compared to traditional surveillance, include its timeliness, lower costs, and broader reach, it is limited by a lack of control over the characteristics of the population sample. Modeling and simulation can help overcome this limitation as well as provide real-time and long-term forecasting of influenza activity in data-poor parts of the world. ©John S Brownstein, Shuyu Chu, Achla Marathe, Madhav V Marathe, Andre T Nguyen, Daniela Paolotti, Nicola Perra, Daniela Perrotta, Mauricio Santillana, Samarth Swarup, Michele Tizzoni, Alessandro Vespignani, Anil Kumar S Vullikanti, Mandy L Wilson, Qian Zhang. Originally published in JMIR Public Health and Surveillance (http://publichealth.jmir.org), 01.11.2017.

Epidemic spreading in metapopulation networks with heterogeneous infection rates

NASA Astrophysics Data System (ADS)

Gong, Yong-Wang; Song, Yu-Rong; Jiang, Guo-Ping

2014-12-01

In this paper, we study epidemic spreading in metapopulation networks wherein each node represents a subpopulation symbolizing a city or an urban area and links connecting nodes correspond to the human traveling routes among cities. Differently from previous studies, we introduce a heterogeneous infection rate to characterize the effect of nodes' local properties, such as population density, individual health habits, and social conditions, on epidemic infectivity. By means of a mean-field approach and Monte Carlo simulations, we explore how the heterogeneity of the infection rate affects the epidemic dynamics, and find that large fluctuations of the infection rate have a profound impact on the epidemic threshold as well as the temporal behavior of the prevalence above the epidemic threshold. This work can refine our understanding of epidemic spreading in metapopulation networks with the effect of nodes' local properties.

Computational model of a vector-mediated epidemic

NASA Astrophysics Data System (ADS)

Dickman, Adriana Gomes; Dickman, Ronald

2015-05-01

We discuss a lattice model of vector-mediated transmission of a disease to illustrate how simulations can be applied in epidemiology. The population consists of two species, human hosts and vectors, which contract the disease from one another. Hosts are sedentary, while vectors (mosquitoes) diffuse in space. Examples of such diseases are malaria, dengue fever, and Pierce's disease in vineyards. The model exhibits a phase transition between an absorbing (infection free) phase and an active one as parameters such as infection rates and vector density are varied.

A modelling approach to vaccination and contraception programmes for rabies control in fox populations.

PubMed Central

Suppo, C; Naulin, J M; Langlais, M; Artois, M

2000-01-01

In a previous study, three of the authors designed a one-dimensional model to simulate the propagation of rabies within a growing fox population; the influence of various parameters on the epidemic model was studied, including oral-vaccination programmes. In this work, a two-dimensional model of a fox population having either an exponential or a logistic growth pattern was considered. Using numerical simulations, the efficiencies of two prophylactic methods (fox contraception and vaccination against rabies) were assessed, used either separately or jointly. It was concluded that far lower rates of administration are necessary to eradicate rabies, and that the undesirable side-effects of each programme disappear, when both are used together. PMID:11007334

Modelling the impact of co-circulating low pathogenic avian influenza viruses on epidemics of highly pathogenic avian influenza in poultry.

PubMed

Nickbakhsh, Sema; Hall, Matthew D; Dorigatti, Ilaria; Lycett, Samantha J; Mulatti, Paolo; Monne, Isabella; Fusaro, Alice; Woolhouse, Mark E J; Rambaut, Andrew; Kao, Rowland R

2016-12-01

It is well known that highly pathogenic avian influenza (HPAI) viruses emerge through mutation of precursor low pathogenic avian influenza (LPAI) viruses in domestic poultry populations. The potential for immunological cross-protection between these pathogenic variants is recognised but the epidemiological impact during co-circulation is not well understood. Here we use mathematical models to investigate whether altered flock infection parameters consequent to primary LPAI infections can impact on the spread of HPAI at the population level. First we used mechanistic models reflecting the co-circulatory dynamics of LPAI and HPAI within a single commercial poultry flock. We found that primary infections with LPAI led to HPAI prevalence being maximised under a scenario of high but partial cross-protection. We then tested the population impact in spatially-explicit simulations motivated by a major avian influenza A(H7N1) epidemic that afflicted the Italian poultry industry in 1999-2001. We found that partial cross-protection can lead to a prolongation of HPAI epidemic duration. Our findings have implications for the control of HPAI in poultry particularly for settings in which LPAI and HPAI frequently co-circulate. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Detecting nonlinearity and chaos in epidemic data

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ellner, S.; Gallant, A.R.; Theiler, J.

1993-08-01

Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude ofmore » epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.« less

Focus expansion and stability of the spread parameter estimate of the power law model for dispersal gradients

PubMed Central

Gent, David H.; Mehra, Lucky K.; Christie, David; Magarey, Roger

2017-01-01

Empirical and mechanistic modeling indicate that pathogens transmitted via aerially dispersed inoculum follow a power law, resulting in dispersive epidemic waves. The spread parameter (b) of the power law model, which is an indicator of the distance of the epidemic wave front from an initial focus per unit time, has been found to be approximately 2 for several animal and plant diseases over a wide range of spatial scales under conditions favorable for disease spread. Although disease spread and epidemic expansion can be influenced by several factors, the stability of the parameter b over multiple epidemic years has not been determined. Additionally, the size of the initial epidemic area is expected to be strongly related to the final epidemic extent for epidemics, but the stability of this relationship is also not well established. Here, empirical data of cucurbit downy mildew epidemics collected from 2008 to 2014 were analyzed using a spatio-temporal model of disease spread that incorporates logistic growth in time with a power law function for dispersal. Final epidemic extent ranged from 4.16 ×108 km2 in 2012 to 6.44 ×108 km2 in 2009. Current epidemic extent became significantly associated (P < 0.0332; 0.56 < R2 < 0.99) with final epidemic area beginning near the end of April, with the association increasing monotonically to 1.0 by the end of the epidemic season in July. The position of the epidemic wave-front became exponentially more distant with time, and epidemic velocity increased linearly with distance. Slopes from the temporal and spatial regression models varied with about a 2.5-fold range across epidemic years. Estimates of b varied substantially ranging from 1.51 to 4.16 across epidemic years. We observed a significant b ×time (or distance) interaction (P < 0.05) for epidemic years where data were well described by the power law model. These results suggest that the spread parameter b may not be stable over multiple epidemic years. However, b ≈ 2 may be considered the lower limit of the distance traveled by epidemic wave-fronts for aerially transmitted pathogens that follow a power law dispersal function. PMID:28649473

Improving the Effect and Efficiency of FMD Control by Enlarging Protection or Surveillance Zones

PubMed Central

Halasa, Tariq; Toft, Nils; Boklund, Anette

2015-01-01

An epidemic of foot-and-mouth disease (FMD) in a FMD-free country with large exports of livestock and livestock products would result in profound economic damage. This could be reduced by rapid and efficient control of the disease spread. The objectives of this study were to estimate the economic impact of a hypothetical FMD outbreak in Denmark based on changes to the economic assumptions of the model, and to investigate whether the control of an FMD epidemic can be improved by combining the enlargement of protection or surveillance zones with pre-emptive depopulation or emergency vaccination. The stochastic spatial simulation model DTU-DADS was used to simulate the spread of FMD in Denmark. The control strategies were the basic EU and Danish strategy, pre-emptive depopulation, suppressive or protective vaccination, enlarging protection or surveillance zones, and a combination of pre-emptive depopulation or emergency vaccination with enlarged protection or surveillance zones. Herds are detected either based on basic detection through the appearance of clinical signs, or as a result of surveillance in the control zones. The economic analyses consisted of direct costs and export losses. Sensitivity analysis was performed on uncertain and potentially influential input parameters. Enlarging the surveillance zones from 10 to 15 km, combined with pre-emptive depopulation over a 1-km radius around detected herds resulted in the lowest total costs. This was still the case even when the different input parameters were changed in the sensitivity analysis. Changing the resources for clinical surveillance did not affect the epidemic consequences. In conclusion, an FMD epidemic in Denmark would have a larger economic impact on the agricultural sector than previously anticipated. Furthermore, the control of a potential FMD outbreak in Denmark may be improved by combining pre-emptive depopulation with an enlarged protection or surveillance zone. PMID:26664996

Improving the Effect and Efficiency of FMD Control by Enlarging Protection or Surveillance Zones.

PubMed

Halasa, Tariq; Toft, Nils; Boklund, Anette

2015-01-01

An epidemic of foot-and-mouth disease (FMD) in a FMD-free country with large exports of livestock and livestock products would result in profound economic damage. This could be reduced by rapid and efficient control of the disease spread. The objectives of this study were to estimate the economic impact of a hypothetical FMD outbreak in Denmark based on changes to the economic assumptions of the model, and to investigate whether the control of an FMD epidemic can be improved by combining the enlargement of protection or surveillance zones with pre-emptive depopulation or emergency vaccination. The stochastic spatial simulation model DTU-DADS was used to simulate the spread of FMD in Denmark. The control strategies were the basic EU and Danish strategy, pre-emptive depopulation, suppressive or protective vaccination, enlarging protection or surveillance zones, and a combination of pre-emptive depopulation or emergency vaccination with enlarged protection or surveillance zones. Herds are detected either based on basic detection through the appearance of clinical signs, or as a result of surveillance in the control zones. The economic analyses consisted of direct costs and export losses. Sensitivity analysis was performed on uncertain and potentially influential input parameters. Enlarging the surveillance zones from 10 to 15 km, combined with pre-emptive depopulation over a 1-km radius around detected herds resulted in the lowest total costs. This was still the case even when the different input parameters were changed in the sensitivity analysis. Changing the resources for clinical surveillance did not affect the epidemic consequences. In conclusion, an FMD epidemic in Denmark would have a larger economic impact on the agricultural sector than previously anticipated. Furthermore, the control of a potential FMD outbreak in Denmark may be improved by combining pre-emptive depopulation with an enlarged protection or surveillance zone.

Dynamics of a stochastic multi-strain SIS epidemic model driven by Lévy noise

NASA Astrophysics Data System (ADS)

Chen, Can; Kang, Yanmei

2017-01-01

A stochastic multi-strain SIS epidemic model is formulated by introducing Lévy noise into the disease transmission rate of each strain. First, we prove that the stochastic model admits a unique global positive solution, and, by the comparison theorem, we show that the solution remains within a positively invariant set almost surely. Next we investigate stochastic stability of the disease-free equilibrium, including stability in probability and pth moment asymptotic stability. Then sufficient conditions for persistence in the mean of the disease are established. Finally, based on an Euler scheme for Lévy-driven stochastic differential equations, numerical simulations for a stochastic two-strain model are carried out to verify the theoretical results. Moreover, numerical comparison results of the stochastic two-strain model and the deterministic version are also given. Lévy noise can cause the two strains to become extinct almost surely, even though there is a dominant strain that persists in the deterministic model. It can be concluded that the introduction of Lévy noise reduces the disease extinction threshold, which indicates that Lévy noise may suppress the disease outbreak.

Disease prevention versus data privacy: using landcover maps to inform spatial epidemic models.

PubMed

Tildesley, Michael J; Ryan, Sadie J

2012-01-01

The availability of epidemiological data in the early stages of an outbreak of an infectious disease is vital for modelers to make accurate predictions regarding the likely spread of disease and preferred intervention strategies. However, in some countries, the necessary demographic data are only available at an aggregate scale. We investigated the ability of models of livestock infectious diseases to predict epidemic spread and obtain optimal control policies in the event of imperfect, aggregated data. Taking a geographic information approach, we used land cover data to predict UK farm locations and investigated the influence of using these synthetic location data sets upon epidemiological predictions in the event of an outbreak of foot-and-mouth disease. When broadly classified land cover data were used to create synthetic farm locations, model predictions deviated significantly from those simulated on true data. However, when more resolved subclass land use data were used, moderate to highly accurate predictions of epidemic size, duration and optimal vaccination and ring culling strategies were obtained. This suggests that a geographic information approach may be useful where individual farm-level data are not available, to allow predictive analyses to be carried out regarding the likely spread of disease. This method can also be used for contingency planning in collaboration with policy makers to determine preferred control strategies in the event of a future outbreak of infectious disease in livestock.

Disease Prevention versus Data Privacy: Using Landcover Maps to Inform Spatial Epidemic Models

PubMed Central

Tildesley, Michael J.; Ryan, Sadie J.

2012-01-01

The availability of epidemiological data in the early stages of an outbreak of an infectious disease is vital for modelers to make accurate predictions regarding the likely spread of disease and preferred intervention strategies. However, in some countries, the necessary demographic data are only available at an aggregate scale. We investigated the ability of models of livestock infectious diseases to predict epidemic spread and obtain optimal control policies in the event of imperfect, aggregated data. Taking a geographic information approach, we used land cover data to predict UK farm locations and investigated the influence of using these synthetic location data sets upon epidemiological predictions in the event of an outbreak of foot-and-mouth disease. When broadly classified land cover data were used to create synthetic farm locations, model predictions deviated significantly from those simulated on true data. However, when more resolved subclass land use data were used, moderate to highly accurate predictions of epidemic size, duration and optimal vaccination and ring culling strategies were obtained. This suggests that a geographic information approach may be useful where individual farm-level data are not available, to allow predictive analyses to be carried out regarding the likely spread of disease. This method can also be used for contingency planning in collaboration with policy makers to determine preferred control strategies in the event of a future outbreak of infectious disease in livestock. PMID:23133352

Insights into the transmission of respiratory infectious diseases through empirical human contact networks

PubMed Central

Huang, Chunlin; Liu, Xingwu; Sun, Shiwei; Li, Shuai Cheng; Deng, Minghua; He, Guangxue; Zhang, Haicang; Wang, Chao; Zhou, Yang; Zhao, Yanlin; Bu, Dongbo

2016-01-01

In this study, we present representative human contact networks among Chinese college students. Unlike schools in the US, human contacts within Chinese colleges are extremely clustered, partly due to the highly organized lifestyle of Chinese college students. Simulations of influenza spreading across real contact networks are in good accordance with real influenza records; however, epidemic simulations across idealized scale-free or small-world networks show considerable overestimation of disease prevalence, thus challenging the widely-applied idealized human contact models in epidemiology. Furthermore, the special contact pattern within Chinese colleges results in disease spreading patterns distinct from those of the US schools. Remarkably, class cancelation, though simple, shows a mitigating power equal to quarantine/vaccination applied on ~25% of college students, which quantitatively explains its success in Chinese colleges during the SARS period. Our findings greatly facilitate reliable prediction of epidemic prevalence, and thus should help establishing effective strategies for respiratory infectious diseases control. PMID:27526868

Early warnings of the potential for malaria transmission in Rural Africa using the Hydrology, Entomology and Malaria Transmission Simulator (HYDREMATS)

NASA Astrophysics Data System (ADS)

Yamana, T. K.; Eltahir, E. A.

2010-12-01

Early warnings of malaria transmission allow health officials to better prepare for future epidemics. Monitoring rainfall is recognized as an important part of malaria early warning systems, as outlined by the Roll Back Malaria Initiative. The Hydrology, Entomology and Malaria Simulator (HYDREMATS) is a mechanistic model that relates rainfall to malaria transmission, and could be used to provide early warnings of malaria epidemics. HYDREMATS is used to make predictions of mosquito populations and vectorial capacity for 2005, 2006, and 2007 in Banizoumbou village in western Niger. HYDREMATS is forced by observed rainfall, followed by a rainfall prediction based on the seasonal mean rainfall for a period two or four weeks into the future. Predictions made using this method provided reasonable estimates of mosquito populations and vectorial capacity, two to four weeks in advance. The predictions were significantly improved compared to those made when HYDREMATS was forced with seasonal mean rainfall alone.

Focal Points, Endogenous Processes, and Exogenous Shocks in the Autism Epidemic

PubMed Central

Liu, Kayuet; Bearman, Peter S.

2014-01-01

Autism prevalence has increased rapidly in the United States during the past two decades. We have previously shown that the diffusion of information about autism through spatially proximate social relations has contributed significantly to the epidemic. This study expands on this finding by identifying the focal points for interaction that drive the proximity effect on subsequent diagnoses. We then consider how diffusion dynamics through interaction at critical focal points, in tandem with exogenous shocks, could have shaped the spatial dynamics of autism in California. We achieve these goals through an empirically calibrated simulation model of the whole population of 3- to 9-year-olds in California. We show that in the absence of interaction at these foci—principally malls and schools—we would not observe an autism epidemic. We also explore the idea that epigenetic changes affecting one generation in the distal past could shape the precise spatial patterns we observe among the next generation. PMID:26166907

Mitigating Infectious Disease Outbreaks

NASA Astrophysics Data System (ADS)

Davey, Victoria

The emergence of new, transmissible infections poses a significant threat to human populations. As the 2009 novel influenza A/H1N1 pandemic and the 2014-2015 Ebola epidemic demonstrate, we have observed the effects of rapid spread of illness in non-immune populations and experienced disturbing uncertainty about future potential for human suffering and societal disruption. Clinical and epidemiologic characteristics of a newly emerged infectious organism are usually gathered in retrospect as the outbreak evolves and affects populations. Knowledge of potential effects of outbreaks and epidemics and most importantly, mitigation at community, regional, national and global levels is needed to inform policy that will prepare and protect people. Study of possible outcomes of evolving epidemics and application of mitigation strategies is not possible in observational or experimental research designs, but computational modeling allows conduct of `virtual' experiments. Results of well-designed computer simulations can aid in the selection and implementation of strategies that limit illness and death, and maintain systems of healthcare and other critical resources that are vital to public protection. Mitigating Infectious Disease Outbreaks.

The relationship between human behavior and the process of epidemic spreading in a real social network

NASA Astrophysics Data System (ADS)

Grabowski, A.; Rosińska, M.

2012-07-01

On the basis of experimental data on interactions between humans we have investigated the process of epidemic spreading in a social network. We found that the distribution of the number of contacts maintained in one day is exponential. Data on frequency and duration of interpersonal interactions are presented. They allow us to simulate the spread of droplet-/-air-borne infections and to investigate the influence of human dynamics on the epidemic spread. Specifically, we investigated the influence of the distribution of frequency and duration of those contacts on magnitude, epidemic threshold and peak timing of epidemics propagating in respective networks. It turns out that a large increase in the magnitude of an epidemic and a decrease in epidemic threshold are visible if and only if both are taken into account. We have found that correlation between contact frequency and duration strongly influences the effectiveness of control measures like mass immunization campaigns.

How does the host population's network structure affect the estimation accuracy of epidemic parameters?

NASA Astrophysics Data System (ADS)

Yashima, Kenta; Ito, Kana; Nakamura, Kazuyuki

2013-03-01

When an Infectious disease where to prevail throughout the population, epidemic parameters such as the basic reproduction ratio, initial point of infection etc. are estimated from the time series data of infected population. However, it is unclear how does the structure of host population affects this estimation accuracy. In other words, what kind of city is difficult to estimate its epidemic parameters? To answer this question, epidemic data are simulated by constructing a commuting network with different network structure and running the infection process over this network. From the given time series data for each network structure, we would like to analyzed estimation accuracy of epidemic parameters.

The impact of mass gatherings and holiday traveling on the course of an influenza pandemic: a computational model.

PubMed

Shi, Pengyi; Keskinocak, Pinar; Swann, Julie L; Lee, Bruce Y

2010-12-21

During the 2009 H1N1 influenza pandemic, concerns arose about the potential negative effects of mass public gatherings and travel on the course of the pandemic. Better understanding the potential effects of temporal changes in social mixing patterns could help public officials determine if and when to cancel large public gatherings or enforce regional travel restrictions, advisories, or surveillance during an epidemic. We develop a computer simulation model using detailed data from the state of Georgia to explore how various changes in social mixing and contact patterns, representing mass gatherings and holiday traveling, may affect the course of an influenza pandemic. Various scenarios with different combinations of the length of the mass gatherings or traveling period (range: 0.5 to 5 days), the proportion of the population attending the mass gathering events or on travel (range: 1% to 50%), and the initial reproduction numbers R0 (1.3, 1.5, 1.8) are explored. Mass gatherings that occur within 10 days before the epidemic peak can result in as high as a 10% relative increase in the peak prevalence and the total attack rate, and may have even worse impacts on local communities and travelers' families. Holiday traveling can lead to a second epidemic peak under certain scenarios. Conversely, mass traveling or gatherings may have little effect when occurring much earlier or later than the epidemic peak, e.g., more than 40 days earlier or 20 days later than the peak when the initial R0 = 1.5. Our results suggest that monitoring, postponing, or cancelling large public gatherings may be warranted close to the epidemic peak but not earlier or later during the epidemic. Influenza activity should also be closely monitored for a potential second peak if holiday traveling occurs when prevalence is high.

From public outrage to the burst of public violence: An epidemic-like model

NASA Astrophysics Data System (ADS)

Nizamani, Sarwat; Memon, Nasrullah; Galam, Serge

2014-12-01

This study extends classical models of spreading epidemics to describe the phenomenon of contagious public outrage, which eventually leads to the spread of violence following a disclosure of some unpopular political decisions and/or activity. Accordingly, a mathematical model is proposed to simulate from the start, the internal dynamics by which an external event is turned into internal violence within a population. Five kinds of agents are considered: “Upset” (U), “Violent” (V), “Sensitive” (S), “Immune” (I), and “Relaxed” (R), leading to a set of ordinary differential equations, which in turn yield the dynamics of spreading of each type of agents among the population. The process is stopped with the deactivation of the associated issue. Conditions coinciding with a twofold spreading of public violence are singled out. The results shed new light to understand terror activity and provides some hint on how to curb the spreading of violence within population globally sensitive to specific world issues. Recent violent events in the world are discussed.

A new epidemic modeling approach: Multi-regions discrete-time model with travel-blocking vicinity optimal control strategy.

PubMed

Zakary, Omar; Rachik, Mostafa; Elmouki, Ilias

2017-08-01

First, we devise in this paper, a multi-regions discrete-time model which describes the spatial-temporal spread of an epidemic which starts from one region and enters to regions which are connected with their neighbors by any kind of anthropological movement. We suppose homogeneous Susceptible-Infected-Removed (SIR) populations, and we consider in our simulations, a grid of colored cells, which represents the whole domain affected by the epidemic while each cell can represent a sub-domain or region. Second, in order to minimize the number of infected individuals in one region, we propose an optimal control approach based on a travel-blocking vicinity strategy which aims to control only one cell by restricting movements of infected people coming from all neighboring cells. Thus, we show the influence of the optimal control approach on the controlled cell. We should also note that the cellular modeling approach we propose here, can also describes infection dynamics of regions which are not necessarily attached one to an other, even if no empty space can be viewed between cells. The theoretical method we follow for the characterization of the travel-locking optimal controls, is based on a discrete version of Pontryagin's maximum principle while the numerical approach applied to the multi-points boundary value problems we obtain here, is based on discrete progressive-regressive iterative schemes. We illustrate our modeling and control approaches by giving an example of 100 regions.

Potential Impact of Sexual Transmission on Ebola Virus Epidemiology: Sierra Leone as a Case Study.

PubMed

Abbate, Jessica L; Murall, Carmen Lia; Richner, Heinz; Althaus, Christian L

2016-05-01

Sexual transmission of Ebola virus disease (EVD) 6 months after onset of symptoms has been recently documented, and Ebola virus RNA has been detected in semen of survivors up to 9 months after onset of symptoms. As countries affected by the 2013-2015 epidemic in West Africa, by far the largest to date, are declared free of Ebola virus disease (EVD), it remains unclear what threat is posed by rare sexual transmission events that could arise from survivors. We devised a compartmental mathematical model that includes sexual transmission from convalescent survivors: a SEICR (susceptible-exposed-infectious-convalescent-recovered) transmission model. We fitted the model to weekly incidence of EVD cases from the 2014-2015 epidemic in Sierra Leone. Sensitivity analyses and Monte Carlo simulations showed that a 0.1% per sex act transmission probability and a 3-month convalescent period (the two key unknown parameters of sexual transmission) create very few additional cases, but would extend the epidemic by 83 days [95% CI: 68-98 days] (p < 0.0001) on average. Strikingly, a 6-month convalescent period extended the average epidemic by 540 days (95% CI: 508-572 days), doubling the current length, despite an insignificant rise in the number of new cases generated. Our results show that reductions in the per sex act transmission probability via abstinence and condom use should reduce the number of sporadic sexual transmission events, but will not significantly reduce the epidemic size and may only minimally shorten the length of time the public health community must maintain response preparedness. While the number of infectious survivors is expected to greatly decline over the coming months, our results show that transmission events may still be expected for quite some time as each event results in a new potential cluster of non-sexual transmission. Precise measurement of the convalescent period is thus important for planning ongoing surveillance efforts.

Modelling H5N1 in Bangladesh across spatial scales: Model complexity and zoonotic transmission risk.

PubMed

Hill, Edward M; House, Thomas; Dhingra, Madhur S; Kalpravidh, Wantanee; Morzaria, Subhash; Osmani, Muzaffar G; Yamage, Mat; Xiao, Xiangming; Gilbert, Marius; Tildesley, Michael J

2017-09-01

Highly pathogenic avian influenza H5N1 remains a persistent public health threat, capable of causing infection in humans with a high mortality rate while simultaneously negatively impacting the livestock industry. A central question is to determine regions that are likely sources of newly emerging influenza strains with pandemic causing potential. A suitable candidate is Bangladesh, being one of the most densely populated countries in the world and having an intensifying farming system. It is therefore vital to establish the key factors, specific to Bangladesh, that enable both continued transmission within poultry and spillover across the human-animal interface. We apply a modelling framework to H5N1 epidemics in the Dhaka region of Bangladesh, occurring from 2007 onwards, that resulted in large outbreaks in the poultry sector and a limited number of confirmed human cases. This model consisted of separate poultry transmission and zoonotic transmission components. Utilising poultry farm spatial and population information a set of competing nested models of varying complexity were fitted to the observed case data, with parameter inference carried out using Bayesian methodology and goodness-of-fit verified by stochastic simulations. For the poultry transmission component, successfully identifying a model of minimal complexity, which enabled the accurate prediction of the size and spatial distribution of cases in H5N1 outbreaks, was found to be dependent on the administration level being analysed. A consistent outcome of non-optimal reporting of infected premises materialised in each poultry epidemic of interest, though across the outbreaks analysed there were substantial differences in the estimated transmission parameters. The zoonotic transmission component found the main contributor to spillover transmission of H5N1 in Bangladesh was found to differ from one poultry epidemic to another. We conclude by discussing possible explanations for these discrepancies in transmission behaviour between epidemics, such as changes in surveillance sensitivity and biosecurity practices. Copyright © 2017 The Authors. Published by Elsevier B.V. All rights reserved.

Epidemic spreading on complex networks with overlapping and non-overlapping community structure

NASA Astrophysics Data System (ADS)

Shang, Jiaxing; Liu, Lianchen; Li, Xin; Xie, Feng; Wu, Cheng

2015-02-01

Many real-world networks exhibit community structure where vertices belong to one or more communities. Recent studies show that community structure plays an import role in epidemic spreading. In this paper, we investigate how the extent of overlap among communities affects epidemics. In order to experiment on the characteristic of overlapping communities, we propose a rewiring algorithm that can change the community structure from overlapping to non-overlapping while maintaining the degree distribution of the network. We simulate the Susceptible-Infected-Susceptible (SIS) epidemic process on synthetic scale-free networks and real-world networks by applying our rewiring algorithm. Experiments show that epidemics spread faster on networks with higher level of overlapping communities. Furthermore, overlapping communities' effect interacts with the average degree's effect. Our work further illustrates the important role of overlapping communities in the process of epidemic spreading.

Stochastic effects in a seasonally forced epidemic model

NASA Astrophysics Data System (ADS)

Rozhnova, G.; Nunes, A.

2010-10-01

The interplay of seasonality, the system’s nonlinearities and intrinsic stochasticity, is studied for a seasonally forced susceptible-exposed-infective-recovered stochastic model. The model is explored in the parameter region that corresponds to childhood infectious diseases such as measles. The power spectrum of the stochastic fluctuations around the attractors of the deterministic system that describes the model in the thermodynamic limit is computed analytically and validated by stochastic simulations for large system sizes. Size effects are studied through additional simulations. Other effects such as switching between coexisting attractors induced by stochasticity often mentioned in the literature as playing an important role in the dynamics of childhood infectious diseases are also investigated. The main conclusion is that stochastic amplification, rather than these effects, is the key ingredient to understand the observed incidence patterns.

Modeling household and community transmission of Ebola virus disease: Epidemic growth, spatial dynamics and insights for epidemic control

PubMed Central

Kiskowski, Maria; Chowell, Gerardo

2016-01-01

The mechanisms behind the sub-exponential growth dynamics of the West Africa Ebola virus disease epidemic could be related to improved control of the epidemic and the result of reduced disease transmission in spatially constrained contact structures. An individual-based, stochastic network model is used to model immediate and delayed epidemic control in the context of social contact networks and investigate the extent to which the relative role of these factors may be determined during an outbreak. We find that in general, epidemics quickly establish a dynamic equilibrium of infections in the form of a wave of fixed size and speed traveling through the contact network. Both greater epidemic control and limited community mixing decrease the size of an infectious wave. However, for a fixed wave size, epidemic control (in contrast with limited community mixing) results in lower community saturation and a wave that moves more quickly through the contact network. We also found that the level of epidemic control has a disproportionately greater reductive effect on larger waves, so that a small wave requires nearly as much epidemic control as a larger wave to end an epidemic. PMID:26399855

Modeling household and community transmission of Ebola virus disease: Epidemic growth, spatial dynamics and insights for epidemic control.

PubMed

Kiskowski, Maria; Chowell, Gerardo

2016-01-01

The mechanisms behind the sub-exponential growth dynamics of the West Africa Ebola virus disease epidemic could be related to improved control of the epidemic and the result of reduced disease transmission in spatially constrained contact structures. An individual-based, stochastic network model is used to model immediate and delayed epidemic control in the context of social contact networks and investigate the extent to which the relative role of these factors may be determined during an outbreak. We find that in general, epidemics quickly establish a dynamic equilibrium of infections in the form of a wave of fixed size and speed traveling through the contact network. Both greater epidemic control and limited community mixing decrease the size of an infectious wave. However, for a fixed wave size, epidemic control (in contrast with limited community mixing) results in lower community saturation and a wave that moves more quickly through the contact network. We also found that the level of epidemic control has a disproportionately greater reductive effect on larger waves, so that a small wave requires nearly as much epidemic control as a larger wave to end an epidemic.

Parameter estimation and prediction for the course of a single epidemic outbreak of a plant disease.

PubMed

Kleczkowski, A; Gilligan, C A

2007-10-22

Many epidemics of plant diseases are characterized by large variability among individual outbreaks. However, individual epidemics often follow a well-defined trajectory which is much more predictable in the short term than the ensemble (collection) of potential epidemics. In this paper, we introduce a modelling framework that allows us to deal with individual replicated outbreaks, based upon a Bayesian hierarchical analysis. Information about 'similar' replicate epidemics can be incorporated into a hierarchical model, allowing both ensemble and individual parameters to be estimated. The model is used to analyse the data from a replicated experiment involving spread of Rhizoctonia solani on radish in the presence or absence of a biocontrol agent, Trichoderma viride. The rate of primary (soil-to-plant) infection is found to be the most variable factor determining the final size of epidemics. Breakdown of biological control in some replicates results in high levels of primary infection and increased variability. The model can be used to predict new outbreaks of disease based upon knowledge from a 'library' of previous epidemics and partial information about the current outbreak. We show that forecasting improves significantly with knowledge about the history of a particular epidemic, whereas the precision of hindcasting to identify the past course of the epidemic is largely independent of detailed knowledge of the epidemic trajectory. The results have important consequences for parameter estimation, inference and prediction for emerging epidemic outbreaks.

Hydroclimatological And Anthropogenic Drivers For Cholera Spreading

NASA Astrophysics Data System (ADS)

Righetto, Lorenzo; Bertuzzo, Enrico; Mari, Lorenzo; Casagrandi, Renato; Gatto, Marino; Rinaldo, Andrea

2010-05-01

The nature of waterborne diseases, among which cholera has a prominent importance, calls for a better understanding of the link between epidemic spreading, water and climate. To this end, we have developed a framework which involves a network-based description of a river system, connected with local communities which act as nodes of the network. This has allowed us to produce consistent simulations of real case studies. More recent investigations comprise the evaluation of the spreading velocity of an epidemic wave by means of a reaction-diffusion modeling approach. In particular, we have found that both transport processes and epidemiological quantities, such as the basic reproduction number, have a crucial effect in controlling the spreading of the epidemics. We first developed a description of bacterial movement along the network driven by advection and diffusion; afterward, we have included the movement of human populations. This latter model allowed us to establish the conditions that can trigger epidemic waves that start from the coastal region, where bacteria are autochthonous, and travel inland. In particular, our findings suggest that even relatively low values of human diffusion can have the epidemic propagate upstream. The interaction between climate, hydrology and epidemic events is still much debated, since no clear correlation between climatologic and epidemiological phenomena has emerged so far. However, a spatial assessment of hydrological and epidemiological mechanisms could be crucial to understand the evolution of cholera outbreaks. In particular, a hotly debated topic is the understanding of the mechanisms that can generate patterns of cholera incidence that exhibit an intra-annual double peak, as frequently observed in endemic region such as Bangladesh. One of the possible explanations proposed in the literature is that spring droughts cause bacteria concentration in water to rise dramatically, triggering the first peak. On the other hand similar mechanisms can occur during flood recessions in autumn together with major water sanitation system failures and higher population density. We show here the results of an ecohydrological model that couples the dynamics of the disease to a description of both the local water reservoir and of the local river section. The goal of this modeling exercise is to reproduce and understand the mechanisms behind intra-annual cholera incidence dynamics driven by hydrologic variability.

Using phenomenological models for forecasting the 2015 Ebola challenge.

PubMed

Pell, Bruce; Kuang, Yang; Viboud, Cecile; Chowell, Gerardo

2018-03-01

The rising number of novel pathogens threatening the human population has motivated the application of mathematical modeling for forecasting the trajectory and size of epidemics. We summarize the real-time forecasting results of the logistic equation during the 2015 Ebola challenge focused on predicting synthetic data derived from a detailed individual-based model of Ebola transmission dynamics and control. We also carry out a post-challenge comparison of two simple phenomenological models. In particular, we systematically compare the logistic growth model and a recently introduced generalized Richards model (GRM) that captures a range of early epidemic growth profiles ranging from sub-exponential to exponential growth. Specifically, we assess the performance of each model for estimating the reproduction number, generate short-term forecasts of the epidemic trajectory, and predict the final epidemic size. During the challenge the logistic equation consistently underestimated the final epidemic size, peak timing and the number of cases at peak timing with an average mean absolute percentage error (MAPE) of 0.49, 0.36 and 0.40, respectively. Post-challenge, the GRM which has the flexibility to reproduce a range of epidemic growth profiles ranging from early sub-exponential to exponential growth dynamics outperformed the logistic growth model in ascertaining the final epidemic size as more incidence data was made available, while the logistic model underestimated the final epidemic even with an increasing amount of data of the evolving epidemic. Incidence forecasts provided by the generalized Richards model performed better across all scenarios and time points than the logistic growth model with mean RMS decreasing from 78.00 (logistic) to 60.80 (GRM). Both models provided reasonable predictions of the effective reproduction number, but the GRM slightly outperformed the logistic growth model with a MAPE of 0.08 compared to 0.10, averaged across all scenarios and time points. Our findings further support the consideration of transmission models that incorporate flexible early epidemic growth profiles in the forecasting toolkit. Such models are particularly useful for quickly evaluating a developing infectious disease outbreak using only case incidence time series of the early phase of an infectious disease outbreak. Copyright © 2016 The Authors. Published by Elsevier B.V. All rights reserved.

Evaluating potential fire behavior in lodgepole pine-dominated forests after a mountain pine beetle epidemic in north-central Colorado

Treesearch

Jennifer G. Klutsch; Mike A. Battaglia; Daniel R. West; Sheryl L. Costello; Jose F. Negron

2011-01-01

A mountain pine beetle outbreak in Colorado lodgepole pine forests has altered stand and fuel characteristics that affect potential fire behavior. Using the Fire and Fuels Extension to the Forest Vegetation Simulator, potential fire behavior was modeled for uninfested and mountain pine beetle-affected plots 7 years after outbreak initiation and 10 and 80% projected...

Bifurcation analysis of a discrete SIS model with bilinear incidence depending on new infection.

PubMed

Cao, Hui; Zhou, Yicang; Ma, Zhien

2013-01-01

A discrete SIS epidemic model with the bilinear incidence depending on the new infection is formulated and studied. The condition for the global stability of the disease free equilibrium is obtained. The existence of the endemic equilibrium and its stability are investigated. More attention is paid to the existence of the saddle-node bifurcation, the flip bifurcation, and the Hopf bifurcation. Sufficient conditions for those bifurcations have been obtained. Numerical simulations are conducted to demonstrate our theoretical results and the complexity of the model.

Percolation and epidemics in a two-dimensional small world

NASA Astrophysics Data System (ADS)

Newman, M. E.; Jensen, I.; Ziff, R. M.

2002-02-01

Percolation on two-dimensional small-world networks has been proposed as a model for the spread of plant diseases. In this paper we give an analytic solution of this model using a combination of generating function methods and high-order series expansion. Our solution gives accurate predictions for quantities such as the position of the percolation threshold and the typical size of disease outbreaks as a function of the density of ``shortcuts'' in the small-world network. Our results agree with scaling hypotheses and numerical simulations for the same model.

Real-time numerical forecast of global epidemic spreading: case study of 2009 A/H1N1pdm.

PubMed

Tizzoni, Michele; Bajardi, Paolo; Poletto, Chiara; Ramasco, José J; Balcan, Duygu; Gonçalves, Bruno; Perra, Nicola; Colizza, Vittoria; Vespignani, Alessandro

2012-12-13

Mathematical and computational models for infectious diseases are increasingly used to support public-health decisions; however, their reliability is currently under debate. Real-time forecasts of epidemic spread using data-driven models have been hindered by the technical challenges posed by parameter estimation and validation. Data gathered for the 2009 H1N1 influenza crisis represent an unprecedented opportunity to validate real-time model predictions and define the main success criteria for different approaches. We used the Global Epidemic and Mobility Model to generate stochastic simulations of epidemic spread worldwide, yielding (among other measures) the incidence and seeding events at a daily resolution for 3,362 subpopulations in 220 countries. Using a Monte Carlo Maximum Likelihood analysis, the model provided an estimate of the seasonal transmission potential during the early phase of the H1N1 pandemic and generated ensemble forecasts for the activity peaks in the northern hemisphere in the fall/winter wave. These results were validated against the real-life surveillance data collected in 48 countries, and their robustness assessed by focusing on 1) the peak timing of the pandemic; 2) the level of spatial resolution allowed by the model; and 3) the clinical attack rate and the effectiveness of the vaccine. In addition, we studied the effect of data incompleteness on the prediction reliability. Real-time predictions of the peak timing are found to be in good agreement with the empirical data, showing strong robustness to data that may not be accessible in real time (such as pre-exposure immunity and adherence to vaccination campaigns), but that affect the predictions for the attack rates. The timing and spatial unfolding of the pandemic are critically sensitive to the level of mobility data integrated into the model. Our results show that large-scale models can be used to provide valuable real-time forecasts of influenza spreading, but they require high-performance computing. The quality of the forecast depends on the level of data integration, thus stressing the need for high-quality data in population-based models, and of progressive updates of validated available empirical knowledge to inform these models.

Stability analysis of multi-group deterministic and stochastic epidemic models with vaccination rate

NASA Astrophysics Data System (ADS)

Wang, Zhi-Gang; Gao, Rui-Mei; Fan, Xiao-Ming; Han, Qi-Xing

2014-09-01

We discuss in this paper a deterministic multi-group MSIR epidemic model with a vaccination rate, the basic reproduction number ℛ0, a key parameter in epidemiology, is a threshold which determines the persistence or extinction of the disease. By using Lyapunov function techniques, we show if ℛ0 is greater than 1 and the deterministic model obeys some conditions, then the disease will prevail, the infective persists and the endemic state is asymptotically stable in a feasible region. If ℛ0 is less than or equal to 1, then the infective disappear so the disease dies out. In addition, stochastic noises around the endemic equilibrium will be added to the deterministic MSIR model in order that the deterministic model is extended to a system of stochastic ordinary differential equations. In the stochastic version, we carry out a detailed analysis on the asymptotic behavior of the stochastic model. In addition, regarding the value of ℛ0, when the stochastic system obeys some conditions and ℛ0 is greater than 1, we deduce the stochastic system is stochastically asymptotically stable. Finally, the deterministic and stochastic model dynamics are illustrated through computer simulations.

Heterogeneous network epidemics: real-time growth, variance and extinction of infection.

PubMed

Ball, Frank; House, Thomas

2017-09-01

Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular choice in theoretical studies since it combines the ability to specify the distribution of the number of contacts (degree) with analytical tractability. Here we consider the early real-time behaviour of the Markovian SIR epidemic model on a configuration model network using a multitype branching process. We find closed-form analytic expressions for the mean and variance of the number of infectious individuals as a function of time and the degree of the initially infected individual(s), and write down a system of differential equations for the probability of extinction by time t that are numerically fast compared to Monte Carlo simulation. We show that these quantities are all sensitive to the degree distribution-in particular we confirm that the mean prevalence of infection depends on the first two moments of the degree distribution and the variance in prevalence depends on the first three moments of the degree distribution. In contrast to most existing analytic approaches, the accuracy of these results does not depend on having a large number of infectious individuals, meaning that in the large population limit they would be asymptotically exact even for one initial infectious individual.

Inhomogeneity of epidemic spreading with entropy-based infected clusters.

PubMed

Wen-Jie, Zhou; Xing-Yuan, Wang

2013-12-01

Considering the difference in the sizes of the infected clusters in the dynamic complex networks, the normalized entropy based on infected clusters (δ*) is proposed to characterize the inhomogeneity of epidemic spreading. δ* gives information on the variability of the infected clusters in the system. We investigate the variation in the inhomogeneity of the distribution of the epidemic with the absolute velocity v of moving agent, the infection density ρ, and the interaction radius r. By comparing δ* in the dynamic networks with δH* in homogeneous mode, the simulation experiments show that the inhomogeneity of epidemic spreading becomes smaller with the increase of v, ρ, r.

On the estimation of the reproduction number based on misreported epidemic data.

PubMed

Azmon, Amin; Faes, Christel; Hens, Niel

2014-03-30

Epidemic data often suffer from underreporting and delay in reporting. In this paper, we investigated the impact of delays and underreporting on estimates of reproduction number. We used a thinned version of the epidemic renewal equation to describe the epidemic process while accounting for the underlying reporting system. Assuming a constant reporting parameter, we used different delay patterns to represent the delay structure in our model. Instead of assuming a fixed delay distribution, we estimated the delay parameters while assuming a smooth function for the reproduction number over time. In order to estimate the parameters, we used a Bayesian semiparametric approach with penalized splines, allowing both flexibility and exact inference provided by MCMC. To show the performance of our method, we performed different simulation studies. We conducted sensitivity analyses to investigate the impact of misspecification of the delay pattern and the impact of assuming nonconstant reporting parameters on the estimates of the reproduction numbers. We showed that, whenever available, additional information about time-dependent underreporting can be taken into account. As an application of our method, we analyzed confirmed daily A(H1N1) v2009 cases made publicly available by the World Health Organization for Mexico and the USA. Copyright © 2013 John Wiley & Sons, Ltd.

Evolution of scaling emergence in large-scale spatial epidemic spreading.

PubMed

Wang, Lin; Li, Xiang; Zhang, Yi-Qing; Zhang, Yan; Zhang, Kan

2011-01-01

Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified. In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence. The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease.

A Distributed Platform for Global-Scale Agent-Based Models of Disease Transmission

PubMed Central

Parker, Jon; Epstein, Joshua M.

2013-01-01

The Global-Scale Agent Model (GSAM) is presented. The GSAM is a high-performance distributed platform for agent-based epidemic modeling capable of simulating a disease outbreak in a population of several billion agents. It is unprecedented in its scale, its speed, and its use of Java. Solutions to multiple challenges inherent in distributing massive agent-based models are presented. Communication, synchronization, and memory usage are among the topics covered in detail. The memory usage discussion is Java specific. However, the communication and synchronization discussions apply broadly. We provide benchmarks illustrating the GSAM’s speed and scalability. PMID:24465120

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Zhang, Xinhong; Jiang, Daqing; Hayat, Tasawar; Ahmad, Bashir

2017-10-01

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s < 1, the disease of stochastic autonomous SVIR model will die out exponentially; if R˜0s > 1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R˜0s > 1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

Global stability and optimal control of epidemic spreading on multiplex networks with nonlinear mutual interaction

NASA Astrophysics Data System (ADS)

Jia, Nan; Ding, Li; Liu, Yu-Jing; Hu, Ping

2018-07-01

In this paper, we consider two interacting pathogens spreading on multiplex networks. Each pathogen spreads only on its single layer, and different layers have the same individuals but different network topology. A state-dependent infectious rate is proposed to describe the nonlinear mutual interaction during the propagation of two pathogens. Then a novel epidemic spreading model incorporating treatment control strategy is established. We investigate the global asymptotic stability of the equilibrium points by using Dulac's criterion, Poincaré-Bendixson theorem and Lyapunov method. Furthermore, we discuss an optimal strategy to minimize the total number of the infected individuals and the cost associated with treatment control for both spreading of two pathogens. Finally, numerical simulations are presented to show the validity and efficiency of our results.

Application Architecture of Avian Influenza Research Collaboration Network in Korea e-Science

NASA Astrophysics Data System (ADS)

Choi, Hoon; Lee, Junehawk

In the pursuit of globalization of the AI e-Science environment, KISTI is fostering to extend the AI research community to the AI research institutes of neighboring countries and to share the AI e-Science environment with them in the near future. In this paper we introduce the application architecture of AI research collaboration network (AIRCoN). AIRCoN is a global e-Science environment for AI research conducted by KISTI. It consists of AI virus sequence information sharing system for sufficing data requirement of research community, integrated analysis environment for analyzing the mutation pattern of AI viruses and their risks, epidemic modeling and simulation environment for establishing national effective readiness strategy against AI pandemics, and knowledge portal for sharing expertise of epidemic study and unpublished research results with community members.

Evaluating neighborhood structures for modeling intercity diffusion of large-scale dengue epidemics.

PubMed

Wen, Tzai-Hung; Hsu, Ching-Shun; Hu, Ming-Che

2018-05-03

Dengue fever is a vector-borne infectious disease that is transmitted by contact between vector mosquitoes and susceptible hosts. The literature has addressed the issue on quantifying the effect of individual mobility on dengue transmission. However, there are methodological concerns in the spatial regression model configuration for examining the effect of intercity-scale human mobility on dengue diffusion. The purposes of the study are to investigate the influence of neighborhood structures on intercity epidemic progression from pre-epidemic to epidemic periods and to compare definitions of different neighborhood structures for interpreting the spread of dengue epidemics. We proposed a framework for assessing the effect of model configurations on dengue incidence in 2014 and 2015, which were the most severe outbreaks in 70 years in Taiwan. Compared with the conventional model configuration in spatial regression analysis, our proposed model used a radiation model, which reflects population flow between townships, as a spatial weight to capture the structure of human mobility. The results of our model demonstrate better model fitting performance, indicating that the structure of human mobility has better explanatory power in dengue diffusion than the geometric structure of administration boundaries and geographic distance between centroids of cities. We also identified spatial-temporal hierarchy of dengue diffusion: dengue incidence would be influenced by its immediate neighboring townships during pre-epidemic and epidemic periods, and also with more distant neighbors (based on mobility) in pre-epidemic periods. Our findings suggest that the structure of population mobility could more reasonably capture urban-to-urban interactions, which implies that the hub cities could be a "bridge" for large-scale transmission and make townships that immediately connect to hub cities more vulnerable to dengue epidemics.

A study on spatial decision support systems for HIV/AIDS prevention based on COM GIS technology

NASA Astrophysics Data System (ADS)

Yang, Kun; Luo, Huasong; Peng, Shungyun; Xu, Quanli

2007-06-01

Based on the deeply analysis of the current status and the existing problems of GIS technology applications in Epidemiology, this paper has proposed the method and process for establishing the spatial decision support systems of AIDS epidemic prevention by integrating the COM GIS, Spatial Database, GPS, Remote Sensing, and Communication technologies, as well as ASP and ActiveX software development technologies. One of the most important issues for constructing the spatial decision support systems of AIDS epidemic prevention is how to integrate the AIDS spreading models with GIS. The capabilities of GIS applications in the AIDS epidemic prevention have been described here in this paper firstly. Then some mature epidemic spreading models have also been discussed for extracting the computation parameters. Furthermore, a technical schema has been proposed for integrating the AIDS spreading models with GIS and relevant geospatial technologies, in which the GIS and model running platforms share a common spatial database and the computing results can be spatially visualized on Desktop or Web GIS clients. Finally, a complete solution for establishing the decision support systems of AIDS epidemic prevention has been offered in this paper based on the model integrating methods and ESRI COM GIS software packages. The general decision support systems are composed of data acquisition sub-systems, network communication sub-systems, model integrating sub-systems, AIDS epidemic information spatial database sub-systems, AIDS epidemic information querying and statistical analysis sub-systems, AIDS epidemic dynamic surveillance sub-systems, AIDS epidemic information spatial analysis and decision support sub-systems, as well as AIDS epidemic information publishing sub-systems based on Web GIS.

REPRODUCTIVE NUMBERS, EPIDEMIC SPREAD AND CONTROL IN A COMMUNITY OF HOUSEHOLDS

PubMed Central

Goldstein, E.; Paur, K.; Fraser, C.; Kenah, E.; Wallinga, J.; Lipsitch, M.

2009-01-01

Many of the studies on emerging epidemics (such as SARS and pandemic flu) use mass action models to estimate reproductive numbers and the needed control measures. In reality, transmission patterns are more complex due to the presence of various social networks. One level of complexity can be accommodated by considering a community of households. Our study of transmission dynamics in a community of households emphasizes five types of reproductive numbers for the epidemic spread: household-to-household reproductive number, leaky vaccine-associated reproductive numbers, perfect vaccine reproductive number, growth rate reproductive number, and the individual reproductive number. Each of those carries different information about the transmission dynamics and the required control measures, and often some of those can be estimated from the data while others cannot. Simulations have shown that under certain scenarios there is an ordering for those reproductive numbers. We have proven a number of ordering inequalities under general assumptions about the individual infectiousness profiles. Those inequalities allow, for instance, to estimate the needed vaccine coverage and other control measures without knowing the various transmission parameters in the models. Along the way, we’ve also shown that in choosing between increasing vaccine efficacy and increasing coverage levels by the same factor, preference should go to efficacy. PMID:19559715

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches.

PubMed

Wiratsudakul, Anuwat; Suparit, Parinya; Modchang, Charin

2018-01-01

The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms "dynamics," "mathematical model," "modeling," and "vector-borne" together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were "compartmental," "spatial," "metapopulation," "network," "individual-based," "agent-based" AND "Zika." All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation.

The threshold of a stochastic delayed SIR epidemic model with temporary immunity

NASA Astrophysics Data System (ADS)

Liu, Qun; Chen, Qingmei; Jiang, Daqing

2016-05-01

This paper is concerned with the asymptotic properties of a stochastic delayed SIR epidemic model with temporary immunity. Sufficient conditions for extinction and persistence in the mean of the epidemic are established. The threshold between persistence in the mean and extinction of the epidemic is obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number R0 of the deterministic system.

School closure as an influenza mitigation strategy: how variations in legal authority and plan criteria can alter the impact.

PubMed

Potter, Margaret A; Brown, Shawn T; Cooley, Phillip C; Sweeney, Patricia M; Hershey, Tina B; Gleason, Sherrianne M; Lee, Bruce Y; Keane, Christopher R; Grefenstette, John; Burke, Donald S

2012-11-14

States' pandemic influenza plans and school closure statutes are intended to guide state and local officials, but most faced a great deal of uncertainty during the 2009 influenza H1N1 epidemic. Questions remained about whether, when, and for how long to close schools and about which agencies and officials had legal authority over school closures. This study began with analysis of states' school-closure statutes and pandemic influenza plans to identify the variations among them. An agent-based model of one state was used to represent as constants a population's demographics, commuting patterns, work and school attendance, and community mixing patterns while repeated simulations explored the effects of variations in school closure authority, duration, closure thresholds, and reopening criteria. The results show no basis on which to justify statewide rather than school-specific or community-specific authority for school closures. Nor do these simulations offer evidence to require school closures promptly at the earliest stage of an epidemic. More important are criteria based on monitoring of local case incidence and on authority to sustain closure periods sufficiently to achieve epidemic mitigation. This agent-based simulation suggests several ways to improve statutes and influenza plans. First, school closure should remain available to state and local authorities as an influenza mitigation strategy. Second, influenza plans need not necessarily specify the threshold for school closures but should clearly define provisions for early and ongoing local monitoring. Finally, school closure authority may be exercised at the statewide or local level, so long as decisions are informed by monitoring incidence in local communities and schools.

A Method to Estimate the Size and Characteristics of HIV-positive Populations Using an Individual-based Stochastic Simulation Model.

PubMed

Nakagawa, Fumiyo; van Sighem, Ard; Thiebaut, Rodolphe; Smith, Colette; Ratmann, Oliver; Cambiano, Valentina; Albert, Jan; Amato-Gauci, Andrew; Bezemer, Daniela; Campbell, Colin; Commenges, Daniel; Donoghoe, Martin; Ford, Deborah; Kouyos, Roger; Lodwick, Rebecca; Lundgren, Jens; Pantazis, Nikos; Pharris, Anastasia; Quinten, Chantal; Thorne, Claire; Touloumi, Giota; Delpech, Valerie; Phillips, Andrew

2016-03-01

It is important not only to collect epidemiologic data on HIV but to also fully utilize such information to understand the epidemic over time and to help inform and monitor the impact of policies and interventions. We describe and apply a novel method to estimate the size and characteristics of HIV-positive populations. The method was applied to data on men who have sex with men living in the UK and to a pseudo dataset to assess performance for different data availability. The individual-based simulation model was calibrated using an approximate Bayesian computation-based approach. In 2013, 48,310 (90% plausibility range: 39,900-45,560) men who have sex with men were estimated to be living with HIV in the UK, of whom 10,400 (6,160-17,350) were undiagnosed. There were an estimated 3,210 (1,730-5,350) infections per year on average between 2010 and 2013. Sixty-two percent of the total HIV-positive population are thought to have viral load <500 copies/ml. In the pseudo-epidemic example, HIV estimates have narrower plausibility ranges and are closer to the true number, the greater the data availability to calibrate the model. We demonstrate that our method can be applied to settings with less data, however plausibility ranges for estimates will be wider to reflect greater uncertainty of the data used to fit the model.

Power law incidence rate in epidemic models. Comment on: "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Allen, Linda J. S.

2016-09-01

Dr. Chowell and colleagues emphasize the importance of considering a variety of modeling approaches to characterize the growth of an epidemic during the early stages [1]. A fit of data from the 2009 H1N1 influenza pandemic and the 2014-2015 Ebola outbreak to models indicates sub-exponential growth, in contrast to the classic, homogeneous-mixing SIR model with exponential growth. With incidence rate βSI / N and S approximately equal to the total population size N, the number of new infections in an SIR epidemic model grows exponentially as in the differential equation,

Information spreading in complex networks with participation of independent spreaders

NASA Astrophysics Data System (ADS)

Ma, Kun; Li, Weihua; Guo, Quantong; Zheng, Xiaoqi; Zheng, Zhiming; Gao, Chao; Tang, Shaoting

2018-02-01

Information diffusion dynamics in complex networks is often modeled as a contagion process among neighbors which is analogous to epidemic diffusion. The attention of previous literature is mainly focused on epidemic diffusion within one network, which, however neglects the possible interactions between nodes beyond the underlying network. The disease can be transmitted to other nodes by other means without following the links in the focal network. Here we account for this phenomenon by introducing the independent spreaders in a susceptible-infectious-recovered contagion process. We derive the critical epidemic thresholds on Erdős-Rényi and scale-free networks as a function of infectious rate, recovery rate and the activeness of independent spreaders. We also present simulation results on ER and SF networks, as well as on a real-world email network. The result shows that the extent to which a disease can infect might be more far-reaching, than we can explain in terms of link contagion only. Besides, these results also help to explain how activeness of independent spreaders can affect the diffusion process, which can be used to explore many other dynamical processes.

Dynamics of public opinion under the influence of epidemic spreading

NASA Astrophysics Data System (ADS)

Wu, Junhui; Ni, Shunjiang; Shen, Shifei

2016-02-01

In this paper, we propose a novel model with dynamically adjusted confidence level of others to investigate the propagation of public opinion on whether to buy chicken in the case of avian influenza infection in humans. We study how people adjust their confidence level in other people’s opinions according to their perceived infection risk and how the opinion evolution and epidemic spreading affect each other on different complex networks by taking into account the spreading feature of avian influenza, that is, only people who buy chicken are possible to be infected. The simulation results show that in a closed system, people who support buying chicken and people who are infected can achieve a dynamic balance after a few time-steps, and the final stable state is mainly dependent on the level of people’s risk perception, rather than the initial distribution of the different opinions. Our results imply that in the course of the epidemic spread, transparent and timely announcement of the number of infections and the risk of infection can help people take the right self-protection actions, and thus help control the spread of avian influenza.

A simulation analysis to characterize the dynamics of vaccinating behaviour on contact networks.

PubMed

Perisic, Ana; Bauch, Chris T

2009-05-28

Human behavior influences infectious disease transmission, and numerous "prevalence-behavior" models have analyzed this interplay. These previous analyses assumed homogeneously mixing populations without spatial or social structure. However, spatial and social heterogeneity are known to significantly impact transmission dynamics and are particularly relevant for certain diseases. Previous work has demonstrated that social contact structure can change the individual incentive to vaccinate, thus enabling eradication of a disease under a voluntary vaccination policy when the corresponding homogeneous mixing model predicts that eradication is impossible due to free rider effects. Here, we extend this work and characterize the range of possible behavior-prevalence dynamics on a network. We simulate transmission of a vaccine-preventable infection through a random, static contact network. Individuals choose whether or not to vaccinate on any given day according to perceived risks of vaccination and infection. We find three possible outcomes for behavior-prevalence dynamics on this type of network: small final number vaccinated and final epidemic size (due to rapid control through voluntary ring vaccination); large final number vaccinated and significant final epidemic size (due to imperfect voluntary ring vaccination), and little or no vaccination and large final epidemic size (corresponding to little or no voluntary ring vaccination). We also show that the social contact structure enables eradication under a broad range of assumptions, except when vaccine risk is sufficiently high, the disease risk is sufficiently low, or individuals vaccinate too late for the vaccine to be effective. For populations where infection can spread only through social contact network, relatively small differences in parameter values relating to perceived risk or vaccination behavior at the individual level can translate into large differences in population-level outcomes such as final size and final number vaccinated. The qualitative outcome of rational, self interested behaviour under a voluntary vaccination policy can vary substantially depending on interactions between social contact structure, perceived vaccine and disease risks, and the way that individual vaccination decision-making is modelled.

A simulation analysis to characterize the dynamics of vaccinating behaviour on contact networks

PubMed Central

2009-01-01

Background Human behavior influences infectious disease transmission, and numerous "prevalence-behavior" models have analyzed this interplay. These previous analyses assumed homogeneously mixing populations without spatial or social structure. However, spatial and social heterogeneity are known to significantly impact transmission dynamics and are particularly relevant for certain diseases. Previous work has demonstrated that social contact structure can change the individual incentive to vaccinate, thus enabling eradication of a disease under a voluntary vaccination policy when the corresponding homogeneous mixing model predicts that eradication is impossible due to free rider effects. Here, we extend this work and characterize the range of possible behavior-prevalence dynamics on a network. Methods We simulate transmission of a vaccine-prevetable infection through a random, static contact network. Individuals choose whether or not to vaccinate on any given day according to perceived risks of vaccination and infection. Results We find three possible outcomes for behavior-prevalence dynamics on this type of network: small final number vaccinated and final epidemic size (due to rapid control through voluntary ring vaccination); large final number vaccinated and significant final epidemic size (due to imperfect voluntary ring vaccination), and little or no vaccination and large final epidemic size (corresponding to little or no voluntary ring vaccination). We also show that the social contact structure enables eradication under a broad range of assumptions, except when vaccine risk is sufficiently high, the disease risk is sufficiently low, or individuals vaccinate too late for the vaccine to be effective. Conclusion For populations where infection can spread only through social contact network, relatively small differences in parameter values relating to perceived risk or vaccination behavior at the individual level can translate into large differences in population-level outcomes such as final size and final number vaccinated. The qualitative outcome of rational, self interested behaviour under a voluntary vaccination policy can vary substantially depending on interactions between social contact structure, perceived vaccine and disease risks, and the way that individual vaccination decision-making is modelled. PMID:19476616

Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks

PubMed Central

Vestergaard, Christian L.; Génois, Mathieu

2015-01-01

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling. PMID:26517860

Temporal Gillespie Algorithm: Fast Simulation of Contagion Processes on Time-Varying Networks.

PubMed

Vestergaard, Christian L; Génois, Mathieu

2015-10-01

Stochastic simulations are one of the cornerstones of the analysis of dynamical processes on complex networks, and are often the only accessible way to explore their behavior. The development of fast algorithms is paramount to allow large-scale simulations. The Gillespie algorithm can be used for fast simulation of stochastic processes, and variants of it have been applied to simulate dynamical processes on static networks. However, its adaptation to temporal networks remains non-trivial. We here present a temporal Gillespie algorithm that solves this problem. Our method is applicable to general Poisson (constant-rate) processes on temporal networks, stochastically exact, and up to multiple orders of magnitude faster than traditional simulation schemes based on rejection sampling. We also show how it can be extended to simulate non-Markovian processes. The algorithm is easily applicable in practice, and as an illustration we detail how to simulate both Poissonian and non-Markovian models of epidemic spreading. Namely, we provide pseudocode and its implementation in C++ for simulating the paradigmatic Susceptible-Infected-Susceptible and Susceptible-Infected-Recovered models and a Susceptible-Infected-Recovered model with non-constant recovery rates. For empirical networks, the temporal Gillespie algorithm is here typically from 10 to 100 times faster than rejection sampling.

A Mechanistic Model of Botrytis cinerea on Grapevines That Includes Weather, Vine Growth Stage, and the Main Infection Pathways

PubMed Central

González-Domínguez, Elisa; Caffi, Tito; Ciliberti, Nicola; Rossi, Vittorio

2015-01-01

A mechanistic model for Botrytis cinerea on grapevine was developed. The model, which accounts for conidia production on various inoculum sources and for multiple infection pathways, considers two infection periods. During the first period (“inflorescences clearly visible” to “berries groat-sized”), the model calculates: i) infection severity on inflorescences and young clusters caused by conidia (SEV1). During the second period (“majority of berries touching” to “berries ripe for harvest”), the model calculates: ii) infection severity of ripening berries by conidia (SEV2); and iii) severity of berry-to-berry infection caused by mycelium (SEV3). The model was validated in 21 epidemics (vineyard × year combinations) between 2009 and 2014 in Italy and France. A discriminant function analysis (DFA) was used to: i) evaluate the ability of the model to predict mild, intermediate, and severe epidemics; and ii) assess how SEV1, SEV2, and SEV3 contribute to epidemics. The model correctly classified the severity of 17 of 21 epidemics. Results from DFA were also used to calculate the daily probabilities that an ongoing epidemic would be mild, intermediate, or severe. SEV1 was the most influential variable in discriminating between mild and intermediate epidemics, whereas SEV2 and SEV3 were relevant for discriminating between intermediate and severe epidemics. The model represents an improvement of previous B. cinerea models in viticulture and could be useful for making decisions about Botrytis bunch rot control. PMID:26457808

Leveraging contact network structure in the design of cluster randomized trials.

PubMed

Harling, Guy; Wang, Rui; Onnela, Jukka-Pekka; De Gruttola, Victor

2017-02-01

In settings like the Ebola epidemic, where proof-of-principle trials have provided evidence of efficacy but questions remain about the effectiveness of different possible modes of implementation, it may be useful to conduct trials that not only generate information about intervention effects but also themselves provide public health benefit. Cluster randomized trials are of particular value for infectious disease prevention research by virtue of their ability to capture both direct and indirect effects of intervention, the latter of which depends heavily on the nature of contact networks within and across clusters. By leveraging information about these networks-in particular the degree of connection across randomized units, which can be obtained at study baseline-we propose a novel class of connectivity-informed cluster trial designs that aim both to improve public health impact (speed of epidemic control) and to preserve the ability to detect intervention effects. We several designs for cluster randomized trials with staggered enrollment, in each of which the order of enrollment is based on the total number of ties (contacts) from individuals within a cluster to individuals in other clusters. Our designs can accommodate connectivity based either on the total number of external connections at baseline or on connections only to areas yet to receive the intervention. We further consider a "holdback" version of the designs in which control clusters are held back from re-randomization for some time interval. We investigate the performance of these designs in terms of epidemic control outcomes (time to end of epidemic and cumulative incidence) and power to detect intervention effect, by simulating vaccination trials during an SEIR-type epidemic outbreak using a network-structured agent-based model. We compare results to those of a traditional Stepped Wedge trial. In our simulation studies, connectivity-informed designs lead to a 20% reduction in cumulative incidence compared to comparable traditional study designs, but have little impact on epidemic length. Power to detect intervention effect is reduced in all connectivity-informed designs, but "holdback" versions provide power that is very close to that of a traditional Stepped Wedge approach. Incorporating information about cluster connectivity in the design of cluster randomized trials can increase their public health impact, especially in acute outbreak settings. Using this information helps control outbreaks-by minimizing the number of cross-cluster infections-with very modest cost in terms of power to detect effectiveness.

The Stochastic Modelling of Endemic Diseases

NASA Astrophysics Data System (ADS)

Susvitasari, Kurnia; Siswantining, Titin

2017-01-01

A study about epidemic has been conducted since a long time ago, but genuine progress was hardly forthcoming until the end of the 19th century (Bailey, 1975). Both deterministic and stochastic models were used to describe these. Then, from 1927 to 1939 Kermack and McKendrick introduced a generality of this model, including some variables to consider such as rate of infection and recovery. The purpose of this project is to investigate the behaviour of the models when we set the basic reproduction number, R0. This quantity is defined as the expected number of contacts made by a typical infective to susceptibles in the population. According to the epidemic threshold theory, when R0 ≤ 1, minor epidemic occurs with probability one in both approaches, but when R0 > 1, the deterministic and stochastic models have different interpretation. In the deterministic approach, major epidemic occurs with probability one when R0 > 1 and predicts that the disease will settle down to an endemic equilibrium. Stochastic models, on the other hand, identify that the minor epidemic can possibly occur. If it does, then the epidemic will die out quickly. Moreover, if we let the population size be large and the major epidemic occurs, then it will take off and then reach the endemic level and move randomly around the deterministic’s equilibrium.

Estimating the Delay between Host Infection and Disease (Incubation Period) and Assessing Its Significance to the Epidemiology of Plant Diseases

PubMed Central

Leclerc, Melen; Doré, Thierry; Gilligan, Christopher A.; Lucas, Philippe; Filipe, João A. N.

2014-01-01

Knowledge of the incubation period of infectious diseases (time between host infection and expression of disease symptoms) is crucial to our epidemiological understanding and the design of appropriate prevention and control policies. Plant diseases cause substantial damage to agricultural and arboricultural systems, but there is still very little information about how the incubation period varies within host populations. In this paper, we focus on the incubation period of soilborne plant pathogens, which are difficult to detect as they spread and infect the hosts underground and above-ground symptoms occur considerably later. We conducted experiments on Rhizoctonia solani in sugar beet, as an example patho-system, and used modelling approaches to estimate the incubation period distribution and demonstrate the impact of differing estimations on our epidemiological understanding of plant diseases. We present measurements of the incubation period obtained in field conditions, fit alternative probability models to the data, and show that the incubation period distribution changes with host age. By simulating spatially-explicit epidemiological models with different incubation-period distributions, we study the conditions for a significant time lag between epidemics of cryptic infection and the associated epidemics of symptomatic disease. We examine the sensitivity of this lag to differing distributional assumptions about the incubation period (i.e. exponential versus Gamma). We demonstrate that accurate information about the incubation period distribution of a pathosystem can be critical in assessing the true scale of pathogen invasion behind early disease symptoms in the field; likewise, it can be central to model-based prediction of epidemic risk and evaluation of disease management strategies. Our results highlight that reliance on observation of disease symptoms can cause significant delay in detection of soil-borne pathogen epidemics and mislead practitioners and epidemiologists about the timing, extent, and viability of disease control measures for limiting economic loss. PMID:24466153

Estimating the delay between host infection and disease (incubation period) and assessing its significance to the epidemiology of plant diseases.

PubMed

Leclerc, Melen; Doré, Thierry; Gilligan, Christopher A; Lucas, Philippe; Filipe, João A N

2014-01-01

Knowledge of the incubation period of infectious diseases (time between host infection and expression of disease symptoms) is crucial to our epidemiological understanding and the design of appropriate prevention and control policies. Plant diseases cause substantial damage to agricultural and arboricultural systems, but there is still very little information about how the incubation period varies within host populations. In this paper, we focus on the incubation period of soilborne plant pathogens, which are difficult to detect as they spread and infect the hosts underground and above-ground symptoms occur considerably later. We conducted experiments on Rhizoctonia solani in sugar beet, as an example patho-system, and used modelling approaches to estimate the incubation period distribution and demonstrate the impact of differing estimations on our epidemiological understanding of plant diseases. We present measurements of the incubation period obtained in field conditions, fit alternative probability models to the data, and show that the incubation period distribution changes with host age. By simulating spatially-explicit epidemiological models with different incubation-period distributions, we study the conditions for a significant time lag between epidemics of cryptic infection and the associated epidemics of symptomatic disease. We examine the sensitivity of this lag to differing distributional assumptions about the incubation period (i.e. exponential versus Gamma). We demonstrate that accurate information about the incubation period distribution of a pathosystem can be critical in assessing the true scale of pathogen invasion behind early disease symptoms in the field; likewise, it can be central to model-based prediction of epidemic risk and evaluation of disease management strategies. Our results highlight that reliance on observation of disease symptoms can cause significant delay in detection of soil-borne pathogen epidemics and mislead practitioners and epidemiologists about the timing, extent, and viability of disease control measures for limiting economic loss.

Quarantine-generated phase transition in epidemic spreading

NASA Astrophysics Data System (ADS)

Lagorio, C.; Dickison, M.; Vazquez, F.; Braunstein, L. A.; Macri, P. A.; Migueles, M. V.; Havlin, S.; Stanley, H. E.

2011-02-01

We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold wc separating a phase (w

Quarantine generated phase transition in epidemic spreading

NASA Astrophysics Data System (ADS)

Dicksion, Mark; Lagorio, Cecilia; Vazquez, F.; Braunstein, L.; Macri, P. A.; Migueles, M. V.; Havlin, S.; Stanley, H. E.

2011-03-01

We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered (SIR) model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w, and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold wc separating a phase (w =wc) where the disease does not spread out. We find that in our model the topology of the network strongly affects the size of the propagation, and that wc increases with the mean degree and heterogeneity of the network. We also find that wc is reduced if we perform a preferential rewiring, in which the rewiring probability is proportional to the degree of infected nodes.

Epidemics spread in heterogeneous populations

NASA Astrophysics Data System (ADS)

Capała, Karol; Dybiec, Bartłomiej

2017-05-01

Individuals building populations are subject to variability. This variability affects progress of epidemic outbreaks, because individuals tend to be more or less resistant. Individuals also differ with respect to their recovery rate. Here, properties of the SIR model in inhomogeneous populations are studied. It is shown that a small change in model's parameters, e.g. recovery or infection rate, can substantially change properties of final states which is especially well-visible in distributions of the epidemic size. In addition to the epidemic size and radii distributions, the paper explores first passage time properties of epidemic outbreaks.

Epidemic Percolation Networks, Epidemic Outcomes, and Interventions

DOE PAGES

Kenah, Eben; Miller, Joel C.

2011-01-01

Epidemic percolation networks (EPNs) are directed random networks that can be used to analyze stochastic “Susceptible-Infectious-Removed” (SIR) and “Susceptible-Exposed-Infectious-Removed” (SEIR) epidemic models, unifying and generalizing previous uses of networks and branching processes to analyze mass-action and network-based S(E)IR models. This paper explains the fundamental concepts underlying the definition and use of EPNs, using them to build intuition about the final outcomes of epidemics. We then show how EPNs provide a novel and useful perspective on the design of vaccination strategies.

Epidemic Percolation Networks, Epidemic Outcomes, and Interventions

PubMed Central

Kenah, Eben; Miller, Joel C.

2011-01-01

Epidemic percolation networks (EPNs) are directed random networks that can be used to analyze stochastic “Susceptible-Infectious-Removed” (SIR) and “Susceptible-Exposed-Infectious-Removed” (SEIR) epidemic models, unifying and generalizing previous uses of networks and branching processes to analyze mass-action and network-based S(E)IR models. This paper explains the fundamental concepts underlying the definition and use of EPNs, using them to build intuition about the final outcomes of epidemics. We then show how EPNs provide a novel and useful perspective on the design of vaccination strategies. PMID:21437002

Role of word-of-mouth for programs of voluntary vaccination: A game-theoretic approach.

PubMed

Bhattacharyya, Samit; Bauch, Chris T; Breban, Romulus

2015-11-01

We propose a model describing the synergetic feedback between word-of-mouth (WoM) and epidemic dynamics controlled by voluntary vaccination. The key feature consists in combining a game-theoretic model for the spread of WoM and a compartmental model describing VSIR disease dynamics in the presence of a program of voluntary vaccination. We evaluate and compare two scenarios for determinants of behavior, depending on what WoM disseminates: (1) vaccine advertising, which may occur whether or not an epidemic is ongoing and (2) epidemic status, notably disease prevalence. Understanding the synergy between the two strategies could be particularly important for designing voluntary vaccination campaigns. We find that, in the initial phase of an epidemic, vaccination uptake is determined more by vaccine advertising than the epidemic status. As the epidemic progresses, epidemic status becomes increasingly important for vaccination uptake, considerably accelerating vaccination uptake toward a stable vaccination coverage. Copyright © 2015 Elsevier Inc. All rights reserved.

Human mobility and time spent at destination: impact on spatial epidemic spreading.

PubMed

Poletto, Chiara; Tizzoni, Michele; Colizza, Vittoria

2013-12-07

Host mobility plays a fundamental role in the spatial spread of infectious diseases. Previous theoretical works based on the integration of network theory into the metapopulation framework have shown that the heterogeneities that characterize real mobility networks favor the propagation of epidemics. Nevertheless, the studies conducted so far assumed the mobility process to be either Markovian (in which the memory of the origin of each traveler is lost) or non-Markovian with a fixed traveling time scale (in which individuals travel to a destination and come back at a constant rate). Available statistics however show that the time spent by travelers at destination is characterized by wide fluctuations, ranging from a single day up to several months. Such varying length of stay crucially affects the chance and duration of mixing events among hosts and may therefore have a strong impact on the spread of an emerging disease. Here, we present an analytical and a computational study of epidemic processes on a complex subpopulation network where travelers have memory of their origin and spend a heterogeneously distributed time interval at their destination. Through analytical calculations and numerical simulations we show that the heterogeneity of the length of stay alters the expression of the threshold between local outbreak and global invasion, and, moreover, it changes the epidemic behavior of the system in case of a global outbreak. Additionally, our theoretical framework allows us to study the effect of changes in the traveling behavior in response to the infection, by considering a scenario in which sick individuals do not leave their home location. Finally, we compare the results of our non-Markovian framework with those obtained with a classic Markovian approach and find relevant differences between the two, in the estimate of the epidemic invasion potential, as well as of the timing and the pattern of its spatial spread. These results highlight the importance of properly accounting for host trip duration in epidemic models and open the path to the inclusion of such an additional layer of complexity to the existing modeling approaches. © 2013 Elsevier Ltd. All rights reserved.

Predicting Subnational Ebola Virus Disease Epidemic Dynamics from Sociodemographic Indicators

PubMed Central

Valeri, Linda; Patterson-Lomba, Oscar; Gurmu, Yared; Ablorh, Akweley; Bobb, Jennifer; Townes, F. William; Harling, Guy

2016-01-01

Background The recent Ebola virus disease (EVD) outbreak in West Africa has spread wider than any previous human EVD epidemic. While individual-level risk factors that contribute to the spread of EVD have been studied, the population-level attributes of subnational regions associated with outbreak severity have not yet been considered. Methods To investigate the area-level predictors of EVD dynamics, we integrated time series data on cumulative reported cases of EVD from the World Health Organization and covariate data from the Demographic and Health Surveys. We first estimated the early growth rates of epidemics in each second-level administrative district (ADM2) in Guinea, Sierra Leone and Liberia using exponential, logistic and polynomial growth models. We then evaluated how these growth rates, as well as epidemic size within ADM2s, were ecologically associated with several demographic and socio-economic characteristics of the ADM2, using bivariate correlations and multivariable regression models. Results The polynomial growth model appeared to best fit the ADM2 epidemic curves, displaying the lowest residual standard error. Each outcome was associated with various regional characteristics in bivariate models, however in stepwise multivariable models only mean education levels were consistently associated with a worse local epidemic. Discussion By combining two common methods—estimation of epidemic parameters using mathematical models, and estimation of associations using ecological regression models—we identified some factors predicting rapid and severe EVD epidemics in West African subnational regions. While care should be taken interpreting such results as anything more than correlational, we suggest that our approach of using data sources that were publicly available in advance of the epidemic or in real-time provides an analytic framework that may assist countries in understanding the dynamics of future outbreaks as they occur. PMID:27732614

Averting HIV Infections in New York City: A Modeling Approach Estimating the Future Impact of Additional Behavioral and Biomedical HIV Prevention Strategies

PubMed Central

Kessler, Jason; Myers, Julie E.; Nucifora, Kimberly A.; Mensah, Nana; Kowalski, Alexis; Sweeney, Monica; Toohey, Christopher; Khademi, Amin; Shepard, Colin; Cutler, Blayne; Braithwaite, R. Scott

2013-01-01

Background New York City (NYC) remains an epicenter of the HIV epidemic in the United States. Given the variety of evidence-based HIV prevention strategies available and the significant resources required to implement each of them, comparative studies are needed to identify how to maximize the number of HIV cases prevented most economically. Methods A new model of HIV disease transmission was developed integrating information from a previously validated micro-simulation HIV disease progression model. Specification and parameterization of the model and its inputs, including the intervention portfolio, intervention effects and costs were conducted through a collaborative process between the academic modeling team and the NYC Department of Health and Mental Hygiene. The model projects the impact of different prevention strategies, or portfolios of prevention strategies, on the HIV epidemic in NYC. Results Ten unique interventions were able to provide a prevention benefit at an annual program cost of less than $360,000, the threshold for consideration as a cost-saving intervention (because of offsets by future HIV treatment costs averted). An optimized portfolio of these specific interventions could result in up to a 34% reduction in new HIV infections over the next 20 years. The cost-per-infection averted of the portfolio was estimated to be $106,378; the total cost was in excess of $2 billion (over the 20 year period, or approximately $100 million per year, on average). The cost-savings of prevented infections was estimated at more than $5 billion (or approximately $250 million per year, on average). Conclusions Optimal implementation of a portfolio of evidence-based interventions can have a substantial, favorable impact on the ongoing HIV epidemic in NYC and provide future cost-saving despite significant initial costs. PMID:24058465

On the Spatial Spread of Rabies among Foxes

NASA Astrophysics Data System (ADS)

Murray, J. D.; Stanley, E. A.; Brown, D. L.

1986-11-01

We present a simple model for the spatial spread of rabies among foxes and use it to quantify its progress in England if rabies were introduced. The model is based on the known ecology of fox behaviour and on the assumption that the main vector for the spread of the disease is the rabid fox. Known data and facts are used to determine real parameter values involved in the model. We calculate the speed of propagation of the epizootic front, the threshold for the existence of an epidemic, the period and distance apart of the subsequent cyclical epidemics which follow the main front, and finally we quantify a means for control of the spatial spread of the disease. By way of illustration we use the model to determine the progress of rabies up through the southern part of England if it were introduced near Southampton. Estimates for the current fox density in England were used in the simulations. These suggest that the disease would reach Manchester within about 3.5 years, moving at speeds as high as 100 km per year in the central region. The model further indicates that although it might seem that the disease had disappeared after the wave had passed it would reappear in the south of England after just over 6 years and at periodic times after that. We consider the possibility of stopping the spread of the disease by creating a rabies `break' ahead of the front through vaccination to reduce the population to a level below the threshold for an epidemic to exist. Based on parameter values relevant to England, we estimate its minimum width to be about 15 km. The model suggests that vaccination has considerable advantages over severe culling.

Stochastic dynamics for reinfection by transmitted diseases

NASA Astrophysics Data System (ADS)

Barros, Alessandro S.; Pinho, Suani T. R.

2017-06-01

The use of stochastic models to study the dynamics of infectious diseases is an important tool to understand the epidemiological process. For several directly transmitted diseases, reinfection is a relevant process, which can be expressed by endogenous reactivation of the pathogen or by exogenous reinfection due to direct contact with an infected individual (with smaller reinfection rate σ β than infection rate β ). In this paper, we examine the stochastic susceptible, infected, recovered, infected (SIRI) model simulating the endogenous reactivation by a spontaneous reaction, while exogenous reinfection by a catalytic reaction. Analyzing the mean-field approximations of a site and pairs of sites, and Monte Carlo (MC) simulations for the particular case of exogenous reinfection, we obtained continuous phase transitions involving endemic, epidemic, and no transmission phases for the simple approach; the approach of pairs is better to describe the phase transition from endemic phase (susceptible, infected, susceptible (SIS)-like model) to epidemic phase (susceptible, infected, and removed or recovered (SIR)-like model) considering the comparison with MC results; the reinfection increases the peaks of outbreaks until the system reaches endemic phase. For the particular case of endogenous reactivation, the approach of pairs leads to a continuous phase transition from endemic phase (SIS-like model) to no transmission phase. Finally, there is no phase transition when both effects are taken into account. We hope the results of this study can be generalized for the susceptible, exposed, infected, and removed or recovered (SEIRIE) model, for which the state exposed (infected but not infectious), describing more realistically transmitted diseases such as tuberculosis. In future work, we also intend to investigate the effect of network topology on phase transitions when the SIRI model describes both transmitted diseases (σ <1 ) and social contagions (σ >1 ).

A discrete epidemic model for bovine Babesiosis disease and tick populations

NASA Astrophysics Data System (ADS)

Aranda, Diego F.; Trejos, Deccy Y.; Valverde, Jose C.

2017-06-01

In this paper, we provide and study a discrete model for the transmission of Babesiosis disease in bovine and tick populations. This model supposes a discretization of the continuous-time model developed by us previously. The results, here obtained by discrete methods as opposed to continuous ones, show that similar conclusions can be obtained for the discrete model subject to the assumption of some parametric constraints which were not necessary in the continuous case. We prove that these parametric constraints are not artificial and, in fact, they can be deduced from the biological significance of the model. Finally, some numerical simulations are given to validate the model and verify our theoretical study.

A Simple Model for Complex Dynamical Transitions in Epidemics

NASA Astrophysics Data System (ADS)

Earn, David J. D.; Rohani, Pejman; Bolker, Benjamin M.; Grenfell, Bryan T.

2000-01-01

Dramatic changes in patterns of epidemics have been observed throughout this century. For childhood infectious diseases such as measles, the major transitions are between regular cycles and irregular, possibly chaotic epidemics, and from regionally synchronized oscillations to complex, spatially incoherent epidemics. A simple model can explain both kinds of transitions as the consequences of changes in birth and vaccination rates. Measles is a natural ecological system that exhibits different dynamical transitions at different times and places, yet all of these transitions can be predicted as bifurcations of a single nonlinear model.

The threshold of a stochastic delayed SIR epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing

2016-11-01

In this paper, we study the threshold dynamics of a stochastic delayed SIR epidemic model with vaccination. We obtain sufficient conditions for extinction and persistence in the mean of the epidemic. The threshold between persistence in the mean and extinction of the stochastic system is also obtained. Compared with the corresponding deterministic model, the threshold affected by the white noise is smaller than the basic reproduction number Rbar0 of the deterministic system. Results show that time delay has important effects on the persistence and extinction of the epidemic.

A graph theoretical perspective of a drug abuse epidemic model

NASA Astrophysics Data System (ADS)

Nyabadza, F.; Mukwembi, S.; Rodrigues, B. G.

2011-05-01

A drug use epidemic can be represented by a finite number of states and transition rules that govern the dynamics of drug use in each discrete time step. This paper investigates the spread of drug use in a community where some users are in treatment and others are not in treatment, citing South Africa as an example. In our analysis, we consider the neighbourhood prevalence of each individual, i.e., the proportion of the individual’s drug user contacts who are not in treatment amongst all of his or her contacts. We introduce parameters α∗, β∗ and γ∗, depending on the neighbourhood prevalence, which govern the spread of drug use. We examine how changes in α∗, β∗ and γ∗ affect the system dynamics. Simulations presented support the theoretical results.

Risk-based input-output analysis of influenza epidemic consequences on interdependent workforce sectors.

PubMed

Santos, Joost R; May, Larissa; Haimar, Amine El

2013-09-01

Outbreaks of contagious diseases underscore the ever-looming threat of new epidemics. Compared to other disasters that inflict physical damage to infrastructure systems, epidemics can have more devastating and prolonged impacts on the population. This article investigates the interdependent economic and productivity risks resulting from epidemic-induced workforce absenteeism. In particular, we develop a dynamic input-output model capable of generating sector-disaggregated economic losses based on different magnitudes of workforce disruptions. An ex post analysis of the 2009 H1N1 pandemic in the national capital region (NCR) reveals the distribution of consequences across different economic sectors. Consequences are categorized into two metrics: (i) economic loss, which measures the magnitude of monetary losses incurred in each sector, and (ii) inoperability, which measures the normalized monetary losses incurred in each sector relative to the total economic output of that sector. For a simulated mild pandemic scenario in NCR, two distinct rankings are generated using the economic loss and inoperability metrics. Results indicate that the majority of the critical sectors ranked according to the economic loss metric comprise of sectors that contribute the most to the NCR's gross domestic product (e.g., federal government enterprises). In contrast, the majority of the critical sectors generated by the inoperability metric include sectors that are involved with epidemic management (e.g., hospitals). Hence, prioritizing sectors for recovery necessitates consideration of the balance between economic loss, inoperability, and other objectives. Although applied specifically to the NCR, the proposed methodology can be customized for other regions. © 2012 Society for Risk Analysis.

Evolution of Scaling Emergence in Large-Scale Spatial Epidemic Spreading

PubMed Central

Wang, Lin; Li, Xiang; Zhang, Yi-Qing; Zhang, Yan; Zhang, Kan

2011-01-01

Background Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings on the dependence between these two scalings, which has still hardly been clarified. Methodology/Principal Findings In this article, we observe an evolution process of the scalings: the Zipf's law and the Heaps' law are naturally shaped to coexist at the initial time, while the crossover comes with the emergence of their inconsistency at the larger time before reaching a stable state, where the Heaps' law still exists with the disappearance of strict Zipf's law. Such findings are illustrated with a scenario of large-scale spatial epidemic spreading, and the empirical results of pandemic disease support a universal analysis of the relation between the two laws regardless of the biological details of disease. Employing the United States domestic air transportation and demographic data to construct a metapopulation model for simulating the pandemic spread at the U.S. country level, we uncover that the broad heterogeneity of the infrastructure plays a key role in the evolution of scaling emergence. Conclusions/Significance The analyses of large-scale spatial epidemic spreading help understand the temporal evolution of scalings, indicating the coexistence of the Zipf's law and the Heaps' law depends on the collective dynamics of epidemic processes, and the heterogeneity of epidemic spread indicates the significance of performing targeted containment strategies at the early time of a pandemic disease. PMID:21747932

Risk-Based Input-Output Analysis of Influenza Epidemic Consequences on Interdependent Workforce Sectors

PubMed Central

Santos, Joost R.; May, Larissa; Haimar, Amine El

2013-01-01

Outbreaks of contagious diseases underscore the ever-looming threat of new epidemics. Compared to other disasters that inflict physical damage to infrastructure systems, epidemics can have more devastating and prolonged impacts on the population. This paper investigates the interdependent economic and productivity risks resulting from epidemic-induced workforce absenteeism. In particular, we develop a dynamic input-output model capable of generating sector-disaggregated economic losses based on different magnitudes of workforce disruptions. An ex post analysis of the 2009 H1N1 pandemic in the National Capital Region (NCR) reveals the distribution of consequences across different economic sectors. Consequences are categorized into two metrics: (i) economic loss, which measures the magnitude of monetary losses incurred in each sector, and (ii) inoperability, which measures the normalized monetary losses incurred in each sector relative to the total economic output of that sector. For a simulated mild pandemic scenario in NCR, two distinct rankings are generated using the economic loss and inoperability metrics. Results indicate that the majority of the critical sectors ranked according to the economic loss metric comprise of sectors that contribute the most to the NCR's gross domestic product (e.g., federal government enterprises). In contrast, the majority of the critical sectors generated by the inoperability metric include sectors that are involved with epidemic management (e.g., hospitals). Hence, prioritizing sectors for recovery necessitates consideration of the balance between economic loss, inoperability, and other objectives. Although applied specifically to the NCR region, the proposed methodology can be customized for other regions. PMID:23278756

Dynamical processes and epidemic threshold on nonlinear coupled multiplex networks

NASA Astrophysics Data System (ADS)

Gao, Chao; Tang, Shaoting; Li, Weihua; Yang, Yaqian; Zheng, Zhiming

2018-04-01

Recently, the interplay between epidemic spreading and awareness diffusion has aroused the interest of many researchers, who have studied models mainly based on linear coupling relations between information and epidemic layers. However, in real-world networks the relation between two layers may be closely correlated with the property of individual nodes and exhibits nonlinear dynamical features. Here we propose a nonlinear coupled information-epidemic model (I-E model) and present a comprehensive analysis in a more generalized scenario where the upload rate differs from node to node, deletion rate varies between susceptible and infected states, and infection rate changes between unaware and aware states. In particular, we develop a theoretical framework of the intra- and inter-layer dynamical processes with a microscopic Markov chain approach (MMCA), and derive an analytic epidemic threshold. Our results suggest that the change of upload and deletion rate has little effect on the diffusion dynamics in the epidemic layer.

Weather-Driven Variation in Dengue Activity in Australia Examined Using a Process-Based Modeling Approach

PubMed Central

Bannister-Tyrrell, Melanie; Williams, Craig; Ritchie, Scott A.; Rau, Gina; Lindesay, Janette; Mercer, Geoff; Harley, David

2013-01-01

The impact of weather variation on dengue transmission in Cairns, Australia, was determined by applying a process-based dengue simulation model (DENSiM) that incorporated local meteorologic, entomologic, and demographic data. Analysis showed that inter-annual weather variation is one of the significant determinants of dengue outbreak receptivity. Cross-correlation analyses showed that DENSiM simulated epidemics of similar relative magnitude and timing to those historically recorded in reported dengue cases in Cairns during 1991–2009, (r = 0.372, P < 0.01). The DENSiM model can now be used to study the potential impacts of future climate change on dengue transmission. Understanding the impact of climate variation on the geographic range, seasonality, and magnitude of dengue transmission will enhance development of adaptation strategies to minimize future disease burden in Australia. PMID:23166197

Epidemics Modelings: Some New Challenges

NASA Astrophysics Data System (ADS)

Boatto, Stefanella; Khouri, Renata Stella; Solerman, Lucas; Codeço, Claudia; Bonnet, Catherine

2010-09-01

Epidemics modeling has been particularly growing in the past years. In epidemics studies, mathematical modeling is used in particular to reach a better understanding of some neglected diseases (dengue, malaria, …) and of new emerging ones (SARS, influenza A,….) of big agglomerates. Such studies offer new challenges both from the modeling point of view (searching for simple models which capture the main characteristics of the disease spreading), data analysis and mathematical complexity. We are facing often with complex networks especially when modeling the city dynamics. Such networks can be static (in first approximation) and homogeneous, static and not homogeneous and/or not static (when taking into account the city structure, micro-climates, people circulation, etc.). The objective being studying epidemics dynamics and being able to predict its spreading.

Discrete time Markov chains (DTMC) susceptible infected susceptible (SIS) epidemic model with two pathogens in two patches

NASA Astrophysics Data System (ADS)

Lismawati, Eka; Respatiwulan; Widyaningsih, Purnami

2017-06-01

The SIS epidemic model describes the pattern of disease spread with characteristics that recovered individuals can be infected more than once. The number of susceptible and infected individuals every time follows the discrete time Markov process. It can be represented by the discrete time Markov chains (DTMC) SIS. The DTMC SIS epidemic model can be developed for two pathogens in two patches. The aims of this paper are to reconstruct and to apply the DTMC SIS epidemic model with two pathogens in two patches. The model was presented as transition probabilities. The application of the model obtain that the number of susceptible individuals decreases while the number of infected individuals increases for each pathogen in each patch.

Assessing evidence for behaviour change affecting the course of HIV epidemics: a new mathematical modelling approach and application to data from Zimbabwe.

PubMed

Hallett, Timothy B; Gregson, Simon; Mugurungi, Owen; Gonese, Elizabeth; Garnett, Geoff P

2009-06-01

Determining whether interventions to reduce HIV transmission have worked is essential, but complicated by the potential for generalised epidemics to evolve over time without individuals changing risk behaviour. We aimed to develop a method to evaluate evidence for changes in risk behaviour altering the course of an HIV epidemic. We developed a mathematical model of HIV transmission, incorporating the potential for natural changes in the epidemic as it matures and the introduction of antiretroviral treatment, and applied a Bayesian Melding framework, in which the model and observed trends in prevalence can be compared. We applied the model to Zimbabwe, using HIV prevalence estimates from antenatal clinic surveillance and house-hold based surveys, and basing model parameters on data from sexual behaviour surveys. There was strong evidence for reductions in risk behaviour stemming HIV transmission. We estimate these changes occurred between 1999 and 2004 and averted 660,000 (95% credible interval: 460,000-860,000) infections by 2008. The model and associated analysis framework provide a robust way to evaluate the evidence for changes in risk behaviour affecting the course of HIV epidemics, avoiding confounding by the natural evolution of HIV epidemics.

DengueME: A Tool for the Modeling and Simulation of Dengue Spatiotemporal Dynamics †

PubMed Central

de Lima, Tiago França Melo; Lana, Raquel Martins; de Senna Carneiro, Tiago Garcia; Codeço, Cláudia Torres; Machado, Gabriel Souza; Ferreira, Lucas Saraiva; de Castro Medeiros, Líliam César; Davis Junior, Clodoveu Augusto

2016-01-01

The prevention and control of dengue are great public health challenges for many countries, particularly since 2015, as other arboviruses have been observed to interact significantly with dengue virus. Different approaches and methodologies have been proposed and discussed by the research community. An important tool widely used is modeling and simulation, which help us to understand epidemic dynamics and create scenarios to support planning and decision making processes. With this aim, we proposed and developed DengueME, a collaborative open source platform to simulate dengue disease and its vector’s dynamics. It supports compartmental and individual-based models, implemented over a GIS database, that represent Aedes aegypti population dynamics, human demography, human mobility, urban landscape and dengue transmission mediated by human and mosquito encounters. A user-friendly graphical interface was developed to facilitate model configuration and data input, and a library of models was developed to support teaching-learning activities. DengueME was applied in study cases and evaluated by specialists. Other improvements will be made in future work, to enhance its extensibility and usability. PMID:27649226

Dynamics of epidemic diseases on a growing adaptive network

PubMed Central

Demirel, Güven; Barter, Edmund; Gross, Thilo

2017-01-01

The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists. PMID:28186146

Dynamics of epidemic diseases on a growing adaptive network.

PubMed

Demirel, Güven; Barter, Edmund; Gross, Thilo

2017-02-10

The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists.

Dynamics of epidemic diseases on a growing adaptive network

NASA Astrophysics Data System (ADS)

Demirel, Güven; Barter, Edmund; Gross, Thilo

2017-02-01

The study of epidemics on static networks has revealed important effects on disease prevalence of network topological features such as the variance of the degree distribution, i.e. the distribution of the number of neighbors of nodes, and the maximum degree. Here, we analyze an adaptive network where the degree distribution is not independent of epidemics but is shaped through disease-induced dynamics and mortality in a complex interplay. We study the dynamics of a network that grows according to a preferential attachment rule, while nodes are simultaneously removed from the network due to disease-induced mortality. We investigate the prevalence of the disease using individual-based simulations and a heterogeneous node approximation. Our results suggest that in this system in the thermodynamic limit no epidemic thresholds exist, while the interplay between network growth and epidemic spreading leads to exponential networks for any finite rate of infectiousness when the disease persists.

The patient-zero problem with noisy observations

NASA Astrophysics Data System (ADS)

Altarelli, Fabrizio; Braunstein, Alfredo; Dall'Asta, Luca; Ingrosso, Alessandro; Zecchina, Riccardo

2014-10-01

A belief propagation approach has been recently proposed for the patient-zero problem in SIR epidemics. The patient-zero problem consists of finding the initial source of an epidemic outbreak given observations at a later time. In this work, we study a more difficult but related inference problem, in which observations are noisy and there is confusion between observed states. In addition to studying the patient-zero problem, we also tackle the problem of completing and correcting the observations to possibly find undiscovered infected individuals and false test results. Moreover, we devise a set of equations, based on the variational expression of the Bethe free energy, to find the patient-zero along with maximum-likelihood epidemic parameters. We show, by means of simulated epidemics, that this method is able to infer details on the past history of an epidemic outbreak based solely on the topology of the contact network and a single snapshot of partial and noisy observations.

Human mobility and epidemic invasion

NASA Astrophysics Data System (ADS)

Colizza, Vittoria

2010-03-01

The current H1N1 influenza pandemic is just the latest example of how human mobility helps drive infectious diseases. Travel has grown explosively in the last decades, contributing to an emerging complex pattern of traffic flows that unfolds at different scales, shaping the spread of epidemics. Restrictions on people's mobility are thus investigated to design possible containment measures. By considering a theoretical framework in terms of reaction-diffusion processes, it is possible to study the invasion dynamics of epidemics in a metapopulation system with heterogeneous mobility patterns. The system is found to exhibit a global invasion threshold that sets the critical mobility rate below which the epidemic is contained. The results provide a general framework for the understanding of the numerical evidence from detailed data-driven simulations that show the limited benefit provided by travel flows reduction in slowing down or containing an emerging epidemic.

Integrated travel network model for studying epidemics: Interplay between journeys and epidemic

PubMed Central

Ruan, Zhongyuan; Wang, Chaoqing; Ming Hui, Pak; Liu, Zonghua

2015-01-01

The ease of travelling between cities has contributed much to globalization. Yet, it poses a threat on epidemic outbreaks. It is of great importance for network science and health control to understand the impact of frequent journeys on epidemics. We stress that a new framework of modelling that takes a traveller’s viewpoint is needed. Such integrated travel network (ITN) model should incorporate the diversity among links as dictated by the distances between cities and different speeds of different modes of transportation, diversity among nodes as dictated by the population and the ease of travelling due to infrastructures and economic development of a city, and round-trip journeys to targeted destinations via the paths of shortest travel times typical of human journeys. An example is constructed for 116 cities in China with populations over one million that are connected by high-speed train services and highways. Epidemic spread on the constructed network is studied. It is revealed both numerically and theoretically that the traveling speed and frequency are important factors of epidemic spreading. Depending on the infection rate, increasing the traveling speed would result in either an enhanced or suppressed epidemic, while increasing the traveling frequency enhances the epidemic spreading. PMID:26073191

Integrated travel network model for studying epidemics: Interplay between journeys and epidemic

NASA Astrophysics Data System (ADS)

Ruan, Zhongyuan; Wang, Chaoqing; Ming Hui, Pak; Liu, Zonghua

2015-06-01

The ease of travelling between cities has contributed much to globalization. Yet, it poses a threat on epidemic outbreaks. It is of great importance for network science and health control to understand the impact of frequent journeys on epidemics. We stress that a new framework of modelling that takes a traveller’s viewpoint is needed. Such integrated travel network (ITN) model should incorporate the diversity among links as dictated by the distances between cities and different speeds of different modes of transportation, diversity among nodes as dictated by the population and the ease of travelling due to infrastructures and economic development of a city, and round-trip journeys to targeted destinations via the paths of shortest travel times typical of human journeys. An example is constructed for 116 cities in China with populations over one million that are connected by high-speed train services and highways. Epidemic spread on the constructed network is studied. It is revealed both numerically and theoretically that the traveling speed and frequency are important factors of epidemic spreading. Depending on the infection rate, increasing the traveling speed would result in either an enhanced or suppressed epidemic, while increasing the traveling frequency enhances the epidemic spreading.

Integrated travel network model for studying epidemics: Interplay between journeys and epidemic.

PubMed

Ruan, Zhongyuan; Wang, Chaoqing; Hui, Pak Ming; Liu, Zonghua

2015-06-15

The ease of travelling between cities has contributed much to globalization. Yet, it poses a threat on epidemic outbreaks. It is of great importance for network science and health control to understand the impact of frequent journeys on epidemics. We stress that a new framework of modelling that takes a traveller's viewpoint is needed. Such integrated travel network (ITN) model should incorporate the diversity among links as dictated by the distances between cities and different speeds of different modes of transportation, diversity among nodes as dictated by the population and the ease of travelling due to infrastructures and economic development of a city, and round-trip journeys to targeted destinations via the paths of shortest travel times typical of human journeys. An example is constructed for 116 cities in China with populations over one million that are connected by high-speed train services and highways. Epidemic spread on the constructed network is studied. It is revealed both numerically and theoretically that the traveling speed and frequency are important factors of epidemic spreading. Depending on the infection rate, increasing the traveling speed would result in either an enhanced or suppressed epidemic, while increasing the traveling frequency enhances the epidemic spreading.

Extinction times in the subcritical stochastic SIS logistic epidemic.

PubMed

Brightwell, Graham; House, Thomas; Luczak, Malwina

2018-01-31

Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights into the near-critical regime by considering the stochastic SIS logistic epidemic, a well-known birth-and-death chain used to model the spread of an epidemic within a population of a given size N. We study the behaviour of the process as the population size N tends to infinity. Our results cover the entire subcritical regime, including the "barely subcritical" regime, where the recovery rate exceeds the infection rate by an amount that tends to 0 as [Formula: see text] but more slowly than [Formula: see text]. We derive precise asymptotics for the distribution of the extinction time and the total number of cases throughout the subcritical regime, give a detailed description of the course of the epidemic, and compare to numerical results for a range of parameter values. We hypothesise that features of the course of the epidemic will be seen in a wide class of other epidemic models, and we use real data to provide some tentative and preliminary support for this theory.

Network-level reproduction number and extinction threshold for vector-borne diseases.

PubMed

Xue, Ling; Scoglio, Caterina

2015-06-01

The basic reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or not. Thresholds for disease extinction contribute crucial knowledge of disease control, elimination, and mitigation of infectious diseases. Relationships between basic reproduction numbers of two deterministic network-based ordinary differential equation vector-host models, and extinction thresholds of corresponding stochastic continuous-time Markov chain models are derived under some assumptions. Numerical simulation results for malaria and Rift Valley fever transmission on heterogeneous networks are in agreement with analytical results without any assumptions, reinforcing that the relationships may always exist and proposing a mathematical problem for proving existence of the relationships in general. Moreover, numerical simulations show that the basic reproduction number does not monotonically increase or decrease with the extinction threshold. Consistent trends of extinction probability observed through numerical simulations provide novel insights into mitigation strategies to increase the disease extinction probability. Research findings may improve understandings of thresholds for disease persistence in order to control vector-borne diseases.

Epidemic models with an infected-infectious period

NASA Astrophysics Data System (ADS)

Méndez, Vicenç

1998-03-01

The introduction of an infective-infectious period on the geographic spread of epidemics is considered in two different models. The classical evolution equations arising in the literature are generalized and the existence of epidemic wave fronts is revised. The asymptotic speed is obtained and improves previous results for the Black Death plague.

Probabilistic information transmission in a network of coupled oscillators reveals speed-accuracy trade-off in responding to threats

PubMed Central

Chicoli, Amanda; Paley, Derek A.

2016-01-01

Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion. PMID:27907996

Probabilistic information transmission in a network of coupled oscillators reveals speed-accuracy trade-off in responding to threats

NASA Astrophysics Data System (ADS)

Chicoli, Amanda; Paley, Derek A.

2016-11-01

Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion.

Probabilistic information transmission in a network of coupled oscillators reveals speed-accuracy trade-off in responding to threats.

PubMed

Chicoli, Amanda; Paley, Derek A

2016-11-01

Individuals in a group may obtain information from other group members about the environment, including the location of a food source or the presence of a predator. Here, we model how information spreads in a group using a susceptible-infected-removed epidemic model. We apply this model to a simulated shoal of fish using the motion dynamics of a coupled oscillator model, in order to test the biological hypothesis that polarized or aligned shoaling leads to faster and more accurate escape responses. The contributions of this study are the (i) application of a probabilistic model of epidemics to the study of collective animal behavior; (ii) testing the biological hypothesis that group cohesion improves predator escape; (iii) quantification of the effect of social cues on startle propagation; and (iv) investigation of the variation in response based on network connectivity. We find that when perfectly aligned individuals in a group are startled, there is a rapid escape by individuals that directly detect the threat, as well as by individuals responding to their neighbors. However, individuals that are not startled do not head away from the threat. In startled groups that are randomly oriented, there is a rapid, accurate response by individuals that directly detect the threat, followed by less accurate responses by individuals responding to neighbor cues. Over the simulation duration, however, even unstartled individuals head away from the threat. This study illustrates a potential speed-accuracy trade-off in the startle response of animal groups, in agreement with several previous experimental studies. Additionally, the model can be applied to a variety of group decision-making processes, including those involving higher-dimensional motion.

Susceptible-infected-recovered epidemics in random networks with population awareness

NASA Astrophysics Data System (ADS)

Wu, Qingchu; Chen, Shufang

2017-10-01

The influence of epidemic information-based awareness on the spread of infectious diseases on networks cannot be ignored. Within the effective degree modeling framework, we discuss the susceptible-infected-recovered model in complex networks with general awareness and general degree distribution. By performing the linear stability analysis, the conditions of epidemic outbreak can be deduced and the results of the previous research can be further expanded. Results show that the local awareness can suppress significantly the epidemic spreading on complex networks via raising the epidemic threshold and such effects are closely related to the formulation of awareness functions. In addition, our results suggest that the recovered information-based awareness has no effect on the critical condition of epidemic outbreak.

Disease dynamics in a dynamic social network

NASA Astrophysics Data System (ADS)

Christensen, Claire; Albert, István; Grenfell, Bryan; Albert, Réka

2010-07-01

We develop a framework for simulating a realistic, evolving social network (a city) into which a disease is introduced. We compare our results to prevaccine era measles data for England and Wales, and find that they capture the quantitative and qualitative features of epidemics in populations spanning two orders of magnitude. Our results provide unique insight into how and why the social topology of the contact network influences the propagation of the disease through the population. We argue that network simulation is suitable for concurrently probing contact network dynamics and disease dynamics in ways that prior modeling approaches cannot and it can be extended to the study of less well-documented diseases.

Role of animal movement and indirect contact among farms in transmission of porcine epidemic diarrhea virus.

PubMed

VanderWaal, Kimberly; Perez, Andres; Torremorrell, Montse; Morrison, Robert M; Craft, Meggan

2018-04-12

Epidemiological models of the spread of pathogens in livestock populations primarily focus on direct contact between farms based on animal movement data, and in some cases, local spatial spread based on proximity between premises. The roles of other types of indirect contact among farms is rarely accounted for. In addition, data on animal movements is seldom available in the United States. However, the spread of porcine epidemic diarrhea virus (PEDv) in U.S. swine represents one of the best documented emergences of a highly infectious pathogen in the U.S. livestock industry, providing an opportunity to parameterize models of pathogen spread via direct and indirect transmission mechanisms in swine. Using observed data on pig movements during the initial phase of the PEDv epidemic, we developed a network-based and spatially explicit epidemiological model that simulates the spread of PEDv via both indirect and direct movement-related contact in order to answer unresolved questions concerning factors facilitating between-farm transmission. By modifying the likelihood of each transmission mechanism and fitting this model to observed epidemiological dynamics, our results suggest that between-farm transmission was primarily driven by direct mechanisms related to animal movement and indirect mechanisms related to local spatial spread based on geographic proximity. However, other forms of indirect transmission among farms, including contact via contaminated vehicles and feed, were responsible for high consequence transmission events resulting in the introduction of the virus into new geographic areas. This research is among the first reports of farm-level animal movements in the U.S. swine industry and, to our knowledge, represents the first epidemiological model of commercial U.S. swine using actual data on farm-level animal movement. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

An information propagation model considering incomplete reading behavior in microblog

NASA Astrophysics Data System (ADS)

Su, Qiang; Huang, Jiajia; Zhao, Xiande

2015-02-01

Microblog is one of the most popular communication channels on the Internet, and has already become the third largest source of news and public opinions in China. Although researchers have studied the information propagation in microblog using the epidemic models, previous studies have not considered the incomplete reading behavior among microblog users. Therefore, the model cannot fit the real situations well. In this paper, we proposed an improved model entitled Microblog-Susceptible-Infected-Removed (Mb-SIR) for information propagation by explicitly considering the user's incomplete reading behavior. We also tested the effectiveness of the model using real data from Sina Microblog. We demonstrate that the new proposed model is more accurate in describing the information propagation in microblog. In addition, we also investigate the effects of the critical model parameters, e.g., reading rate, spreading rate, and removed rate through numerical simulations. The simulation results show that, compared with other parameters, reading rate plays the most influential role in the information propagation performance in microblog.

Bayesian hierarchical Poisson models with a hidden Markov structure for the detection of influenza epidemic outbreaks.

PubMed

Conesa, D; Martínez-Beneito, M A; Amorós, R; López-Quílez, A

2015-04-01

Considerable effort has been devoted to the development of statistical algorithms for the automated monitoring of influenza surveillance data. In this article, we introduce a framework of models for the early detection of the onset of an influenza epidemic which is applicable to different kinds of surveillance data. In particular, the process of the observed cases is modelled via a Bayesian Hierarchical Poisson model in which the intensity parameter is a function of the incidence rate. The key point is to consider this incidence rate as a normal distribution in which both parameters (mean and variance) are modelled differently, depending on whether the system is in an epidemic or non-epidemic phase. To do so, we propose a hidden Markov model in which the transition between both phases is modelled as a function of the epidemic state of the previous week. Different options for modelling the rates are described, including the option of modelling the mean at each phase as autoregressive processes of order 0, 1 or 2. Bayesian inference is carried out to provide the probability of being in an epidemic state at any given moment. The methodology is applied to various influenza data sets. The results indicate that our methods outperform previous approaches in terms of sensitivity, specificity and timeliness. © The Author(s) 2011 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

[Evaluation of the effect of varicella outbreak control measures through a discrete time delay SEIR model].

PubMed

Pan, Jin-ren; Huang, Zheng-qiang; Chen, Kun

2012-04-01

forecast the epidemic trend and to evaluate the effect of outbreak control measures by investigation of a varicella outbreak event with a discrete time delay SEIR model. A discrete time delay model was formulated by discretization method based on a continuous SEIR model with the consideration of the time delay effect on latent period and communicable period. The epidemic trend forecast was carried out based on the number of expected cases. The theoretical effect evaluation was assessed by comparing the results from different emergency control measures. Without any control measures, the theoretical attack rate was 30.16% (504/1671). The course of the epidemic lasted for 4 months and the peak epidemic time was 78 days after the onset of the first case. 'Generation' phenomenon had been observed in the course of the epidemic with the interval of two weeks. The actual number of cases was decreased by 89.48% (451/504) compared with the number of expected cases under no control measure scenario. With the rigorous quarantine measure for all cases on their onset day, when the measure was conducted on 0, 14, 28, 42 days after the onset of the first case, the total numbers of expected cases were 22, 59, 127 and 220 respectively. With the quarantine measure conducted on 14 days after the onset of the first case, when the proportion of quarantine was 30%, 50%, 70%, 90%, the total number of expected cases were 485, 457, 386 and 169, respectively. With the emergent vaccination for all persons, when the measure was conducted on 0, 14, 28, 42 days after the onset of the first case, the total numbers of expected cases were 7, 26, 81 and 202 respectively. With the emergent vaccination conducted on 14 days after the onset of the first case, when the immunization coverage rate was 30%, 50%, 70%, 90%, the total numbers of expected cases were 354, 246, 127 and 40, respectively. The number of expected cases can be regarded as the reference to evaluate the effect of control measures. The simulation results suggest that it will get more benefits to conduct control measures earlier in varicella outbreak events, and the effect of emergent vaccination is better than that of quarantine measure under the same conditions.

An epidemiological model with vaccination strategies

NASA Astrophysics Data System (ADS)

Prates, Dérek B.; Silva, Jaqueline M.; Gomes, Jessica L.; Kritz, Maurício V.

2016-06-01

Mathematical models can be widely found in the literature describing epidemics. The epidemical models that use differential equations to represent mathematically such description are especially sensible to parameters. This work analyze a variation of the SIR model when applied to a epidemic scenario including several aspects, as constant vaccination, pulse vaccination, seasonality, cross-immunity factor, birth and dead rate. The analysis and results are performed through numerical solutions of the model and a special attention is given to the discussion generated by the paramenters variation.

Dynamics of Zika virus outbreaks: an overview of mathematical modeling approaches

PubMed Central

Wiratsudakul, Anuwat; Suparit, Parinya

2018-01-01

Background The Zika virus was first discovered in 1947. It was neglected until a major outbreak occurred on Yap Island, Micronesia, in 2007. Teratogenic effects resulting in microcephaly in newborn infants is the greatest public health threat. In 2016, the Zika virus epidemic was declared as a Public Health Emergency of International Concern (PHEIC). Consequently, mathematical models were constructed to explicitly elucidate related transmission dynamics. Survey Methodology In this review article, two steps of journal article searching were performed. First, we attempted to identify mathematical models previously applied to the study of vector-borne diseases using the search terms “dynamics,” “mathematical model,” “modeling,” and “vector-borne” together with the names of vector-borne diseases including chikungunya, dengue, malaria, West Nile, and Zika. Then the identified types of model were further investigated. Second, we narrowed down our survey to focus on only Zika virus research. The terms we searched for were “compartmental,” “spatial,” “metapopulation,” “network,” “individual-based,” “agent-based” AND “Zika.” All relevant studies were included regardless of the year of publication. We have collected research articles that were published before August 2017 based on our search criteria. In this publication survey, we explored the Google Scholar and PubMed databases. Results We found five basic model architectures previously applied to vector-borne virus studies, particularly in Zika virus simulations. These include compartmental, spatial, metapopulation, network, and individual-based models. We found that Zika models carried out for early epidemics were mostly fit into compartmental structures and were less complicated compared to the more recent ones. Simple models are still commonly used for the timely assessment of epidemics. Nevertheless, due to the availability of large-scale real-world data and computational power, recently there has been growing interest in more complex modeling frameworks. Discussion Mathematical models are employed to explore and predict how an infectious disease spreads in the real world, evaluate the disease importation risk, and assess the effectiveness of intervention strategies. As the trends in modeling of infectious diseases have been shifting towards data-driven approaches, simple and complex models should be exploited differently. Simple models can be produced in a timely fashion to provide an estimation of the possible impacts. In contrast, complex models integrating real-world data require more time to develop but are far more realistic. The preparation of complicated modeling frameworks prior to the outbreaks is recommended, including the case of future Zika epidemic preparation. PMID:29593941

Epidemic spreading on interconnected networks.

PubMed

Saumell-Mendiola, Anna; Serrano, M Ángeles; Boguñá, Marián

2012-08-01

Many real networks are not isolated from each other but form networks of networks, often interrelated in nontrivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop a heterogeneous mean-field approach that allows us to calculate the conditions for the emergence of an endemic state. Interestingly, a global endemic state may arise in the coupled system even though the epidemics is not able to propagate on each network separately and even when the number of coupling connections is small. Our analytic results are successfully confronted against large-scale numerical simulations.

Epidemic spreading on interconnected networks

NASA Astrophysics Data System (ADS)

Saumell-Mendiola, Anna; Serrano, M. Ángeles; Boguñá, Marián

2012-08-01

Many real networks are not isolated from each other but form networks of networks, often interrelated in nontrivial ways. Here, we analyze an epidemic spreading process taking place on top of two interconnected complex networks. We develop a heterogeneous mean-field approach that allows us to calculate the conditions for the emergence of an endemic state. Interestingly, a global endemic state may arise in the coupled system even though the epidemics is not able to propagate on each network separately and even when the number of coupling connections is small. Our analytic results are successfully confronted against large-scale numerical simulations.

Epidemic characterization and modeling within herd transmission dynamics of an "emerging trans-boundary" camel disease epidemic in Ethiopia.

PubMed

Megersa, Bekele; Biffa, Demelash; Abunna, Fufa; Regassa, Alemayehu; Bohlin, Jon; Skjerve, Eystein

2012-10-01

A highly acute and contagious camel disease, an epidemic wave of unknown etiology, referred to here as camel sudden death syndrome, has plagued camel population in countries in the Horn of Africa. To better understand its epidemic patterns and transmission dynamics, we used epidemiologic parameters and differential equation deterministic modeling (SEIR/D-model) to predict the outcome likelihood following an exposure of susceptible camel population. Our results showed 45.7, 17.6, and 38.6 % overall morbidity, mortality, and case fatality rates of the epidemic, respectively. Pregnant camels had the highest mortality and case fatality rates, followed by breeding males, and lactating females, implying serious socioeconomic consequences. Disease dynamics appeared to be linked to livestock trade route and animal movements. The epidemic exhibited a strong basic reproductive number (R (0)) with an average of 16 camels infected by one infectious case during the entire infectious period. The epidemic curve suggested that the critical moment of the disease development is approximately between 30 and 40 days, where both infected/exposed and infectious camels are at their highest numbers. The lag between infected/infectious curves indicates a time-shift of approximately 3-5 days from when a camel is infected and until it becomes infectious. According to this predictive model, of all animals exposed to the infection, 66.8 % (n = 868) and 33.2 % (n = 431) had recovered and died, respectively, at the end of epidemic period. Hence, if early measures are not taken, such an epidemic could cause a much more devastative effect, within short period of time than the anticipated proportion.

[A prognostic model of a cholera epidemic].

PubMed

Boev, B V; Bondarenko, V M; Prokop'eva, N V; San Román, R T; Raygoza-Anaya, M; García de Alba, R

1994-01-01

A new model for the prognostication of cholera epidemic on the territory of a large city is proposed. This model reflects the characteristic feature of contacting infection by sensitive individuals due to the preservation of Vibrio cholerae in their water habitat. The mathematical model of the epidemic quantitatively reflects the processes of the spread of infection by kinetic equations describing the interaction of the streams of infected persons, the causative agents and susceptible persons. The functions and parameters of the model are linked with the distribution of individuals according to the duration of the incubation period and infectious process, as well as the period of asymptomatic carrier state. The computer realization of the model by means of IBM PC/AT made it possible to study the cholera epidemic which took place in Mexico in 1833. The verified model of the cholera epidemic was used for the prognostication of the possible spread of this infection in Guadalajara, taking into account changes in the epidemiological situation and the size of the population, as well as improvements in sanitary and hygienic conditions, in the city.

Spectral analysis and slow spreading dynamics on complex networks.

PubMed

Odor, Géza

2013-09-01

The susceptible-infected-susceptible (SIS) model is one of the simplest memoryless systems for describing information or epidemic spreading phenomena with competing creation and spontaneous annihilation reactions. The effect of quenched disorder on the dynamical behavior has recently been compared to quenched mean-field (QMF) approximations in scale-free networks. QMF can take into account topological heterogeneity and clustering effects of the activity in the steady state by spectral decomposition analysis of the adjacency matrix. Therefore, it can provide predictions on possible rare-region effects, thus on the occurrence of slow dynamics. I compare QMF results of SIS with simulations on various large dimensional graphs. In particular, I show that for Erdős-Rényi graphs this method predicts correctly the occurrence of rare-region effects. It also provides a good estimate for the epidemic threshold in case of percolating graphs. Griffiths Phases emerge if the graph is fragmented or if we apply a strong, exponentially suppressing weighting scheme on the edges. The latter model describes the connection time distributions in the face-to-face experiments. In case of a generalized Barabási-Albert type of network with aging connections, strong rare-region effects and numerical evidence for Griffiths Phase dynamics are shown. The dynamical simulation results agree well with the predictions of the spectral analysis applied for the weighted adjacency matrices.

A chaotic model for the epidemic of Ebola virus disease in West Africa (2013-2016)

NASA Astrophysics Data System (ADS)

Mangiarotti, Sylvain; Peyre, Marisa; Huc, Mireille

2016-11-01

An epidemic of Ebola Virus Disease (EVD) broke out in Guinea in December 2013. It was only identified in March 2014 while it had already spread out in Liberia and Sierra Leone. The spill over of the disease became uncontrollable and the epidemic could not be stopped before 2016. The time evolution of this epidemic is revisited here with the global modeling technique which was designed to obtain the deterministic models from single time series. A generalized formulation of this technique for multivariate time series is introduced. It is applied to the epidemic of EVD in West Africa focusing on the period between March 2014 and January 2015, that is, before any detected signs of weakening. Data gathered by the World Health Organization, based on the official publications of the Ministries of Health of the three main countries involved in this epidemic, are considered in our analysis. Two observed time series are used: the daily numbers of infections and deaths. A four-dimensional model producing a very complex dynamical behavior is obtained. The model is tested in order to investigate its skills and drawbacks. Our global analysis clearly helps to distinguish three main stages during the epidemic. A characterization of the obtained attractor is also performed. In particular, the topology of the chaotic attractor is analyzed and a skeleton is obtained for its structure.

Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009).

PubMed

Nishiura, Hiroshi

2011-02-16

Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance.

Spatial spread of the West Africa Ebola epidemic.

PubMed

Kramer, Andrew M; Pulliam, J Tomlin; Alexander, Laura W; Park, Andrew W; Rohani, Pejman; Drake, John M

2016-08-01

Controlling Ebola outbreaks and planning an effective response to future emerging diseases are enhanced by understanding the role of geography in transmission. Here we show how epidemic expansion may be predicted by evaluating the relative probability of alternative epidemic paths. We compared multiple candidate models to characterize the spatial network over which the 2013-2015 West Africa epidemic of Ebola virus spread and estimate the effects of geographical covariates on transmission during peak spread. The best model was a generalized gravity model where the probability of transmission between locations depended on distance, population density and international border closures between Guinea, Liberia and Sierra Leone and neighbouring countries. This model out-performed alternative models based on diffusive spread, the force of infection, mobility estimated from cell phone records and other hypothesized patterns of spread. These findings highlight the importance of integrated geography to epidemic expansion and may contribute to identifying both the most vulnerable unaffected areas and locations of maximum intervention value.

Spatial spread of the West Africa Ebola epidemic

PubMed Central

Pulliam, J. Tomlin; Alexander, Laura W.; Rohani, Pejman; Drake, John M.

2016-01-01

Controlling Ebola outbreaks and planning an effective response to future emerging diseases are enhanced by understanding the role of geography in transmission. Here we show how epidemic expansion may be predicted by evaluating the relative probability of alternative epidemic paths. We compared multiple candidate models to characterize the spatial network over which the 2013–2015 West Africa epidemic of Ebola virus spread and estimate the effects of geographical covariates on transmission during peak spread. The best model was a generalized gravity model where the probability of transmission between locations depended on distance, population density and international border closures between Guinea, Liberia and Sierra Leone and neighbouring countries. This model out-performed alternative models based on diffusive spread, the force of infection, mobility estimated from cell phone records and other hypothesized patterns of spread. These findings highlight the importance of integrated geography to epidemic expansion and may contribute to identifying both the most vulnerable unaffected areas and locations of maximum intervention value. PMID:27853607

Global epidemiology of HIV infection in men who have sex with men

PubMed Central

Beyrer, Chris; Baral, Stefan D; van Griensven, Frits; Goodreau, Steven M; Chariyalertsak, Suwat; Wirtz, Andrea L; Brookmeyer, Ron

2013-01-01

Epidemics of HIV in men who have sex with men (MSM) continue to expand in most countries. We sought to understand the epidemiological drivers of the global epidemic in MSM and why it continues unabated. We did a comprehensive review of available data for HIV prevalence, incidence, risk factors, and the molecular epidemiology of HIV in MSM from 2007 to 2011, and modelled the dynamics of HIV transmission with an agent-based simulation. Our findings show that the high probability of transmission per act through receptive anal intercourse has a central role in explaining the disproportionate disease burden in MSM. HIV can be transmitted through large MSM networks at great speed. Molecular epidemiological data show substantial clustering of HIV infections in MSM networks, and higher rates of dual-variant and multiple-variant HIV infection in MSM than in heterosexual people in the same populations. Prevention strategies that lower biological transmission and acquisition risks, such as approaches based on antiretrovirals, offer promise for controlling the expanding epidemic in MSM, but their potential effectiveness is limited by structural factors that contribute to low health-seeking behaviours in populations of MSM in many parts of the world. PMID:22819660

Using Relative Humidity Forecasts to Manage Meningitis in the Sahel

NASA Astrophysics Data System (ADS)

Pandya, R. E.; Adams-Forgor, A.; Akweogno, P.; Awine, T.; Dalaba, M.; Dukic, V.; Dumont, A.; Hayden, M.; Hodgson, A.; Hopson, T. M.; Hugonnet, S.; Yoksas, T. C.

2012-12-01

Meningitis epidemics in the Sahel occur quasi-regularly and with devastating impact. In 2008, for example, eighty-eight thousand people contracted meningitis and over five thousand died. Until very recently, the protection provided by the only available vaccine was so limited and short-lived that the only practical strategy for vaccination was reactive: waiting until an epidemic occurred in the region and then vaccinating in that region to prevent the epidemic's further growth. Even with that strategy, there were still times when demand outpaced available vaccine. While a new vaccine has recently been developed that is effective and inexpensive enough to be used more broadly and proactively, it is only effective against the strain of bacteria that causes the most common kind of bacterial meningitis. As a result, there will likely be continued need for reactive vaccination strategies. It is widely known that meningitis epidemics in the Sahel occur only in the dry season. Our project investigated this relationship, and several independent lines of evidence demonstrate a robust relationship between the onset of the rainy season, as marked by weekly average relative humidity above 40%, and the end of meningitis epidemics. These lines of evidence include statistical analysis of two years of weekly meningitis and weather data across the Sahel, cross-correlation of ten years of meningitis and weather data in the Upper East region of northern Ghana, and high-resolution weather simulations of past meningitis seasons to interpolate available weather data. We also adapted two techniques that have been successfully used in public health studies: generalized additive models, which have been used to relate air quality and health, and a linearized version of the compartmental epidemics model that has been used to understand MRSA. Based on these multiple lines of evidence, average weekly relative humidity forecast two weeks in advance appears consistently and strongly related to the number cases of meningitis in the Sahel. Using currently available forecast models contributed through the WMO Thorpex-Tigge project, and applying quantile regression to enhance their accuracy, we can forecast the average weekly relative humidity to two weeks in advance which allows us to anticipate the end of an epidemic in a region of the Sahel up to four weeks in advance. This would allow public health officials to deploy vaccines to areas in which the epidemics are likely to persist due to continued dryness and avoid vaccinating in areas where the epidemics will end with higher humidity. Our presentation will conclude by introducing the relative humidity decision-information tool developed for use by public-health officials. We will also summarize the results of a weekly meningitis forecast exercise held during the 2011-2012 dry season with public health decision makers from several African countries and the World Health Organization. Finally, we highlight some results of concurrent socio-economic research that suggests other interventions for managing meningitis and helps quantify the economic impact of the disease in Ghana. Overall, while our research has demonstrated an actionable relationship between weather and disease, this relationship is only one factor in a complex and coupled human-natural system which merits continued investigation.

Epidemic modeling in complex realities.

PubMed

Colizza, Vittoria; Barthélemy, Marc; Barrat, Alain; Vespignani, Alessandro

2007-04-01

In our global world, the increasing complexity of social relations and transport infrastructures are key factors in the spread of epidemics. In recent years, the increasing availability of computer power has enabled both to obtain reliable data allowing one to quantify the complexity of the networks on which epidemics may propagate and to envision computational tools able to tackle the analysis of such propagation phenomena. These advances have put in evidence the limits of homogeneous assumptions and simple spatial diffusion approaches, and stimulated the inclusion of complex features and heterogeneities relevant in the description of epidemic diffusion. In this paper, we review recent progresses that integrate complex systems and networks analysis with epidemic modelling and focus on the impact of the various complex features of real systems on the dynamics of epidemic spreading.

Contagion processes on the static and activity-driven coupling networks

NASA Astrophysics Data System (ADS)

Lei, Yanjun; Jiang, Xin; Guo, Quantong; Ma, Yifang; Li, Meng; Zheng, Zhiming

2016-03-01

The evolution of network structure and the spreading of epidemic are common coexistent dynamical processes. In most cases, network structure is treated as either static or time-varying, supposing the whole network is observed in the same time window. In this paper, we consider the epidemics spreading on a network which has both static and time-varying structures. Meanwhile, the time-varying part and the epidemic spreading are supposed to be of the same time scale. We introduce a static and activity-driven coupling (SADC) network model to characterize the coupling between the static ("strong") structure and the dynamic ("weak") structure. Epidemic thresholds of the SIS and SIR models are studied using the SADC model both analytically and numerically under various coupling strategies, where the strong structure is of homogeneous or heterogeneous degree distribution. Theoretical thresholds obtained from the SADC model can both recover and generalize the classical results in static and time-varying networks. It is demonstrated that a weak structure might make the epidemic threshold low in homogeneous networks but high in heterogeneous cases. Furthermore, we show that the weak structure has a substantive effect on the outbreak of the epidemics. This result might be useful in designing some efficient control strategies for epidemics spreading in networks.

Universality of Critically Pinned Interfaces in Two-Dimensional Isotropic Random Media

NASA Astrophysics Data System (ADS)

Grassberger, Peter

2018-05-01

Based on extensive simulations, we conjecture that critically pinned interfaces in two-dimensional isotropic random media with short-range correlations are always in the universality class of ordinary percolation. Thus, in contrast to interfaces in >2 dimensions, there is no distinction between fractal (i.e., percolative) and rough but nonfractal interfaces. Our claim includes interfaces in zero-temperature random field Ising models (both with and without spontaneous nucleation), in heterogeneous bootstrap percolation, and in susceptible-weakened-infected-removed epidemics. It does not include models with long-range correlations in the randomness and models where overhangs are explicitly forbidden (which would imply nonisotropy of the medium).

An epidemic model for the future progression of the current Haiti cholera epidemic

NASA Astrophysics Data System (ADS)

Bertuzzo, E.; Mari, L.; Righetto, L.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.

2012-04-01

As a major cholera epidemic progresses in Haiti, and the figures of the infection, up to December 2011, climb to 522,000 cases and 7,000 deaths, the development of general models to track and predict the evolution of the outbreak, so as to guide the allocation of medical supplies and staff, is gaining notable urgency. We propose here a spatially explicit epidemic model that accounts for the dynamics of susceptible and infected individuals as well as the redistribution of Vibrio cholera, the causative agent of the disease, among different human communities. In particular, we model two spreading pathways: the advection of pathogens through hydrologic connections and the dissemination due to human mobility described by means of a gravity-like model. To this end the country has been divided into hydrologic units based on drainage directions derived from a digital terrain model. Moreover the population of each unit has been estimated from census data downscaled to 1 km x 1 km resolution via remotely sensed geomorphological information (LandScan project). The model directly accounts for the role of rainfall patterns in driving the seasonality of cholera outbreaks. The two main outbreaks in fact occurred during the rainy seasons (October and May) when extensive floodings severely worsened the sanitation conditions and, in turn, raised the risk of infection. The model capability to reproduce the spatiotemporal features of the epidemic up to date grants robustness to the foreseen future development. To this end, we generate realistic scenario of future precipitation in order to forecast possible epidemic paths up to the end of the 2013. In this context, the duration of acquired immunity, a hotly debated topic in the scientific community, emerges as a controlling factor for progression of the epidemic in the near future. The framework presented here can straightforwardly be used to evaluate the effectiveness of alternative intervention strategies like mass vaccinations, clean water supply and educational campaigns, thus emerging as an essential component of the control of future cholera epidemics.

On the Use of Human Mobility Proxies for Modeling Epidemics

PubMed Central

Tizzoni, Michele; Bajardi, Paolo; Decuyper, Adeline; Kon Kam King, Guillaume; Schneider, Christian M.; Blondel, Vincent; Smoreda, Zbigniew; González, Marta C.; Colizza, Vittoria

2014-01-01

Human mobility is a key component of large-scale spatial-transmission models of infectious diseases. Correctly modeling and quantifying human mobility is critical for improving epidemic control, but may be hindered by data incompleteness or unavailability. Here we explore the opportunity of using proxies for individual mobility to describe commuting flows and predict the diffusion of an influenza-like-illness epidemic. We consider three European countries and the corresponding commuting networks at different resolution scales, obtained from (i) official census surveys, (ii) proxy mobility data extracted from mobile phone call records, and (iii) the radiation model calibrated with census data. Metapopulation models defined on these countries and integrating the different mobility layers are compared in terms of epidemic observables. We show that commuting networks from mobile phone data capture the empirical commuting patterns well, accounting for more than 87% of the total fluxes. The distributions of commuting fluxes per link from mobile phones and census sources are similar and highly correlated, however a systematic overestimation of commuting traffic in the mobile phone data is observed. This leads to epidemics that spread faster than on census commuting networks, once the mobile phone commuting network is considered in the epidemic model, however preserving to a high degree the order of infection of newly affected locations. Proxies' calibration affects the arrival times' agreement across different models, and the observed topological and traffic discrepancies among mobility sources alter the resulting epidemic invasion patterns. Results also suggest that proxies perform differently in approximating commuting patterns for disease spread at different resolution scales, with the radiation model showing higher accuracy than mobile phone data when the seed is central in the network, the opposite being observed for peripheral locations. Proxies should therefore be chosen in light of the desired accuracy for the epidemic situation under study. PMID:25010676

Temporal percolation of the susceptible network in an epidemic spreading.

PubMed

Valdez, Lucas Daniel; Macri, Pablo Alejandro; Braunstein, Lidia Adriana

2012-01-01

In this work, we study the evolution of the susceptible individuals during the spread of an epidemic modeled by the susceptible-infected-recovered (SIR) process spreading on the top of complex networks. Using an edge-based compartmental approach and percolation tools, we find that a time-dependent quantity ΦS(t), namely, the probability that a given neighbor of a node is susceptible at time t, is the control parameter of a node void percolation process involving those nodes on the network not-reached by the disease. We show that there exists a critical time t(c) above which the giant susceptible component is destroyed. As a consequence, in order to preserve a macroscopic connected fraction of the network composed by healthy individuals which guarantee its functionality, any mitigation strategy should be implemented before this critical time t(c). Our theoretical results are confirmed by extensive simulations of the SIR process.

Economic and Social Impact of Influenza Mitigation Strategies by Demographic Class

PubMed Central

Barrett, Chris; Bisset, Keith; Leidig, Jonathan; Marathe, Achla; Marathe, Madhav

2011-01-01

Background We aim to determine the economic and social impact of typical interventions proposed by the public health officials and preventive behavioral changes adopted by the private citizens in the event of a “flu-like” epidemic. Method We apply an individual-based simulation model to the New River Valley area of Virginia for addressing this critical problem. The economic costs include not only the loss in productivity due to sickness but also the indirect cost incurred through disease avoidance and caring for dependents. Results The results show that the most important factor responsible for preventing income loss is the modification of individual behavior; it drops the total income loss by 62% compared to the base case. The next most important factor is the closure of schools which reduces the total income loss by another 40%. Conclusions The preventive behavior of the private citizens is the most important factor in controlling the epidemic. PMID:21339828

An epidemic model for biological data fusion in ad hoc sensor networks

NASA Astrophysics Data System (ADS)

Chang, K. C.; Kotari, Vikas

2009-05-01

Bio terrorism can be a very refined and a catastrophic approach of attacking a nation. This requires the development of a complete architecture dedicatedly designed for this purpose which includes but is not limited to Sensing/Detection, Tracking and Fusion, Communication, and others. In this paper we focus on one such architecture and evaluate its performance. Various sensors for this specific purpose have been studied. The accent has been on use of Distributed systems such as ad-hoc networks and on application of epidemic data fusion algorithms to better manage the bio threat data. The emphasis has been on understanding the performance characteristics of these algorithms under diversified real time scenarios which are implemented through extensive JAVA based simulations. Through comparative studies on communication and fusion the performance of channel filter algorithm for the purpose of biological sensor data fusion are validated.

Analyzing the impact of modeling choices and assumptions in compartmental epidemiological models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nutaro, James J.; Pullum, Laura L.; Ramanathan, Arvind

In this study, computational models have become increasingly used as part of modeling, predicting, and understanding how infectious diseases spread within large populations. These models can be broadly classified into differential equation-based models (EBM) and agent-based models (ABM). Both types of models are central in aiding public health officials design intervention strategies in case of large epidemic outbreaks. We examine these models in the context of illuminating their hidden assumptions and the impact these may have on the model outcomes. Very few ABM/EBMs are evaluated for their suitability to address a particular public health concern, and drawing relevant conclusions aboutmore » their suitability requires reliable and relevant information regarding the different modeling strategies and associated assumptions. Hence, there is a need to determine how the different modeling strategies, choices of various parameters, and the resolution of information for EBMs and ABMs affect outcomes, including predictions of disease spread. In this study, we present a quantitative analysis of how the selection of model types (i.e., EBM vs. ABM), the underlying assumptions that are enforced by model types to model the disease propagation process, and the choice of time advance (continuous vs. discrete) affect the overall outcomes of modeling disease spread. Our study reveals that the magnitude and velocity of the simulated epidemic depends critically on the selection of modeling principles, various assumptions of disease process, and the choice of time advance.« less

Analyzing the impact of modeling choices and assumptions in compartmental epidemiological models

DOE PAGES

Nutaro, James J.; Pullum, Laura L.; Ramanathan, Arvind; ...

2016-05-01

In this study, computational models have become increasingly used as part of modeling, predicting, and understanding how infectious diseases spread within large populations. These models can be broadly classified into differential equation-based models (EBM) and agent-based models (ABM). Both types of models are central in aiding public health officials design intervention strategies in case of large epidemic outbreaks. We examine these models in the context of illuminating their hidden assumptions and the impact these may have on the model outcomes. Very few ABM/EBMs are evaluated for their suitability to address a particular public health concern, and drawing relevant conclusions aboutmore » their suitability requires reliable and relevant information regarding the different modeling strategies and associated assumptions. Hence, there is a need to determine how the different modeling strategies, choices of various parameters, and the resolution of information for EBMs and ABMs affect outcomes, including predictions of disease spread. In this study, we present a quantitative analysis of how the selection of model types (i.e., EBM vs. ABM), the underlying assumptions that are enforced by model types to model the disease propagation process, and the choice of time advance (continuous vs. discrete) affect the overall outcomes of modeling disease spread. Our study reveals that the magnitude and velocity of the simulated epidemic depends critically on the selection of modeling principles, various assumptions of disease process, and the choice of time advance.« less

Nontrivial periodic solution of a stochastic non-autonomous SISV epidemic model

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar; Alsaedi, Ahmed

2016-11-01

In this paper, we consider a stochastic non-autonomous SISV epidemic model. For the non-autonomous periodic system, firstly, we get the threshold of the system which determines whether the epidemic occurs or not. Then in the case of persistence, we show that there exists at least one nontrivial positive periodic solution of the stochastic system.

Interplay of node connectivity and epidemic rates in the dynamics of epidemic networks

DOE PAGES

Kostova, Tanya

2010-07-09

We present and analyze a discrete-time susceptible-infected epidemic network model which represents each host as a separate entity and allows heterogeneous hosts and contacts. We establish a necessary and sufficient condition for global stability of the disease-free equilibrium of the system (defined as epidemic controllability) which defines the epidemic reproduction number of the network. When this condition is not fulfilled, we show that the system has a unique, locally stable equilibrium. As a result, we further derive sufficient conditions for epidemic controllability in terms of the epidemic rates and the network topology.

A modified chain binomial model to analyse the ongoing measles epidemic in Greece, July 2017 to February 2018

PubMed Central

Lytras, Theodore; Georgakopoulou, Theano; Tsiodras, Sotirios

2018-01-01

Greece is currently experiencing a large measles outbreak, in the context of multiple similar outbreaks across Europe. We devised and applied a modified chain-binomial epidemic model, requiring very simple data, to estimate the transmission parameters of this outbreak. Model results indicate sustained measles transmission among the Greek Roma population, necessitating a targeted mass vaccination campaign to halt further spread of the epidemic. Our model may be useful for other countries facing similar measles outbreaks. PMID:29717695

A modified chain binomial model to analyse the ongoing measles epidemic in Greece, July 2017 to February 2018.

PubMed

Lytras, Theodore; Georgakopoulou, Theano; Tsiodras, Sotirios

2018-04-01

Greece is currently experiencing a large measles outbreak, in the context of multiple similar outbreaks across Europe. We devised and applied a modified chain-binomial epidemic model, requiring very simple data, to estimate the transmission parameters of this outbreak. Model results indicate sustained measles transmission among the Greek Roma population, necessitating a targeted mass vaccination campaign to halt further spread of the epidemic. Our model may be useful for other countries facing similar measles outbreaks.

Can treatment-based HIV prevention curb the epidemic among gay and other men who have sex with men? A narrative synthesis of increasing evidence for moderating and countervailing effects.

PubMed

de Wit, John B F; Adam, Philippe C G

2014-07-01

As HIV epidemics among gay and other men who have sex with men (GMSM) persist worldwide, the importance of novel prevention approaches is recognised. Evidence that antiretroviral therapy (ART) can decrease the likelihood of infection is informing emerging HIV prevention approaches, encompassing early initiation of treatment as prevention by people living with HIV and use of antiretroviral drugs as pre-exposure prophylaxis for people presumed to be uninfected. Despite widespread excitement, robust evidence of the beneficial effects of ART-based HIV prevention for GMSM remains limited. Also, theoretical models project widely varying effects of ART-based prevention on the future course of HIV epidemics among GMSM, drawing attention to the possible moderating role of differences in the achievements of local HIV responses and the critical importance of sustained protective sexual practices into the future. Ecological analyses and simulations of ongoing epidemics in major gay communities illustrate that the preventive effects of ART in many settings are being offset by increased sexual risk-taking, as reflected in stable or increasing HIV infection rates. Also, the effects of scaling up HIV testing and treatment among GMSM in settings that are often considered prime examples of the success of ART-based prevention may be levelling as 'scope for improvement' diminishes. ART-based approaches further extend the HIV prevention toolkit and substantially increase people's options to protect themselves and others. The future impact of ART-based prevention on HIV epidemics among GMSM ultimately depends on whether heralded responses offset, attenuate or compound the ongoing social and behavioural changes that drive increased sexual risk.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim; Shaw, Leah

2012-02-01

Adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a moment-closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and epidemic spread model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim

2013-03-01

Dynamics of adaptive social networks, in which nodes and network structure co-evolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher order topological structures. We propose a systematic approach to moment closure approximation based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the mean-field prediction and simulations of the full network system.

Asymptotically inspired moment-closure approximation for adaptive networks

NASA Astrophysics Data System (ADS)

Shkarayev, Maxim S.; Shaw, Leah B.

2013-11-01

Adaptive social networks, in which nodes and network structure coevolve, are often described using a mean-field system of equations for the density of node and link types. These equations constitute an open system due to dependence on higher-order topological structures. We propose a new approach to moment closure based on the analytical description of the system in an asymptotic regime. We apply the proposed approach to two examples of adaptive networks: recruitment to a cause model and adaptive epidemic model. We show a good agreement between the improved mean-field prediction and simulations of the full network system.

Stochastic dynamics of cholera epidemics

NASA Astrophysics Data System (ADS)

Azaele, Sandro; Maritan, Amos; Bertuzzo, Enrico; Rodriguez-Iturbe, Ignacio; Rinaldo, Andrea

2010-05-01

We describe the predictions of an analytically tractable stochastic model for cholera epidemics following a single initial outbreak. The exact model relies on a set of assumptions that may restrict the generality of the approach and yet provides a realm of powerful tools and results. Without resorting to the depletion of susceptible individuals, as usually assumed in deterministic susceptible-infected-recovered models, we show that a simple stochastic equation for the number of ill individuals provides a mechanism for the decay of the epidemics occurring on the typical time scale of seasonality. The model is shown to provide a reasonably accurate description of the empirical data of the 2000/2001 cholera epidemic which took place in the Kwa Zulu-Natal Province, South Africa, with possibly notable epidemiological implications.

Diagnostic schemes for reducing epidemic size of African viral hemorrhagic fever outbreaks.

PubMed

Okeke, Iruka N; Manning, Robert S; Pfeiffer, Thomas

2014-09-12

Viral hemorrhagic fever (VHF) outbreaks, with high mortality rates, have often been amplified in African health institutions due to person-to-person transmission via infected body fluids.  By collating and analyzing epidemiological data from documented outbreaks, we observed that diagnostic delay contributes to epidemic size for Ebola and Marburg hemorrhagic fever outbreaks. We used a susceptible-exposed-infectious-removed (SEIR) model and data from the 1995 outbreak in Kikwit, Democratic Republic of Congo, to simulate Ebola hemorrhagic fever epidemics. Our model allows us to describe the dynamics for hospital staff separately from that for the general population, and to implement health worker-specific interventions. The model illustrates that implementing World Health Organization/US Centers for Disease Control and Prevention guidelines of isolating patients who do not respond to antimalarial and antibacterial chemotherapy reduces total outbreak size, from a median of 236, by 90% or more. Routinely employing diagnostic testing in post-mortems of patients that died of refractory fevers reduces the median outbreak size by a further 60%. Even greater reductions in outbreak size were seen when all febrile patients were tested for endemic infections or when febrile health-care workers were tested.  The effect of testing strategies was not impaired by the 1-3 day delay that would occur if testing were performed by a reference laboratory. In addition to improving the quality of care for common causes of febrile infections, increased and strategic use of laboratory diagnostics for fever could reduce the chance of hospital amplification of VHFs in resource-limited African health systems.

Epidemic Reconstruction in a Phylogenetics Framework: Transmission Trees as Partitions of the Node Set

PubMed Central

Hall, Matthew; Woolhouse, Mark; Rambaut, Andrew

2015-01-01

The use of genetic data to reconstruct the transmission tree of infectious disease epidemics and outbreaks has been the subject of an increasing number of studies, but previous approaches have usually either made assumptions that are not fully compatible with phylogenetic inference, or, where they have based inference on a phylogeny, have employed a procedure that requires this tree to be fixed. At the same time, the coalescent-based models of the pathogen population that are employed in the methods usually used for time-resolved phylogeny reconstruction are a considerable simplification of epidemic process, as they assume that pathogen lineages mix freely. Here, we contribute a new method that is simultaneously a phylogeny reconstruction method for isolates taken from an epidemic, and a procedure for transmission tree reconstruction. We observe that, if one or more samples is taken from each host in an epidemic or outbreak and these are used to build a phylogeny, a transmission tree is equivalent to a partition of the set of nodes of this phylogeny, such that each partition element is a set of nodes that is connected in the full tree and contains all the tips corresponding to samples taken from one and only one host. We then implement a Monte Carlo Markov Chain (MCMC) procedure for simultaneous sampling from the spaces of both trees, utilising a newly-designed set of phylogenetic tree proposals that also respect node partitions. We calculate the posterior probability of these partitioned trees based on a model that acknowledges the population structure of an epidemic by employing an individual-based disease transmission model and a coalescent process taking place within each host. We demonstrate our method, first using simulated data, and then with sequences taken from the H7N7 avian influenza outbreak that occurred in the Netherlands in 2003. We show that it is superior to established coalescent methods for reconstructing the topology and node heights of the phylogeny and performs well for transmission tree reconstruction when the phylogeny is well-resolved by the genetic data, but caution that this will often not be the case in practice and that existing genetic and epidemiological data should be used to configure such analyses whenever possible. This method is available for use by the research community as part of BEAST, one of the most widely-used packages for reconstruction of dated phylogenies. PMID:26717515

A Household-Based Study of Contact Networks Relevant for the Spread of Infectious Diseases in the Highlands of Peru

PubMed Central

Grijalva, Carlos G.; Goeyvaerts, Nele; Verastegui, Hector; Edwards, Kathryn M.; Gil, Ana I.; Lanata, Claudio F.; Hens, Niel

2015-01-01

Background Few studies have quantified social mixing in remote rural areas of developing countries, where the burden of infectious diseases is usually the highest. Understanding social mixing patterns in those settings is crucial to inform the implementation of strategies for disease prevention and control. We characterized contact and social mixing patterns in rural communities of the Peruvian highlands. Methods and Findings This cross-sectional study was nested in a large prospective household-based study of respiratory infections conducted in the province of San Marcos, Cajamarca-Peru. Members of study households were interviewed using a structured questionnaire of social contacts (conversation or physical interaction) experienced during the last 24 hours. We identified 9015 reported contacts from 588 study household members. The median age of respondents was 17 years (interquartile range [IQR] 4–34 years). The median number of reported contacts was 12 (IQR 8–20) whereas the median number of physical (i.e. skin-to-skin) contacts was 8.5 (IQR 5–14). Study participants had contacts mostly with people of similar age, and with their offspring or parents. The number of reported contacts was mainly determined by the participants’ age, household size and occupation. School-aged children had more contacts than other age groups. Within-household reciprocity of contacts reporting declined with household size (range 70%-100%). Ninety percent of household contact networks were complete, and furthermore, household members' contacts with non-household members showed significant overlap (range 33%-86%), indicating a high degree of contact clustering. A two-level mixing epidemic model was simulated to compare within-household mixing based on observed contact networks and within-household random mixing. No differences in the size or duration of the simulated epidemics were revealed. Conclusion This study of rural low-density communities in the highlands of Peru suggests contact patterns are highly assortative. Study findings support the use of within-household homogenous mixing assumptions for epidemic modeling in this setting. PMID:25734772

Stochastic analysis of epidemics on adaptive time varying networks

NASA Astrophysics Data System (ADS)

Kotnis, Bhushan; Kuri, Joy

2013-06-01

Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an “adaptive threshold,” i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.

Real-time forecasting of an epidemic using a discrete time stochastic model: a case study of pandemic influenza (H1N1-2009)

PubMed Central

2011-01-01

Background Real-time forecasting of epidemics, especially those based on a likelihood-based approach, is understudied. This study aimed to develop a simple method that can be used for the real-time epidemic forecasting. Methods A discrete time stochastic model, accounting for demographic stochasticity and conditional measurement, was developed and applied as a case study to the weekly incidence of pandemic influenza (H1N1-2009) in Japan. By imposing a branching process approximation and by assuming the linear growth of cases within each reporting interval, the epidemic curve is predicted using only two parameters. The uncertainty bounds of the forecasts are computed using chains of conditional offspring distributions. Results The quality of the forecasts made before the epidemic peak appears largely to depend on obtaining valid parameter estimates. The forecasts of both weekly incidence and final epidemic size greatly improved at and after the epidemic peak with all the observed data points falling within the uncertainty bounds. Conclusions Real-time forecasting using the discrete time stochastic model with its simple computation of the uncertainty bounds was successful. Because of the simplistic model structure, the proposed model has the potential to additionally account for various types of heterogeneity, time-dependent transmission dynamics and epidemiological details. The impact of such complexities on forecasting should be explored when the data become available as part of the disease surveillance. PMID:21324153

Spatiotemporal dynamics of the Ebola epidemic in Guinea and implications for vaccination and disease elimination: a computational modeling analysis.

PubMed

Ajelli, Marco; Merler, Stefano; Fumanelli, Laura; Pastore Y Piontti, Ana; Dean, Natalie E; Longini, Ira M; Halloran, M Elizabeth; Vespignani, Alessandro

2016-09-07

Among the three countries most affected by the Ebola virus disease outbreak in 2014-2015, Guinea presents an unusual spatiotemporal epidemic pattern, with several waves and a long tail in the decay of the epidemic incidence. Here, we develop a stochastic agent-based model at the level of a single household that integrates detailed data on Guinean demography, hospitals, Ebola treatment units, contact tracing, and safe burial interventions. The microsimulation-based model is used to assess the effect of each control strategy and the probability of elimination of the epidemic according to different intervention scenarios, including ring vaccination with the recombinant vesicular stomatitis virus-vectored vaccine. The numerical results indicate that the dynamics of the Ebola epidemic in Guinea can be quantitatively explained by the timeline of the implemented interventions. In particular, the early availability of Ebola treatment units and the associated isolation of cases and safe burials helped to limit the number of Ebola cases experienced by Guinea. We provide quantitative evidence of a strong negative correlation between the time series of cases and the number of traced contacts. This result is confirmed by the computational model that suggests that contact tracing effort is a key determinant in the control and elimination of the disease. In data-driven microsimulations, we find that tracing at least 5-10 contacts per case is crucial in preventing epidemic resurgence during the epidemic elimination phase. The computational model is used to provide an analysis of the ring vaccination trial highlighting its potential effect on disease elimination. We identify contact tracing as one of the key determinants of the epidemic's behavior in Guinea, and we show that the early availability of Ebola treatment unit beds helped to limit the number of Ebola cases in Guinea.

Heterogeneous population dynamics and scaling laws near epidemic outbreaks.

PubMed

Widder, Andreas; Kuehn, Christian

2016-10-01

In this paper, we focus on the influence of heterogeneity and stochasticity of the population on the dynamical structure of a basic susceptible-infected-susceptible (SIS) model. First we prove that, upon a suitable mathematical reformulation of the basic reproduction number, the homogeneous system and the heterogeneous system exhibit a completely analogous global behaviour. Then we consider noise terms to incorporate the fluctuation effects and the random import of the disease into the population and analyse the influence of heterogeneity on warning signs for critical transitions (or tipping points). This theory shows that one may be able to anticipate whether a bifurcation point is close before it happens. We use numerical simulations of a stochastic fast-slow heterogeneous population SIS model and show various aspects of heterogeneity have crucial influences on the scaling laws that are used as early-warning signs for the homogeneous system. Thus, although the basic structural qualitative dynamical properties are the same for both systems, the quantitative features for epidemic prediction are expected to change and care has to be taken to interpret potential warning signs for disease outbreaks correctly.

Policies to Reduce Influenza in the Workplace: Impact Assessments Using an Agent-Based Model

PubMed Central

Grefenstette, John J.; Galloway, David; Albert, Steven M.; Burke, Donald S.

2013-01-01

Objectives. We examined the impact of access to paid sick days (PSDs) and stay-at-home behavior on the influenza attack rate in workplaces. Methods. We used an agent-based model of Allegheny County, Pennsylvania, with PSD data from the US Bureau of Labor Statistics, standard influenza epidemic parameters, and the probability of staying home when ill. We compared the influenza attack rate among employees resulting from workplace transmission, focusing on the effects of presenteeism (going to work when ill). Results. In a simulated influenza epidemic (R0 = 1.4), the attack rate among employees owing to workplace transmission was 11.54%. A large proportion (72.00%) of this attack rate resulted from exposure to employees engaging in presenteeism. Universal PSDs reduced workplace infections by 5.86%. Providing 1 or 2 “flu days”—allowing employees with influenza to stay home—reduced workplace infections by 25.33% and 39.22%, respectively. Conclusions. PSDs reduce influenza transmission owing to presenteeism and, hence, the burden of influenza illness in workplaces. PMID:23763426

Quarantine-generated phase transition in epidemic spreading.

PubMed

Lagorio, C; Dickison, M; Vazquez, F; Braunstein, L A; Macri, P A; Migueles, M V; Havlin, S; Stanley, H E

2011-02-01

We study the critical effect of quarantine on the propagation of epidemics on an adaptive network of social contacts. For this purpose, we analyze the susceptible-infected-recovered model in the presence of quarantine, where susceptible individuals protect themselves by disconnecting their links to infected neighbors with probability w and reconnecting them to other susceptible individuals chosen at random. Starting from a single infected individual, we show by an analytical approach and simulations that there is a phase transition at a critical rewiring (quarantine) threshold w(c) separating a phase (w

Effect of modelling slum populations on influenza spread in Delhi

PubMed Central

Chen, Jiangzhuo; Chu, Shuyu; Chungbaek, Youngyun; Khan, Maleq; Kuhlman, Christopher; Marathe, Achla; Mortveit, Henning; Vullikanti, Anil; Xie, Dawen

2016-01-01

Objectives This research studies the impact of influenza epidemic in the slum and non-slum areas of Delhi, the National Capital Territory of India, by taking proper account of slum demographics and residents’ activities, using a highly resolved social contact network of the 13.8 million residents of Delhi. Methods An SEIR model is used to simulate the spread of influenza on two different synthetic social contact networks of Delhi, one where slums and non-slums are treated the same in terms of their demographics and daily sets of activities and the other, where slum and non-slum regions have different attributes. Results Differences between the epidemic outcomes on the two networks are large. Time-to-peak infection is overestimated by several weeks, and the cumulative infection rate and peak infection rate are underestimated by 10–50%, when slum attributes are ignored. Conclusions Slum populations have a significant effect on influenza transmission in urban areas. Improper specification of slums in large urban regions results in underestimation of infections in the entire population and hence will lead to misguided interventions by policy planners. PMID:27687898

Epidemic spreading on hierarchical geographical networks with mobile agents

NASA Astrophysics Data System (ADS)

Han, Xiao-Pu; Zhao, Zhi-Dan; Hadzibeganovic, Tarik; Wang, Bing-Hong

2014-05-01

Hierarchical geographical traffic networks are critical for our understanding of scaling laws in human trajectories. Here, we investigate the susceptible-infected epidemic process evolving on hierarchical networks in which agents randomly walk along the edges and establish contacts in network nodes. We employ a metapopulation modeling framework that allows us to explore the contagion spread patterns in relation to multi-scale mobility behaviors. A series of computer simulations revealed that a shifted power-law-like negative relationship between the peak timing of epidemics τ0 and population density, and a logarithmic positive relationship between τ0 and the network size, can both be explained by the gradual enlargement of fluctuations in the spreading process. We employ a semi-analytical method to better understand the nature of these relationships and the role of pertinent demographic factors. Additionally, we provide a quantitative discussion of the efficiency of a border screening procedure in delaying epidemic outbreaks on hierarchical networks, yielding a rather limited feasibility of this mitigation strategy but also its non-trivial dependence on population density, infector detectability, and the diversity of the susceptible region. Our results suggest that the interplay between the human spatial dynamics, network topology, and demographic factors can have important consequences for the global spreading and control of infectious diseases. These findings provide novel insights into the combined effects of human mobility and the organization of geographical networks on spreading processes, with important implications for both epidemiological research and health policy.

Development of an Agent-Based Model to Investigate the Impact of HIV Self-Testing Programs on Men Who Have Sex With Men in Atlanta and Seattle.

PubMed

Luo, Wei; Katz, David A; Hamilton, Deven T; McKenney, Jennie; Jenness, Samuel M; Goodreau, Steven M; Stekler, Joanne D; Rosenberg, Eli S; Sullivan, Patrick S; Cassels, Susan

2018-06-29

In the United States HIV epidemic, men who have sex with men (MSM) remain the most profoundly affected group. Prevention science is increasingly being organized around HIV testing as a launch point into an HIV prevention continuum for MSM who are not living with HIV and into an HIV care continuum for MSM who are living with HIV. An increasing HIV testing frequency among MSM might decrease future HIV infections by linking men who are living with HIV to antiretroviral care, resulting in viral suppression. Distributing HIV self-test (HIVST) kits is a strategy aimed at increasing HIV testing. Our previous modeling work suggests that the impact of HIV self-tests on transmission dynamics will depend not only on the frequency of tests and testers' behaviors but also on the epidemiological and testing characteristics of the population. The objective of our study was to develop an agent-based model to inform public health strategies for promoting safe and effective HIV self-tests to decrease the HIV incidence among MSM in Atlanta, GA, and Seattle, WA, cities representing profoundly different epidemiological settings. We adapted and extended a network- and agent-based stochastic simulation model of HIV transmission dynamics that was developed and parameterized to investigate racial disparities in HIV prevalence among MSM in Atlanta. The extension comprised several activities: adding a new set of model parameters for Seattle MSM; adding new parameters for tester types (ie, regular, risk-based, opportunistic-only, or never testers); adding parameters for simplified pre-exposure prophylaxis uptake following negative results for HIV tests; and developing a conceptual framework for the ways in which the provision of HIV self-tests might change testing behaviors. We derived city-specific parameters from previous cohort and cross-sectional studies on MSM in Atlanta and Seattle. Each simulated population comprised 10,000 MSM and targeted HIV prevalences are equivalent to 28% and 11% in Atlanta and Seattle, respectively. Previous studies provided sufficient data to estimate the model parameters representing nuanced HIV testing patterns and HIV self-test distribution. We calibrated the models to simulate the epidemics representing Atlanta and Seattle, including matching the expected stable HIV prevalence. The revised model facilitated the estimation of changes in 10-year HIV incidence based on counterfactual scenarios of HIV self-test distribution strategies and their impact on testing behaviors. We demonstrated that the extension of an existing agent-based HIV transmission model was sufficient to simulate the HIV epidemics among MSM in Atlanta and Seattle, to accommodate a more nuanced depiction of HIV testing behaviors than previous models, and to serve as a platform to investigate how HIV self-tests might impact testing and HIV transmission patterns among MSM in Atlanta and Seattle. In our future studies, we will use the model to test how different HIV self-test distribution strategies might affect HIV incidence among MSM. ©Wei Luo, David A Katz, Deven T Hamilton, Jennie McKenney, Samuel M Jenness, Steven M Goodreau, Joanne D Stekler, Eli S Rosenberg, Patrick S Sullivan, Susan Cassels. Originally published in JMIR Public Health and Surveillance (http://publichealth.jmir.org), 29.06.2018.

Developing stochastic epidemiological models to quantify the dynamics of infectious diseases in domestic livestock.

PubMed

MacKenzie, K; Bishop, S C

2001-08-01

A stochastic model describing disease transmission dynamics for a microparasitic infection in a structured domestic animal population is developed and applied to hypothetical epidemics on a pig farm. Rational decision making regarding appropriate control strategies for infectious diseases in domestic livestock requires an understanding of the disease dynamics and risk profiles for different groups of animals. This is best achieved by means of stochastic epidemic models. Methodologies are presented for 1) estimating the probability of an epidemic, given the presence of an infected animal, whether this epidemic is major (requires intervention) or minor (dies out without intervention), and how the location of the infected animal on the farm influences the epidemic probabilities; 2) estimating the basic reproductive ratio, R0 (i.e., the expected number of secondary cases on the introduction of a single infected animal) and the variability of the estimate of this parameter; and 3) estimating the total proportion of animals infected during an epidemic and the total proportion infected at any point in time. The model can be used for assessing impact of altering farm structure on disease dynamics, as well as disease control strategies, including altering farm structure, vaccination, culling, and genetic selection.

Hybrid epidemics--a case study on computer worm conficker.

PubMed

Zhang, Changwang; Zhou, Shi; Chain, Benjamin M

2015-01-01

Conficker is a computer worm that erupted on the Internet in 2008. It is unique in combining three different spreading strategies: local probing, neighbourhood probing, and global probing. We propose a mathematical model that combines three modes of spreading: local, neighbourhood, and global, to capture the worm's spreading behaviour. The parameters of the model are inferred directly from network data obtained during the first day of the Conficker epidemic. The model is then used to explore the tradeoff between spreading modes in determining the worm's effectiveness. Our results show that the Conficker epidemic is an example of a critically hybrid epidemic, in which the different modes of spreading in isolation do not lead to successful epidemics. Such hybrid spreading strategies may be used beneficially to provide the most effective strategies for promulgating information across a large population. When used maliciously, however, they can present a dangerous challenge to current internet security protocols.

Beyond network structure: How heterogeneous susceptibility modulates the spread of epidemics.

PubMed

Smilkov, Daniel; Hidalgo, Cesar A; Kocarev, Ljupco

2014-04-25

The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that-for the SIS model-differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a node's degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated). These results show that the failure to include differential susceptibility to epidemic models can lead to a systematic over/under estimation of fundamental epidemic parameters when the structure of the networks is not independent from the susceptibility of the nodes or when there are correlations between the susceptibility of connected individuals.

Finite size effects in epidemic spreading: the problem of overpopulated systems

NASA Astrophysics Data System (ADS)

Ganczarek, Wojciech

2013-12-01

In this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.

Forecasting techno-social systems: how physics and computing help to fight off global pandemics

NASA Astrophysics Data System (ADS)

Vespignani, Alessandro

2010-03-01

The crucial issue when planning for adequate public health interventions to mitigate the spread and impact of epidemics is risk evaluation and forecast. This amount to the anticipation of where, when and how strong the epidemic will strike. In the last decade advances in performance in computer technology, data acquisition, statistical physics and complex networks theory allow the generation of sophisticated simulations on supercomputer infrastructures to anticipate the spreading pattern of a pandemic. For the first time we are in the position of generating real time forecast of epidemic spreading. I will review the history of the current H1N1 pandemic, the major road-blocks the community has faced in its containment and mitigation and how physics and computing provide predictive tools that help us to battle epidemics.

Analysis of nonlinear relationships in dual epidemics, and its application to the management of grapevine downy and powdery mildews.

PubMed

Savary, Serge; Delbac, Lionel; Rochas, Amélie; Taisant, Guillaume; Willocquet, Laetitia

2009-08-01

Dual epidemics are defined as epidemics developing on two or several plant organs in the course of a cropping season. Agricultural pathosystems where such epidemics develop are often very important, because the harvestable part is one of the organs affected. These epidemics also are often difficult to manage, because the linkage between epidemiological components occurring on different organs is poorly understood, and because prediction of the risk toward the harvestable organs is difficult. In the case of downy mildew (DM) and powdery mildew (PM) of grapevine, nonlinear modeling and logistic regression indicated nonlinearity in the foliage-cluster relationships. Nonlinear modeling enabled the parameterization of a transmission coefficient that numerically links the two components, leaves and clusters, in DM and PM epidemics. Logistic regression analysis yielded a series of probabilistic models that enabled predicting preset levels of cluster infection risks based on DM and PM severities on the foliage at successive crop stages. The usefulness of this framework for tactical decision-making for disease control is discussed.

Modeling the propagation of mobile malware on complex networks

NASA Astrophysics Data System (ADS)

Liu, Wanping; Liu, Chao; Yang, Zheng; Liu, Xiaoyang; Zhang, Yihao; Wei, Zuxue

2016-08-01

In this paper, the spreading behavior of malware across mobile devices is addressed. By introducing complex networks to model mobile networks, which follows the power-law degree distribution, a novel epidemic model for mobile malware propagation is proposed. The spreading threshold that guarantees the dynamics of the model is calculated. Theoretically, the asymptotic stability of the malware-free equilibrium is confirmed when the threshold is below the unity, and the global stability is further proved under some sufficient conditions. The influences of different model parameters as well as the network topology on malware propagation are also analyzed. Our theoretical studies and numerical simulations show that networks with higher heterogeneity conduce to the diffusion of malware, and complex networks with lower power-law exponents benefit malware spreading.

Spatial Evaluation and Verification of Earthquake Simulators

NASA Astrophysics Data System (ADS)

Wilson, John Max; Yoder, Mark R.; Rundle, John B.; Turcotte, Donald L.; Schultz, Kasey W.

2017-06-01

In this paper, we address the problem of verifying earthquake simulators with observed data. Earthquake simulators are a class of computational simulations which attempt to mirror the topological complexity of fault systems on which earthquakes occur. In addition, the physics of friction and elastic interactions between fault elements are included in these simulations. Simulation parameters are adjusted so that natural earthquake sequences are matched in their scaling properties. Physically based earthquake simulators can generate many thousands of years of simulated seismicity, allowing for a robust capture of the statistical properties of large, damaging earthquakes that have long recurrence time scales. Verification of simulations against current observed earthquake seismicity is necessary, and following past simulator and forecast model verification methods, we approach the challenges in spatial forecast verification to simulators; namely, that simulator outputs are confined to the modeled faults, while observed earthquake epicenters often occur off of known faults. We present two methods for addressing this discrepancy: a simplistic approach whereby observed earthquakes are shifted to the nearest fault element and a smoothing method based on the power laws of the epidemic-type aftershock (ETAS) model, which distributes the seismicity of each simulated earthquake over the entire test region at a decaying rate with epicentral distance. To test these methods, a receiver operating characteristic plot was produced by comparing the rate maps to observed m>6.0 earthquakes in California since 1980. We found that the nearest-neighbor mapping produced poor forecasts, while the ETAS power-law method produced rate maps that agreed reasonably well with observations.

Correlation between information diffusion and opinion evolution on social media

NASA Astrophysics Data System (ADS)

Xiong, Fei; Liu, Yun; Zhang, Zhenjiang

2014-12-01

Information diffusion and opinion evolution are often treated as two independent processes. Opinion models assume the topic reaches each agent and agents initially have their own ideas. In fact, the processes of information diffusion and opinion evolution often intertwine with each other. Whether the influence between these two processes plays a role in the system state is unclear. In this paper, we collected more than one million real data from a well-known social platform, and analysed large-scale user diffusion behaviour and opinion formation. We found that user inter-event time follows a two-scaling power-law distribution with two different power exponents. Public opinion stabilizes quickly and evolves toward the direction of convergence, but the consensus state is prevented by a few opponents. We propose a three-state opinion model accompanied by information diffusion. Agents form and exchange their opinions during information diffusion. Conversely, agents' opinions also influence their diffusion actions. Simulations show that the model with a correlation of the two processes produces similar statistical characteristics as empirical results. A fast epidemic process drives individual opinions to converge more obviously. Unlike previous epidemic models, the number of infected agents does not always increase with the update rate, but has a peak with an intermediate value of the rate.

Using heterogeneity in the population structure of U.S. swine farms to compare transmission models for porcine epidemic diarrhoea

PubMed Central

O’Dea, Eamon B.; Snelson, Harry; Bansal, Shweta

2016-01-01

In 2013, U.S. swine producers were confronted with the disruptive emergence of porcine epidemic diarrhoea (PED). Movement of animals among farms is hypothesised to have played a role in the spread of PED among farms. Via this or other mechanisms, the rate of spread may also depend on the geographic density of farms and climate. To evaluate such effects on a large scale, we analyse state-level counts of outbreaks with variables describing the distribution of farm sizes and types, aggregate flows of animals among farms, and an index of climate. Our first main finding is that it is possible for a correlation analysis to be sensitive to transmission model parameters. This finding is based on a global sensitivity analysis of correlations on simulated data that included a biased and noisy observation model based on the available PED data. Our second main finding is that flows are significantly associated with the reports of PED outbreaks. This finding is based on correlations of pairwise relationships and regression modeling of total and weekly outbreak counts. These findings illustrate how variation in population structure may be employed along with observational data to improve understanding of disease spread. PMID:26947420

Cost-Effectiveness of Mass Dog Vaccination Campaigns against Rabies in Flores Island, Indonesia.

PubMed

Wera, E; Mourits, M C M; Siko, M M; Hogeveen, H

2017-12-01

A dynamic deterministic simulation model was developed to determine the cost-effectiveness of different mass dog vaccination strategies against rabies in a dog population representative of a typical village on Flores Island. Cost-effectiveness was measured as public cost per averted dog-rabies case. Simulations started with the introduction of one infectious dog into a susceptible dog population of 399 dogs and subsequently ran for a period of 10 years. The base scenario represented a situation without any control intervention. Evaluated vaccination strategies were as follows: annual vaccination campaigns with short-acting vaccine (immunity duration of 52 weeks) (AV_52), annual campaigns with long-acting vaccine (immunity duration of 156 weeks) (AV_156), biannual campaigns with short-acting vaccine (BV_52) and once-in-2-years campaigns with long-acting vaccine (O2V_156). The effectiveness of the vaccination strategies was simulated for vaccination coverages of 50% and 70%. Cumulative results were reported for the 10-year simulation period. The base scenario resulted in three epidemic waves, with a total of 1274 dog-rabies cases. The public cost of applying AV_52 at a coverage of 50% was US$5342 for a village. This strategy was unfavourable compared to other strategies, as it was costly and ineffective in controlling the epidemic. The costs of AV_52 at a coverage of 70% and AV_156 at a coverage of 70% were, respectively, US$3646 and US$3716, equivalent to US$3.00 and US$3.17 per averted dog-rabies case. Increasing the coverage of AV_156 from 50% to 70% reduced the number of cases by 7% and reduced the cost by US$1452, resulting in a cost-effectiveness ratio of US$1.81 per averted dog-rabies case. This simulation model provides an effective tool to explore the public cost-effectiveness of mass dog vaccination strategies in Flores Island. Insights obtained from the simulation results are useful for animal health authorities to support decision-making in rabies-endemic areas, such as Flores Island. © 2016 Blackwell Verlag GmbH.

The prediction of epidemics through mathematical modeling.

PubMed

Schaus, Catherine

2014-01-01

Mathematical models may be resorted to in an endeavor to predict the development of epidemics. The SIR model is one of the applications. Still too approximate, the use of statistics awaits more data in order to come closer to reality.

A Local Forecast of Land Surface Wetness Conditions, Drought, and St. Louis Encephalitis Virus Transmission Derived from Seasonal Climate Predictions

NASA Astrophysics Data System (ADS)

Shaman, J.; Stieglitz, M.; Zebiak, S.; Cane, M.; Day, J. F.

2002-12-01

We present an ensemble local hydrologic forecast derived from the seasonal forecasts of the International Research Institute (IRI) for Climate Prediction. Three- month seasonal forecasts were used to resample historical meteorological conditions and generate ensemble forcing datasets for a TOPMODEL-based hydrology model. Eleven retrospective forecasts were run at a Florida and New York site. Forecast skill was assessed for mean area modeled water table depth (WTD), i.e. near surface soil wetness conditions, and compared with WTD simulated with observed data. Hydrology model forecast skill was evident at the Florida site but not at the New York site. At the Florida site, persistence of hydrologic conditions and local skill of the IRI seasonal forecast contributed to the local hydrologic forecast skill. This forecast will permit probabilistic prediction of future hydrologic conditions. At the Florida site, we have also quantified the link between modeled WTD (i.e. drought) and the amplification and transmission of St. Louis Encephalitis virus (SLEV). We derive an empirical relationship between modeled land surface wetness and levels of SLEV transmission associated with human clinical cases. We then combine the seasonal forecasts of local, modeled WTD with this empirical relationship and produce retrospective probabilistic seasonal forecasts of epidemic SLEV transmission in Florida. Epidemic SLEV transmission forecast skill is demonstrated. These findings will permit real-time forecast of drought and resultant SLEV transmission in Florida.

The Transmission Dynamics and Control of Cholera in Haiti: An Epidemic Model

PubMed Central

Andrews, Jason R.; Basu, Sanjay

2011-01-01

Background Haiti is experiencing a cholera epidemic. Official epidemic projections, to date, have failed to incorporate existing disease trends or patterns of transmission, while proposed interventions have been debated without comparative estimates of their impact. Methods We designed mathematical models of cholera transmission and fit them to Haiti’s provincial incidence data. We then simulated future epidemic trajectories to estimate the impact of clean water, vaccination and enhanced antibiotic distribution programs. Findings The natural dynamics of cholera are expected to produce a prevalence decline by mid-January 2011. Between March and December 2011, we project 779,000 (95% CI: 599,000–914,000) cases and 11,100 (95% CI: 7,300–17,400) deaths from cholera in Haiti, over half of which would be expected to occur in the Artibonite and Oueste provinces. If contaminated water consumption were reduced by 1% per week, as per current efforts, we expect 105,000 cases (95% CI: 88,000–116,000) and 1,500 (95% CI: 1,100–2,300) deaths to be averted. A plan to vaccinate 10% of the population beginning on March 1 would be predicted to avert 63,000 (95% CI: 48,000–78,000) cases and 900 (95% CI: 600–1,500) deaths over the same period. By contrast, the proposal to extend antibiotic use to all patients with severe dehydration and half of patients with moderate dehydration would be expected to avert 9,000 (95% CI: 8,000–10,000) cases and 1,300 (95% CI: 900–2,000) deaths. Interpretation A decline in cholera prevalence in early 2011 is part of the natural history of the epidemic, and should not be interpreted as reflective of the success of human interventions. Vibrio cholerae in Haiti is expected to produce at least 750,000 cholera cases by November 2011, substantially higher than official estimates currently used for resource allocation. In addition to clean water provision and vaccination, expanded access to antibiotics may avert thousands of deaths. PMID:21414658

Dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases driven by Lévy jumps

NASA Astrophysics Data System (ADS)

Liu, Qun; Jiang, Daqing; Shi, Ningzhong; Hayat, Tasawar

2018-02-01

In this paper, we study the dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases which make the research more complex. The environment variability in this paper is characterized by white noise and Lévy noise. We establish sufficient conditions for extinction and persistence in the mean of the two epidemic diseases. It is shown that: (i) time delay and Lévy noise have important effects on the persistence and extinction of epidemic diseases; (ii) two diseases can coexist under certain conditions.

Properties of highly clustered networks

NASA Astrophysics Data System (ADS)

Newman, M. E.

2003-08-01

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the giant component of the network. We also study susceptible/infective/recovered type epidemic processes within the model and find that clustering decreases the size of epidemics, but also decreases the epidemic threshold, making it easier for diseases to spread. In addition, clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of the network for quite low transmission rates.

The effects of nutrition labeling on consumer food choice: a psychological experiment and computational model.

PubMed

Helfer, Peter; Shultz, Thomas R

2014-12-01

The widespread availability of calorie-dense food is believed to be a contributing cause of an epidemic of obesity and associated diseases throughout the world. One possible countermeasure is to empower consumers to make healthier food choices with useful nutrition labeling. An important part of this endeavor is to determine the usability of existing and proposed labeling schemes. Here, we report an experiment on how four different labeling schemes affect the speed and nutritional value of food choices. We then apply decision field theory, a leading computational model of human decision making, to simulate the experimental results. The psychology experiment shows that quantitative, single-attribute labeling schemes have greater usability than multiattribute and binary ones, and that they remain effective under moderate time pressure. The computational model simulates these psychological results and provides explanatory insights into them. This work shows how experimental psychology and computational modeling can contribute to the evaluation and improvement of nutrition-labeling schemes. © 2014 New York Academy of Sciences.

Toward a generalized theory of epidemic awareness in social networks

NASA Astrophysics Data System (ADS)

Wu, Qingchu; Zhu, Wenfang

We discuss the dynamics of a susceptible-infected-susceptible (SIS) model with local awareness in networks. Individual awareness to the infectious disease is characterized by a general function of epidemic information in its neighborhood. We build a high-accuracy approximate equation governing the spreading dynamics and derive an approximate epidemic threshold above which the epidemic spreads over the whole network. Our results extend the previous work and show that the epidemic threshold is dependent on the awareness function in terms of one infectious neighbor. Interestingly, when a pow-law awareness function is chosen, the epidemic threshold can emerge in infinite networks.

HIV Epidemic Appraisals for Assisting in the Design of Effective Prevention Programmes: Shifting the Paradigm Back to Basics

PubMed Central

Mishra, Sharmistha; Sgaier, Sema K.; Thompson, Laura H.; Moses, Stephen; Ramesh, B. M.; Alary, Michel; Wilson, David; Blanchard, James F.

2012-01-01

Background To design HIV prevention programmes, it is critical to understand the temporal and geographic aspects of the local epidemic and to address the key behaviours that drive HIV transmission. Two methods have been developed to appraise HIV epidemics and guide prevention strategies. The numerical proxy method classifies epidemics based on current HIV prevalence thresholds. The Modes of Transmission (MOT) model estimates the distribution of incidence over one year among risk-groups. Both methods focus on the current state of an epidemic and provide short-term metrics which may not capture the epidemiologic drivers. Through a detailed analysis of country and sub-national data, we explore the limitations of the two traditional methods and propose an alternative approach. Methods and Findings We compared outputs of the traditional methods in five countries for which results were published, and applied the numeric and MOT model to India and six districts within India. We discovered three limitations of the current methods for epidemic appraisal: (1) their results failed to identify the key behaviours that drive the epidemic; (2) they were difficult to apply to local epidemics with heterogeneity across district-level administrative units; and (3) the MOT model was highly sensitive to input parameters, many of which required extraction from non-regional sources. We developed an alternative decision-tree framework for HIV epidemic appraisals, based on a qualitative understanding of epidemiologic drivers, and demonstrated its applicability in India. The alternative framework offered a logical algorithm to characterize epidemics; it required minimal but key data. Conclusions Traditional appraisals that utilize the distribution of prevalent and incident HIV infections in the short-term could misguide prevention priorities and potentially impede efforts to halt the trajectory of the HIV epidemic. An approach that characterizes local transmission dynamics provides a potentially more effective tool with which policy makers can design intervention programmes. PMID:22396756