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

Qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity

NASA Astrophysics Data System (ADS)

Hattaf, Khalid; Mahrouf, Marouane; Adnani, Jihad; Yousfi, Noura

2018-01-01

In this paper, we propose a stochastic delayed epidemic model with specific functional response. The time delay represents temporary immunity period, i.e., time from recovery to becoming susceptible again. We first show that the proposed model is mathematically and biologically well-posed. Moreover, the extinction of the disease and the persistence in the mean are established in the terms of a threshold value R0S which is smaller than the basic reproduction number R0 of the corresponding deterministic system.

Modelling the dynamics of scarlet fever epidemics in the 19th century.

PubMed

Duncan, S R; Scott, S; Duncan, C J

2000-01-01

Annual deaths from scarlet fever in Liverpool, UK during 1848-1900 have been used as a model system for studying the historical dynamics of the epidemics. Mathematical models are developed which include the growth of the population and the death rate from scarlet fever. Time-series analysis of the results shows that there were two distinct phases to the disease (i) 1848-1880: regular epidemics (wavelength = 3.7 years) consistent with the system being driven by an oscillation in the transmission coefficient (deltabeta) at its resonant frequency, probably associated with dry conditions in winter (ii) 1880-1900: an undriven SEIR system with a falling endemic level and decaying epidemics. This period was associated with improved nutritive levels. There is also evidence from time-series analysis that raised wheat prices in pregnancy caused increased susceptibility in the subsequent children. The pattern of epidemics and the demographic characteristics of the population can be replicated in the modelling which provides insights into the detailed epidemiology of scarlet fever in this community in the 19th century.

Seven challenges for metapopulation models of epidemics, including households models.

PubMed

Ball, Frank; Britton, Tom; House, Thomas; Isham, Valerie; Mollison, Denis; Pellis, Lorenzo; Scalia Tomba, Gianpaolo

2015-03-01

This paper considers metapopulation models in the general sense, i.e. where the population is partitioned into sub-populations (groups, patches,...), irrespective of the biological interpretation they have, e.g. spatially segregated large sub-populations, small households or hosts themselves modelled as populations of pathogens. This framework has traditionally provided an attractive approach to incorporating more realistic contact structure into epidemic models, since it often preserves analytic tractability (in stochastic as well as deterministic models) but also captures the most salient structural inhomogeneity in contact patterns in many applied contexts. Despite the progress that has been made in both the theory and application of such metapopulation models, we present here several major challenges that remain for future work, focusing on models that, in contrast to agent-based ones, are amenable to mathematical analysis. The challenges range from clarifying the usefulness of systems of weakly-coupled large sub-populations in modelling the spread of specific diseases to developing a theory for endemic models with household structure. They include also developing inferential methods for data on the emerging phase of epidemics, extending metapopulation models to more complex forms of human social structure, developing metapopulation models to reflect spatial population structure, developing computationally efficient methods for calculating key epidemiological model quantities, and integrating within- and between-host dynamics in models. Copyright © 2014 The Authors. Published by Elsevier B.V. All rights reserved.

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.

[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.

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

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.

A pandemic of the poor: social disadvantage and the U.S. HIV epidemic

PubMed Central

Pellowski, Jennifer A.; Kalichman, Seth C.; Matthews, Karen A.; Adler, Nancy

2013-01-01

The U.S. HIV epidemic has evolved over the past 30 years and is now concentrated in socially marginalized and disenfranchised communities. The health disparities in this epidemic are striking, with most HIV infections occurring in sexual minorities and communities of color. While widely recognized, the health disparities in HIV and AIDS are not often discussed. In this paper, we examine the factors underlying health disparities in the U.S. HIV epidemic. We first discuss the interlocking relationships between biological, social, and behavioral factors that drive HIV epidemics. Guided by a well-established conceptual model of health disparities, we then describe the social positions of those most affected by HIV and AIDS, particularly racial and gender groups. Structural and economic conditions including environmental resources, constraints, access to care, and psychosocial influences are examined in relation to HIV disease trajectories. Greater attention to contextual factors and co-morbidities is needed to reduce the health disparities in HIV infection. PMID:23688088

A pandemic of the poor: social disadvantage and the U.S. HIV epidemic.

PubMed

Pellowski, Jennifer A; Kalichman, Seth C; Matthews, Karen A; Adler, Nancy

2013-01-01

The U.S. HIV/AIDS epidemic has evolved over the past 30 years and is now concentrated in socially marginalized and disenfranchised communities. The health disparities in this epidemic are striking, with most HIV infections occurring in sexual minorities and communities of color. While widely recognized, the health disparities in HIV and AIDS are not often discussed. In this article, we examine the factors underlying health disparities in the U.S. HIV epidemic. We first discuss the interlocking relationships between biological, social, and behavioral factors that drive HIV/AIDS epidemics. Guided by a well-established conceptual model of health disparities, we then describe the social positions of those most affected by HIV and AIDS, particularly racial and gender groups. Structural and economic conditions-including environmental resources, constraints, access to care, and psychosocial influences-are examined in relation to HIV disease trajectories. Greater attention to contextual factors and comorbidities is needed to reduce the health disparities in HIV/AIDS.

Mechanistic movement models to understand epidemic spread.

PubMed

Fofana, Abdou Moutalab; Hurford, Amy

2017-05-05

An overlooked aspect of disease ecology is considering how and why animals come into contact with one and other resulting in disease transmission. Mathematical models of disease spread frequently assume mass-action transmission, justified by stating that susceptible and infectious hosts mix readily, and foregoing any detailed description of host movement. Numerous recent studies have recorded, analysed and modelled animal movement. These movement models describe how animals move with respect to resources, conspecifics and previous movement directions and have been used to understand the conditions for the occurrence and the spread of infectious diseases when hosts perform a type of movement. Here, we summarize the effect of the different types of movement on the threshold conditions for disease spread. We identify gaps in the literature and suggest several promising directions for future research. The mechanistic inclusion of movement in epidemic models may be beneficial for the following two reasons. Firstly, the estimation of the transmission coefficient in an epidemic model is possible because animal movement data can be used to estimate the rate of contacts between conspecifics. Secondly, unsuccessful transmission events, where a susceptible host contacts an infectious host but does not become infected can be quantified. Following an outbreak, this enables disease ecologists to identify 'near misses' and to explore possible alternative epidemic outcomes given shifts in ecological or immunological parameters.This article is part of the themed issue 'Opening the black box: re-examining the ecology and evolution of parasite transmission'. © 2017 The Author(s).

A Dirichlet process model for classifying and forecasting epidemic curves

PubMed Central

2014-01-01

Background A forecast can be defined as an endeavor to quantitatively estimate a future event or probabilities assigned to a future occurrence. Forecasting stochastic processes such as epidemics is challenging since there are several biological, behavioral, and environmental factors that influence the number of cases observed at each point during an epidemic. However, accurate forecasts of epidemics would impact timely and effective implementation of public health interventions. In this study, we introduce a Dirichlet process (DP) model for classifying and forecasting influenza epidemic curves. Methods The DP model is a nonparametric Bayesian approach that enables the matching of current influenza activity to simulated and historical patterns, identifies epidemic curves different from those observed in the past and enables prediction of the expected epidemic peak time. The method was validated using simulated influenza epidemics from an individual-based model and the accuracy was compared to that of the tree-based classification technique, Random Forest (RF), which has been shown to achieve high accuracy in the early prediction of epidemic curves using a classification approach. We also applied the method to forecasting influenza outbreaks in the United States from 1997–2013 using influenza-like illness (ILI) data from the Centers for Disease Control and Prevention (CDC). Results We made the following observations. First, the DP model performed as well as RF in identifying several of the simulated epidemics. Second, the DP model correctly forecasted the peak time several days in advance for most of the simulated epidemics. Third, the accuracy of identifying epidemics different from those already observed improved with additional data, as expected. Fourth, both methods correctly classified epidemics with higher reproduction numbers (R) with a higher accuracy compared to epidemics with lower R values. Lastly, in the classification of seasonal influenza epidemics

A Dirichlet process model for classifying and forecasting epidemic curves.

PubMed

Nsoesie, Elaine O; Leman, Scotland C; Marathe, Madhav V

2014-01-09

A forecast can be defined as an endeavor to quantitatively estimate a future event or probabilities assigned to a future occurrence. Forecasting stochastic processes such as epidemics is challenging since there are several biological, behavioral, and environmental factors that influence the number of cases observed at each point during an epidemic. However, accurate forecasts of epidemics would impact timely and effective implementation of public health interventions. In this study, we introduce a Dirichlet process (DP) model for classifying and forecasting influenza epidemic curves. The DP model is a nonparametric Bayesian approach that enables the matching of current influenza activity to simulated and historical patterns, identifies epidemic curves different from those observed in the past and enables prediction of the expected epidemic peak time. The method was validated using simulated influenza epidemics from an individual-based model and the accuracy was compared to that of the tree-based classification technique, Random Forest (RF), which has been shown to achieve high accuracy in the early prediction of epidemic curves using a classification approach. We also applied the method to forecasting influenza outbreaks in the United States from 1997-2013 using influenza-like illness (ILI) data from the Centers for Disease Control and Prevention (CDC). We made the following observations. First, the DP model performed as well as RF in identifying several of the simulated epidemics. Second, the DP model correctly forecasted the peak time several days in advance for most of the simulated epidemics. Third, the accuracy of identifying epidemics different from those already observed improved with additional data, as expected. Fourth, both methods correctly classified epidemics with higher reproduction numbers (R) with a higher accuracy compared to epidemics with lower R values. Lastly, in the classification of seasonal influenza epidemics based on ILI data from the CDC

An online spatio-temporal prediction model for dengue fever epidemic in Kaohsiung,Taiwan

NASA Astrophysics Data System (ADS)

Cheng, Ming-Hung; Yu, Hwa-Lung; Angulo, Jose; Christakos, George

2013-04-01

Dengue Fever (DF) is one of the most serious vector-borne infectious diseases in tropical and subtropical areas. DF epidemics occur in Taiwan annually especially during summer and fall seasons. Kaohsiung city has been one of the major DF hotspots in decades. The emergence and re-emergence of the DF epidemic is complex and can be influenced by various factors including space-time dynamics of human and vector populations and virus serotypes as well as the associated uncertainties. This study integrates a stochastic space-time "Susceptible-Infected-Recovered" model under Bayesian maximum entropy framework (BME-SIR) to perform real-time prediction of disease diffusion across space-time. The proposed model is applied for spatiotemporal prediction of the DF epidemic at Kaohsiung city during 2002 when the historical series of high DF cases was recorded. The online prediction by BME-SIR model updates the parameters of SIR model and infected cases across districts over time. Results show that the proposed model is rigorous to initial guess of unknown model parameters, i.e. transmission and recovery rates, which can depend upon the virus serotypes and various human interventions. This study shows that spatial diffusion can be well characterized by BME-SIR model, especially at the district surrounding the disease outbreak locations. The prediction performance at DF hotspots, i.e. Cianjhen and Sanmin, can be degraded due to the implementation of various disease control strategies during the epidemics. The proposed online disease prediction BME-SIR model can provide the governmental agency with a valuable reference to timely identify, control, and efficiently prevent DF spread across space-time.

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.

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.

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.

A stochastic SIS epidemic model with vaccination

NASA Astrophysics Data System (ADS)

Cao, Boqiang; Shan, Meijing; Zhang, Qimin; Wang, Weiming

2017-11-01

In this paper, we investigate the basic features of an SIS type infectious disease model with varying population size and vaccinations in presence of environment noise. By applying the Markov semigroup theory, we propose a stochastic reproduction number R0s which can be seen as a threshold parameter to utilize in identifying the stochastic extinction and persistence: If R0s < 1, under some mild extra conditions, there exists a disease-free absorbing set for the stochastic epidemic model, which implies that disease dies out with probability one; while if R0s > 1, under some mild extra conditions, the SDE model has an endemic stationary distribution which results in the stochastic persistence of the infectious disease. The most interesting finding is that large environmental noise can suppress the outbreak of the disease.

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.

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.

A Simulation Study Comparing Epidemic Dynamics on Exponential Random Graph and Edge-Triangle Configuration Type Contact Network Models

PubMed Central

Rolls, David A.; Wang, Peng; McBryde, Emma; Pattison, Philippa; Robins, Garry

2015-01-01

We compare two broad types of empirically grounded random network models in terms of their abilities to capture both network features and simulated Susceptible-Infected-Recovered (SIR) epidemic dynamics. The types of network models are exponential random graph models (ERGMs) and extensions of the configuration model. We use three kinds of empirical contact networks, chosen to provide both variety and realistic patterns of human contact: a highly clustered network, a bipartite network and a snowball sampled network of a “hidden population”. In the case of the snowball sampled network we present a novel method for fitting an edge-triangle model. In our results, ERGMs consistently capture clustering as well or better than configuration-type models, but the latter models better capture the node degree distribution. Despite the additional computational requirements to fit ERGMs to empirical networks, the use of ERGMs provides only a slight improvement in the ability of the models to recreate epidemic features of the empirical network in simulated SIR epidemics. Generally, SIR epidemic results from using configuration-type models fall between those from a random network model (i.e., an Erdős-Rényi model) and an ERGM. The addition of subgraphs of size four to edge-triangle type models does improve agreement with the empirical network for smaller densities in clustered networks. Additional subgraphs do not make a noticeable difference in our example, although we would expect the ability to model cliques to be helpful for contact networks exhibiting household structure. PMID:26555701

Simple model of epidemics with pathogen mutation.

PubMed

Girvan, Michelle; Callaway, Duncan S; Newman, M E J; Strogatz, Steven H

2002-03-01

We study how the interplay between the memory immune response and pathogen mutation affects epidemic dynamics in two related models. The first explicitly models pathogen mutation and individual memory immune responses, with contacted individuals becoming infected only if they are exposed to strains that are significantly different from other strains in their memory repertoire. The second model is a reduction of the first to a system of difference equations. In this case, individuals spend a fixed amount of time in a generalized immune class. In both models, we observe four fundamentally different types of behavior, depending on parameters: (1) pathogen extinction due to lack of contact between individuals; (2) endemic infection; (3) periodic epidemic outbreaks; and (4) one or more outbreaks followed by extinction of the epidemic due to extremely low minima in the oscillations. We analyze both models to determine the location of each transition. Our main result is that pathogens in highly connected populations must mutate rapidly in order to remain viable.

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.

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

Modeling the spatial spread of infectious diseases: the GLobal Epidemic and Mobility computational model

PubMed Central

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

2010-01-01

Here we present the Global Epidemic and Mobility (GLEaM) model that integrates sociodemographic and population mobility data in a spatially structured stochastic disease approach to simulate the spread of epidemics at the worldwide scale. We discuss the flexible structure of the model that is open to the inclusion of different disease structures and local intervention policies. This makes GLEaM suitable for the computational modeling and anticipation of the spatio-temporal patterns of global epidemic spreading, the understanding of historical epidemics, the assessment of the role of human mobility in shaping global epidemics, and the analysis of mitigation and containment scenarios. PMID:21415939

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.

Deriving a model for influenza epidemics from historical data.

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

Ray, Jaideep; Lefantzi, Sophia

In this report we describe how we create a model for influenza epidemics from historical data collected from both civilian and military societies. We derive the model when the population of the society is unknown but the size of the epidemic is known. Our interest lies in estimating a time-dependent infection rate to within a multiplicative constant. The model form fitted is chosen for its similarity to published models for HIV and plague, enabling application of Bayesian techniques to discriminate among infectious agents during an emerging epidemic. We have developed models for the progression of influenza in human populations. Themore » model is framed as a integral, and predicts the number of people who exhibit symptoms and seek care over a given time-period. The start and end of the time period form the limits of integration. The disease progression model, in turn, contains parameterized models for the incubation period and a time-dependent infection rate. The incubation period model is obtained from literature, and the parameters of the infection rate are fitted from historical data including both military and civilian populations. The calibrated infection rate models display a marked difference in which the 1918 Spanish Influenza pandemic differed from the influenza seasons in the US between 2001-2008 and the progression of H1N1 in Catalunya, Spain. The data for the 1918 pandemic was obtained from military populations, while the rest are country-wide or province-wide data from the twenty-first century. We see that the initial growth of infection in all cases were about the same; however, military populations were able to control the epidemic much faster i.e., the decay of the infection-rate curve is much higher. It is not clear whether this was because of the much higher level of organization present in a military society or the seriousness with which the 1918 pandemic was addressed. Each outbreak to which the influenza model was fitted yields a separate

Epidemic as a natural process.

PubMed

Koivu-Jolma, Mikko; Annila, Arto

2018-05-01

Mathematical epidemiology is a well-recognized discipline to model infectious diseases. It also provides guidance for public health officials to limit outbreaks. Nevertheless, epidemics take societies by surprise every now and then, for example, when the Ebola virus epidemic raged seemingly unrestrained in Western Africa. We provide insight to this capricious character of nature by describing the epidemic as a natural process, i.e., a phenomenon governed by thermodynamics. Our account, based on statistical mechanics of open systems, clarifies that it is impossible to predict accurately epidemic courses because everything depends on everything else. Nonetheless, the thermodynamic theory yields a comprehensive and analytical view of the epidemic. The tenet subsumes various processes in a scale-free manner from the molecular to the societal levels. The holistic view accentuates overarching procedures in arresting and eradicating epidemics. Copyright © 2018 Elsevier Inc. All rights reserved.

A social contagious model of the obesity epidemic

NASA Astrophysics Data System (ADS)

Huang, He; Yan, Zhijun; Chen, Yahong; Liu, Fangyan

2016-11-01

Obesity has been recognized as a global epidemic by WHO, followed by many empirical evidences to prove its infectiousness. However, the inter-person spreading dynamics of obesity are seldom studied. A distinguishing feature of the obesity epidemic is that it is driven by a social contagion process which cannot be perfectly described by the infectious disease models. In this paper, we propose a novel belief decision model based on the famous Dempster-Shafer theory of evidence to model obesity epidemic as the competing spread of two obesity-related behaviors: physical inactivity and physical activity. The transition of health states is described by an SIS model. Results reveal the existence of obesity epidemic threshold, above which obesity is quickly eradicated. When increasing the fading level of information spread, enlarging the clustering of initial obese seeds, or introducing small-world characteristics into the network topology, the threshold is easily met. Social discrimination against the obese people plays completely different roles in two cases: on one hand, when obesity cannot be eradicated, social discrimination can reduce the number of obese people; on the other hand, when obesity is eradicable, social discrimination may instead cause it breaking out.

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.

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 double epidemic model for the SARS propagation

PubMed Central

Ng, Tuen Wai; Turinici, Gabriel; Danchin, Antoine

2003-01-01

Background An epidemic of a Severe Acute Respiratory Syndrome (SARS) caused by a new coronavirus has spread from the Guangdong province to the rest of China and to the world, with a puzzling contagion behavior. It is important both for predicting the future of the present outbreak and for implementing effective prophylactic measures, to identify the causes of this behavior. Results In this report, we show first that the standard Susceptible-Infected-Removed (SIR) model cannot account for the patterns observed in various regions where the disease spread. We develop a model involving two superimposed epidemics to study the recent spread of the SARS in Hong Kong and in the region. We explore the situation where these epidemics may be caused either by a virus and one or several mutants that changed its tropism, or by two unrelated viruses. This has important consequences for the future: the innocuous epidemic might still be there and generate, from time to time, variants that would have properties similar to those of SARS. Conclusion We find that, in order to reconcile the existing data and the spread of the disease, it is convenient to suggest that a first milder outbreak protected against the SARS. Regions that had not seen the first epidemic, or that were affected simultaneously with the SARS suffered much more, with a very high percentage of persons affected. We also find regions where the data appear to be inconsistent, suggesting that they are incomplete or do not reflect an appropriate identification of SARS patients. Finally, we could, within the framework of the model, fix limits to the future development of the epidemic, allowing us to identify landmarks that may be useful to set up a monitoring system to follow the evolution of the epidemic. The model also suggests that there might exist a SARS precursor in a large reservoir, prompting for implementation of precautionary measures when the weather cools down. PMID:12964944

Is there a cannabis epidemic model? Evidence from France, Germany and USA.

PubMed

Legleye, Stephane; Piontek, Daniela; Pampel, Fred; Goffette, Céline; Khlat, Myriam; Kraus, Ludwig

2014-11-01

Cannabis is the most popular illicit drug in the world, but the process of its diffusion through the population has rarely been studied. The unfolding of the tobacco epidemic was accompanied by a shift in the educational gradient of users across generations. As a consequence, cannabis may show the same pattern of widening social inequalities. We test the diffusion hypotheses that a positive value in older cohorts - the more educated experimenting more - shifts to a negative one in younger cohorts - the more educated experimenting less, first for males and then females. Three nationwide subsamples (18-64 years old) of representative surveys conducted in France (n=21,818), Germany (n=7887) and USA (n=37,115) in 2009-2010 recorded age at cannabis experimentation (i.e., first use), educational level, gender, and age. Cumulative prevalence of experimentation was plotted for three retrospective cohorts (50-64, 35-49, 18-34 years old at data collection) and multivariate time-discrete logistic regression was computed by gender and generation to model age at experimentation adjusted on age at data collection and educational level. This latter was measured according to four categories derived from the International Standard Classification of Education (ISCED) and a relative (rather than absolute) index of education. The findings demonstrate a consistent pattern of evolution of the prevalence, gender ratio and educational gradient across generations and countries that support the hypothesis of an "epidemic" of cannabis experimentation that mimics the epidemic of tobacco. We provide evidence for a cannabis epidemic model similar to the tobacco epidemic model. In the absence of clues regarding the future of cannabis use, our findings demonstrate that the gender gap is decreasing and, based on the epidemic model, suggest that we may expect widening social inequalities in cannabis experimentation if cannabis use decreases in the future. Copyright © 2014 The Authors. Published by

A lattice-based model of rotavirus epidemics

NASA Astrophysics Data System (ADS)

Lara-Sagahón, A.; Govezensky, T.; Méndez-Sánchez, R. A.; José, M. V.

2006-01-01

The cyclic recurrence of childhood rotavirus epidemics in unvaccinated populations provides one of the best documented phenomena in population dynamics and can become a paradigm for epidemic studies. Herein we analyse the monthly incidence of rotavirus infection from the city of Melbourne, Australia during 1976-2003. We show that there is an inverse nonlinear relationship of the cumulative distribution of the number of cases per month in a log-log plot. It is also shown that the rate of transmission of rotavirus infection follows a symmetric distribution centered on zero. A wavelet phase analysis of rotavirus epidemics is also carried out. We test the hypothesis that rotavirus dynamics could be a realization of a forest-fire model with sparks and with immune trees. Some statistical properties of this model turn out to be similar to the above results of actual rotavirus data.

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.

Computational algebraic geometry of epidemic models

NASA Astrophysics Data System (ADS)

Rodríguez Vega, Martín.

2014-06-01

Computational Algebraic Geometry is applied to the analysis of various epidemic models for Schistosomiasis and Dengue, both, for the case without control measures and for the case where control measures are applied. The models were analyzed using the mathematical software Maple. Explicitly the analysis is performed using Groebner basis, Hilbert dimension and Hilbert polynomials. These computational tools are included automatically in Maple. Each of these models is represented by a system of ordinary differential equations, and for each model the basic reproductive number (R0) is calculated. The effects of the control measures are observed by the changes in the algebraic structure of R0, the changes in Groebner basis, the changes in Hilbert dimension, and the changes in Hilbert polynomials. It is hoped that the results obtained in this paper become of importance for designing control measures against the epidemic diseases described. For future researches it is proposed the use of algebraic epidemiology to analyze models for airborne and waterborne diseases.

From epidemics to information propagation: Striking differences in structurally similar adaptive network models

NASA Astrophysics Data System (ADS)

Trajanovski, Stojan; Guo, Dongchao; Van Mieghem, Piet

2015-09-01

The continuous-time adaptive susceptible-infected-susceptible (ASIS) epidemic model and the adaptive information diffusion (AID) model are two adaptive spreading processes on networks, in which a link in the network changes depending on the infectious state of its end nodes, but in opposite ways: (i) In the ASIS model a link is removed between two nodes if exactly one of the nodes is infected to suppress the epidemic, while a link is created in the AID model to speed up the information diffusion; (ii) a link is created between two susceptible nodes in the ASIS model to strengthen the healthy part of the network, while a link is broken in the AID model due to the lack of interest in informationless nodes. The ASIS and AID models may be considered as first-order models for cascades in real-world networks. While the ASIS model has been exploited in the literature, we show that the AID model is realistic by obtaining a good fit with Facebook data. Contrary to the common belief and intuition for such similar models, we show that the ASIS and AID models exhibit different but not opposite properties. Most remarkably, a unique metastable state always exists in the ASIS model, while there an hourglass-shaped region of instability in the AID model. Moreover, the epidemic threshold is a linear function in the effective link-breaking rate in the AID model, while it is almost constant but noisy in the AID model.

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.

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.

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.

Modelling the human immunodeficiency virus (HIV) epidemic: A review of the substance and role of models in South Africa

PubMed Central

2018-01-01

We review key mathematical models of the South African human immunodeficiency virus (HIV) epidemic from the early 1990s onwards. In our descriptions, we sometimes differentiate between the concepts of a model world and its mathematical or computational implementation. The model world is the conceptual realm in which we explicitly declare the rules – usually some simplification of ‘real world’ processes as we understand them. Computing details of informative scenarios in these model worlds is a task requiring specialist knowledge, but all other aspects of the modelling process, from describing the model world to identifying the scenarios and interpreting model outputs, should be understandable to anyone with an interest in the epidemic. PMID:29568647

SIS and SIR epidemic models under virtual dispersal

PubMed Central

Bichara, Derdei; Kang, Yun; Castillo-Chavez, Carlos; Horan, Richard; Perrings, Charles

2015-01-01

We develop a multi-group epidemic framework via virtual dispersal where the risk of infection is a function of the residence time and local environmental risk. This novel approach eliminates the need to define and measure contact rates that are used in the traditional multi-group epidemic models with heterogeneous mixing. We apply this approach to a general n-patch SIS model whose basic reproduction number R0 is computed as a function of a patch residence-times matrix ℙ. Our analysis implies that the resulting n-patch SIS model has robust dynamics when patches are strongly connected: there is a unique globally stable endemic equilibrium when R0 > 1 while the disease free equilibrium is globally stable when R0 ≤ 1. Our further analysis indicates that the dispersal behavior described by the residence-times matrix ℙ has profound effects on the disease dynamics at the single patch level with consequences that proper dispersal behavior along with the local environmental risk can either promote or eliminate the endemic in particular patches. Our work highlights the impact of residence times matrix if the patches are not strongly connected. Our framework can be generalized in other endemic and disease outbreak models. As an illustration, we apply our framework to a two-patch SIR single outbreak epidemic model where the process of disease invasion is connected to the final epidemic size relationship. We also explore the impact of disease prevalence driven decision using a phenomenological modeling approach in order to contrast the role of constant versus state dependent ℙ on disease dynamics. PMID:26489419

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.

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.

Epidemic typhoid in Chile: analysis by molecular and conventional methods of Salmonella typhi strain diversity in epidemic (1977 and 1981) and nonepidemic (1990) years.

PubMed

Fica, A E; Prat-Miranda, S; Fernandez-Ricci, A; D'Ottone, K; Cabello, F C

1996-07-01

From 1977 to 1986, Chile experienced an important typhoid fever epidemic, despite statistics that indicated apparently improving levels of sanitation of drinking water and sewage disposal. The lack of antibiotic resistance among the Salmonella typhi strains isolated during this period, the mild clinical presentation of the disease, and the initially low level of efficacy of the S. typhi Ty21a vaccine in the population exposed to the epidemic suggested that this epidemic might have resulted from the dissemination of S. typhi strains with unique characteristics. To investigate this hypothesis, we used conventional methods (bacteriophage typing and biotyping) and molecular methods (restriction fragment length polymorphism analysis, ribotyping, IS200 typing, and PCR amplification of the fliC-d gene) to study a population of 149 S. typhi isolates during 1977, 1981, and 1990, the years that included periods with low (when the disease was endemic) and high (when the disease was epidemic) morbidities. Our results indicate that these S. typhi isolates in Chile represent a number of highly diverse variants of the clone of S. typhi with a worldwide distribution described by Selander et al. (R. K. Selander, P. Beltran, N.H. Smith, R. Helmuth, F.A. Rubin, D.J. Kopecko, K. Ferris, B.D. Tall, A. Cravioto, and J.M. Musser, Infect. Immun. 58:2262-2275, 1990). For example, we detected 26 PstI and 10 ClaI ribotypes among 47 and 16 S. typhi strains belonging to this clone, respectively. These results suggest that the Chilean epidemic was probably produced by multiple sources of infection because of deficient sanitary conditions. These findings illustrate the usefulness of molecular methods for characterizing the potential causes of the typhoid epidemics and the possible routes of transmission of S. typhi strains in typhoid epidemics.

Epidemic typhoid in Chile: analysis by molecular and conventional methods of Salmonella typhi strain diversity in epidemic (1977 and 1981) and nonepidemic (1990) years.

PubMed Central

Fica, A E; Prat-Miranda, S; Fernandez-Ricci, A; D'Ottone, K; Cabello, F C

1996-01-01

From 1977 to 1986, Chile experienced an important typhoid fever epidemic, despite statistics that indicated apparently improving levels of sanitation of drinking water and sewage disposal. The lack of antibiotic resistance among the Salmonella typhi strains isolated during this period, the mild clinical presentation of the disease, and the initially low level of efficacy of the S. typhi Ty21a vaccine in the population exposed to the epidemic suggested that this epidemic might have resulted from the dissemination of S. typhi strains with unique characteristics. To investigate this hypothesis, we used conventional methods (bacteriophage typing and biotyping) and molecular methods (restriction fragment length polymorphism analysis, ribotyping, IS200 typing, and PCR amplification of the fliC-d gene) to study a population of 149 S. typhi isolates during 1977, 1981, and 1990, the years that included periods with low (when the disease was endemic) and high (when the disease was epidemic) morbidities. Our results indicate that these S. typhi isolates in Chile represent a number of highly diverse variants of the clone of S. typhi with a worldwide distribution described by Selander et al. (R. K. Selander, P. Beltran, N.H. Smith, R. Helmuth, F.A. Rubin, D.J. Kopecko, K. Ferris, B.D. Tall, A. Cravioto, and J.M. Musser, Infect. Immun. 58:2262-2275, 1990). For example, we detected 26 PstI and 10 ClaI ribotypes among 47 and 16 S. typhi strains belonging to this clone, respectively. These results suggest that the Chilean epidemic was probably produced by multiple sources of infection because of deficient sanitary conditions. These findings illustrate the usefulness of molecular methods for characterizing the potential causes of the typhoid epidemics and the possible routes of transmission of S. typhi strains in typhoid epidemics. PMID:8784573

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.

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.

Understanding impacts of climatic extremes on diarrheal disease epidemics: Insights from mechanistic disease propagation models

NASA Astrophysics Data System (ADS)

Jutla, A.; Akanda, A. S.; Colwell, R. R.

2013-12-01

An epidemic outbreak of diarrheal diseases (primarily cholera) in Haiti in 2010 is a reminder that our understanding on disease triggers, transmission and spreading mechanisms is incomplete. Cholera can occur in two forms - epidemic (defined as sudden outbreak in a historically disease free region) and endemic (recurrence and persistence of the disease for several consecutive years). Examples of countries with epidemic cholera include Pakistan (2008), Congo (2008), and most recently Haiti (2010). A significant difference between endemic and epidemic regions is the mortality rate, i.e., 1% or lower in an endemic regions versus 3-7% during recent epidemic outbreaks. A fundamentally transformational approach - a warning system with several months prediction lead time - is needed to prevent disease outbreak and minimize its impact on population. Lack of information on spatial and temporal variability of disease incidence as well as transmission in human population continues to be significant challenge in the development of early-warning systems for cholera. Using satellite data on regional hydroclimatic processes, water and sanitation infrastructure indices, and biological pathogen growth information, here we present a Simple, Mechanistic, Adaptive, Remote sensing based Regional Transmission or SMART model to (i) identify regions of potential cholera outbreaks and (ii) quantify mechanism of spread of the disease in previously disease free region. Our results indicate that epidemic regions are located near regional rivers and are characterized by sporadic outbreaks, which are likely to be initiated during episodes of prevailing warm air temperature with low river flows, creating favorable environmental conditions for the growth of cholera bacteria. Heavy rainfall, through inundation or breakdown of sanitary infrastructure, accelerates interaction between contaminated water and human activities, resulting in an epidemic. We discuss the above findings in light of

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.

Identifying Cost-Effective Dynamic Policies to Control Epidemics

PubMed Central

Yaesoubi, Reza; Cohen, Ted

2016-01-01

We describe a mathematical decision model for identifying dynamic health policies for controlling epidemics. These dynamic policies aim to select the best current intervention based on accumulating epidemic data and the availability of resources at each decision point. We propose an algorithm to approximate dynamic policies that optimize the population’s net health benefit, a performance measure which accounts for both health and monetary outcomes. We further illustrate how dynamic policies can be defined and optimized for the control of a novel viral pathogen, where a policy maker must decide (i) when to employ or lift a transmission-reducing intervention (e.g. school closure) and (ii) how to prioritize population members for vaccination when a limited quantity of vaccines first become available. Within the context of this application, we demonstrate that dynamic policies can produce higher net health benefit than more commonly described static policies that specify a pre-determined sequence of interventions to employ throughout epidemics. PMID:27449759

On the predictive ability of mechanistic models for the Haitian cholera epidemic.

PubMed

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

2015-03-06

Predictive models of epidemic cholera need to resolve at suitable aggregation levels spatial data pertaining to local communities, epidemiological records, hydrologic drivers, waterways, patterns of human mobility and proxies of exposure rates. We address the above issue in a formal model comparison framework and provide a quantitative assessment of the explanatory and predictive abilities of various model settings with different spatial aggregation levels and coupling mechanisms. Reference is made to records of the recent Haiti cholera epidemics. Our intensive computations and objective model comparisons show that spatially explicit models accounting for spatial connections have better explanatory power than spatially disconnected ones for short-to-intermediate calibration windows, while parsimonious, spatially disconnected models perform better with long training sets. On average, spatially connected models show better predictive ability than disconnected ones. We suggest limits and validity of the various approaches and discuss the pathway towards the development of case-specific predictive tools in the context of emergency management. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

A Weighted Configuration Model and Inhomogeneous Epidemics

NASA Astrophysics Data System (ADS)

Britton, Tom; Deijfen, Maria; Liljeros, Fredrik

2011-12-01

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An expression for the threshold for the appearance of a giant component in the resulting graph is derived using results on multi-type branching processes. The same technique also gives an expression for the basic reproduction number for an epidemic on the graph where the probability that a certain edge is used for transmission is a function of the edge weight (reflecting how closely `connected' the corresponding vertices are). It is demonstrated that, if vertices with large degree tend to have large (small) weights on their edges and if the transmission probability increases with the edge weight, then it is easier (harder) for the epidemic to take off compared to a randomized epidemic with the same degree and weight distribution. A recipe for calculating the probability of a large outbreak in the epidemic and the size of such an outbreak is also given. Finally, the model is fitted to three empirical weighted networks of importance for the spread of contagious diseases and it is shown that R 0 can be substantially over- or underestimated if the correlation between degree and weight is not taken into account.

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.

Climate-Based Models for Understanding and Forecasting Dengue Epidemics

PubMed Central

Descloux, Elodie; Mangeas, Morgan; Menkes, Christophe Eugène; Lengaigne, Matthieu; Leroy, Anne; Tehei, Temaui; Guillaumot, Laurent; Teurlai, Magali; Gourinat, Ann-Claire; Benzler, Justus; Pfannstiel, Anne; Grangeon, Jean-Paul; Degallier, Nicolas; De Lamballerie, Xavier

2012-01-01

Background Dengue dynamics are driven by complex interactions between human-hosts, mosquito-vectors and viruses that are influenced by environmental and climatic factors. The objectives of this study were to analyze and model the relationships between climate, Aedes aegypti vectors and dengue outbreaks in Noumea (New Caledonia), and to provide an early warning system. Methodology/Principal Findings Epidemiological and meteorological data were analyzed from 1971 to 2010 in Noumea. Entomological surveillance indices were available from March 2000 to December 2009. During epidemic years, the distribution of dengue cases was highly seasonal. The epidemic peak (March–April) lagged the warmest temperature by 1–2 months and was in phase with maximum precipitations, relative humidity and entomological indices. Significant inter-annual correlations were observed between the risk of outbreak and summertime temperature, precipitations or relative humidity but not ENSO. Climate-based multivariate non-linear models were developed to estimate the yearly risk of dengue outbreak in Noumea. The best explicative meteorological variables were the number of days with maximal temperature exceeding 32°C during January–February–March and the number of days with maximal relative humidity exceeding 95% during January. The best predictive variables were the maximal temperature in December and maximal relative humidity during October–November–December of the previous year. For a probability of dengue outbreak above 65% in leave-one-out cross validation, the explicative model predicted 94% of the epidemic years and 79% of the non epidemic years, and the predictive model 79% and 65%, respectively. Conclusions/Significance The epidemic dynamics of dengue in Noumea were essentially driven by climate during the last forty years. Specific conditions based on maximal temperature and relative humidity thresholds were determinant in outbreaks occurrence. Their persistence was also

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.

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.

Travelling Wave Solutions in Multigroup Age-Structured Epidemic Models

NASA Astrophysics Data System (ADS)

Ducrot, Arnaut; Magal, Pierre; Ruan, Shigui

2010-01-01

Age-structured epidemic models have been used to describe either the age of individuals or the age of infection of certain diseases and to determine how these characteristics affect the outcomes and consequences of epidemiological processes. Most results on age-structured epidemic models focus on the existence, uniqueness, and convergence to disease equilibria of solutions. In this paper we investigate the existence of travelling wave solutions in a deterministic age-structured model describing the circulation of a disease within a population of multigroups. Individuals of each group are able to move with a random walk which is modelled by the classical Fickian diffusion and are classified into two subclasses, susceptible and infective. A susceptible individual in a given group can be crisscross infected by direct contact with infective individuals of possibly any group. This process of transmission can depend upon the age of the disease of infected individuals. The goal of this paper is to provide sufficient conditions that ensure the existence of travelling wave solutions for the age-structured epidemic model. The case of two population groups is numerically investigated which applies to the crisscross transmission of feline immunodeficiency virus (FIV) and some sexual transmission diseases.

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.

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.

Reconstructing the 2003/2004 H3N2 influenza epidemic in Switzerland with a spatially explicit, individual-based model

PubMed Central

2011-01-01

Background Simulation models of influenza spread play an important role for pandemic preparedness. However, as the world has not faced a severe pandemic for decades, except the rather mild H1N1 one in 2009, pandemic influenza models are inherently hypothetical and validation is, thus, difficult. We aim at reconstructing a recent seasonal influenza epidemic that occurred in Switzerland and deem this to be a promising validation strategy for models of influenza spread. Methods We present a spatially explicit, individual-based simulation model of influenza spread. The simulation model bases upon (i) simulated human travel data, (ii) data on human contact patterns and (iii) empirical knowledge on the epidemiology of influenza. For model validation we compare the simulation outcomes with empirical knowledge regarding (i) the shape of the epidemic curve, overall infection rate and reproduction number, (ii) age-dependent infection rates and time of infection, (iii) spatial patterns. Results The simulation model is capable of reproducing the shape of the 2003/2004 H3N2 epidemic curve of Switzerland and generates an overall infection rate (14.9 percent) and reproduction numbers (between 1.2 and 1.3), which are realistic for seasonal influenza epidemics. Age and spatial patterns observed in empirical data are also reflected by the model: Highest infection rates are in children between 5 and 14 and the disease spreads along the main transport axes from west to east. Conclusions We show that finding evidence for the validity of simulation models of influenza spread by challenging them with seasonal influenza outbreak data is possible and promising. Simulation models for pandemic spread gain more credibility if they are able to reproduce seasonal influenza outbreaks. For more robust modelling of seasonal influenza, serological data complementing sentinel information would be beneficial. PMID:21554680

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.

A Simple Model for a SARS Epidemic

ERIC Educational Resources Information Center

Ang, Keng Cheng

2004-01-01

In this paper, we examine the use of an ordinary differential equation in modelling the SARS outbreak in Singapore. The model provides an excellent example of using mathematics in a real life situation. The mathematical concepts involved are accessible to students with A level Mathematics backgrounds. Data for the SARS epidemic in Singapore are…

How the contagion at links influences epidemic spreading

NASA Astrophysics Data System (ADS)

Ruan, Zhongyuan; Tang, Ming; Liu, Zonghua

2013-04-01

The reaction-diffusion (RD) model of epidemic spreading generally assume that contagion occurs only at the nodes of network, i.e., the links are used only for migration/diffusion of agents. However, in reality, we observe that contagion occurs also among the travelers staying in the same car, train or plane etc., which consist of the links of network. To reflect the contagious effect of links, we here present a traveling-contagion model where contagion occurs not only at nodes but also at links. Considering that the population density in transportation is generally much larger than that in districts, we introduce different infection rates for the nodes and links, respectively, whose two extreme cases correspond to the type-I and type-II reactions in the RD model [V. Colizza, R. Pastor-Satorras, A. Vespignani, Nat. Phys. 3, 276 (2007)]. Through studying three typical diffusion processes, we reveal both numerically and theoretically that the contagion at links can accelerate significantly the epidemic spreading. This finding is helpful in designing the controlling strategies of epidemic spreading.

Hysteresis loop of nonperiodic outbreaks of recurrent epidemics

NASA Astrophysics Data System (ADS)

Liu, Hengcong; Zheng, Muhua; Wu, Dayu; Wang, Zhenhua; Liu, Jinming; Liu, Zonghua

2016-12-01

Most of the studies on epidemics so far have focused on the growing phase, such as how an epidemic spreads and what are the conditions for an epidemic to break out in a variety of cases. However, we discover from real data that on a large scale, the spread of an epidemic is in fact a recurrent event with distinctive growing and recovering phases, i.e., a hysteresis loop. We show here that the hysteresis loop can be reproduced in epidemic models provided that the infectious rate is adiabatically increased or decreased before the system reaches its stationary state. Two ways to the hysteresis loop are revealed, which is helpful in understanding the mechanics of infections in real evolution. Moreover, a theoretical analysis is presented to explain the mechanism of the hysteresis loop.

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.

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

Epidemic Models for SARS and Measles

ERIC Educational Resources Information Center

Rozema, Edward

2007-01-01

Recent events have led to an increased interest in emerging infectious diseases. This article applies various deterministic models to the SARS epidemic of 2003 and a measles outbreak in the Netherlands in 1999-2000. We take a historical approach beginning with the well-known logistic curve and a lesser-known extension popularized by Pearl and Reed…

Epidemic models for phase transitions: application to a physical gel

NASA Astrophysics Data System (ADS)

Bilge, A. H.; Pekcan, O.; Kara, S.; Ogrenci, A. S.

2017-09-01

Carrageenan gels are characterized by reversible sol-gel and gel-sol transitions under cooling and heating processes and these transitions are approximated by generalized logistic growth curves. We express the transitions of carrageenan-water system, as a representative of reversible physical gels, in terms of a modified Susceptible-Infected-Susceptible epidemic model, as opposed to the Susceptible-Infected-Removed model used to represent the (irreversible) chemical gel formation in the previous work. We locate the gel point Tc of sol-gel and gel-sol transitions and we find that, for the sol-gel transition (cooling), Tc > Tsg (transition temperature), i.e. Tc is earlier in time for all carrageenan contents and moves forward in time and gets closer to Tsg as the carrageenan content increases. For the gel-sol transition (heating), Tc is relatively closer to Tgs; it is greater than Tgs, i.e. later in time for low carrageenan contents and moves backward as carrageenan content increases.

Modelling the spreading rate of controlled communicable epidemics through an entropy-based thermodynamic model

NASA Astrophysics Data System (ADS)

Wang, WenBin; Wu, ZiNiu; Wang, ChunFeng; Hu, RuiFeng

2013-11-01

A model based on a thermodynamic approach is proposed for predicting the dynamics of communicable epidemics assumed to be governed by controlling efforts of multiple scales so that an entropy is associated with the system. All the epidemic details are factored into a single and time-dependent coefficient, the functional form of this coefficient is found through four constraints, including notably the existence of an inflexion point and a maximum. The model is solved to give a log-normal distribution for the spread rate, for which a Shannon entropy can be defined. The only parameter, that characterizes the width of the distribution function, is uniquely determined through maximizing the rate of entropy production. This entropy-based thermodynamic (EBT) model predicts the number of hospitalized cases with a reasonable accuracy for SARS in the year 2003. This EBT model can be of use for potential epidemics such as avian influenza and H7N9 in China.

A Pandemic of the Poor: Social Disadvantage and the U.S. HIV Epidemic

ERIC Educational Resources Information Center

Pellowski, Jennifer A.; Kalichman, Seth C.; Matthews, Karen A.; Adler, Nancy

2013-01-01

The U.S. HIV/AIDS epidemic has evolved over the past 30 years and is now concentrated in socially marginalized and disenfranchised communities. The health disparities in this epidemic are striking, with most HIV infections occurring in sexual minorities and communities of color. While widely recognized, the health disparities in HIV and AIDS are…

An epidemic model to evaluate the homogeneous mixing assumption

NASA Astrophysics Data System (ADS)

Turnes, P. P.; Monteiro, L. H. A.

2014-11-01

Many epidemic models are written in terms of ordinary differential equations (ODE). This approach relies on the homogeneous mixing assumption; that is, the topological structure of the contact network established by the individuals of the host population is not relevant to predict the spread of a pathogen in this population. Here, we propose an epidemic model based on ODE to study the propagation of contagious diseases conferring no immunity. The state variables of this model are the percentages of susceptible individuals, infectious individuals and empty space. We show that this dynamical system can experience transcritical and Hopf bifurcations. Then, we employ this model to evaluate the validity of the homogeneous mixing assumption by using real data related to the transmission of gonorrhea, hepatitis C virus, human immunodeficiency virus, and obesity.

Influenza surveillance in Europe: establishing epidemic thresholds by the Moving Epidemic Method

PubMed Central

Vega, Tomás; Lozano, Jose Eugenio; Meerhoff, Tamara; Snacken, René; Mott, Joshua; Ortiz de Lejarazu, Raul; Nunes, Baltazar

2012-01-01

Please cite this paper as: Vega et al. (2012) Influenza surveillance in Europe: establishing epidemic thresholds by the moving epidemic method. Influenza and Other Respiratory Viruses 7(4), 546–558. Background  Timely influenza surveillance is important to monitor influenza epidemics. Objectives  (i) To calculate the epidemic threshold for influenza‐like illness (ILI) and acute respiratory infections (ARI) in 19 countries, as well as the thresholds for different levels of intensity. (ii) To evaluate the performance of these thresholds. Methods  The moving epidemic method (MEM) has been developed to determine the baseline influenza activity and an epidemic threshold. False alerts, detection lags and timeliness of the detection of epidemics were calculated. The performance was evaluated using a cross‐validation procedure. Results  The overall sensitivity of the MEM threshold was 71·8% and the specificity was 95·5%. The median of the timeliness was 1 week (range: 0–4·5). Conclusions  The method produced a robust and specific signal to detect influenza epidemics. The good balance between the sensitivity and specificity of the epidemic threshold to detect seasonal epidemics and avoid false alerts has advantages for public health purposes. This method may serve as standard to define the start of the annual influenza epidemic in countries in Europe. PMID:22897919

Forecasting Influenza Epidemics in Hong Kong.

PubMed

Yang, Wan; Cowling, Benjamin J; Lau, Eric H Y; Shaman, Jeffrey

2015-07-01

Recent advances in mathematical modeling and inference methodologies have enabled development of systems capable of forecasting seasonal influenza epidemics in temperate regions in real-time. However, in subtropical and tropical regions, influenza epidemics can occur throughout the year, making routine forecast of influenza more challenging. Here we develop and report forecast systems that are able to predict irregular non-seasonal influenza epidemics, using either the ensemble adjustment Kalman filter or a modified particle filter in conjunction with a susceptible-infected-recovered (SIR) model. We applied these model-filter systems to retrospectively forecast influenza epidemics in Hong Kong from January 1998 to December 2013, including the 2009 pandemic. The forecast systems were able to forecast both the peak timing and peak magnitude for 44 epidemics in 16 years caused by individual influenza strains (i.e., seasonal influenza A(H1N1), pandemic A(H1N1), A(H3N2), and B), as well as 19 aggregate epidemics caused by one or more of these influenza strains. Average forecast accuracies were 37% (for both peak timing and magnitude) at 1-3 week leads, and 51% (peak timing) and 50% (peak magnitude) at 0 lead. Forecast accuracy increased as the spread of a given forecast ensemble decreased; the forecast accuracy for peak timing (peak magnitude) increased up to 43% (45%) for H1N1, 93% (89%) for H3N2, and 53% (68%) for influenza B at 1-3 week leads. These findings suggest that accurate forecasts can be made at least 3 weeks in advance for subtropical and tropical regions.

Forecasting Influenza Epidemics in Hong Kong

PubMed Central

Yang, Wan; Cowling, Benjamin J.; Lau, Eric H. Y.; Shaman, Jeffrey

2015-01-01

Recent advances in mathematical modeling and inference methodologies have enabled development of systems capable of forecasting seasonal influenza epidemics in temperate regions in real-time. However, in subtropical and tropical regions, influenza epidemics can occur throughout the year, making routine forecast of influenza more challenging. Here we develop and report forecast systems that are able to predict irregular non-seasonal influenza epidemics, using either the ensemble adjustment Kalman filter or a modified particle filter in conjunction with a susceptible-infected-recovered (SIR) model. We applied these model-filter systems to retrospectively forecast influenza epidemics in Hong Kong from January 1998 to December 2013, including the 2009 pandemic. The forecast systems were able to forecast both the peak timing and peak magnitude for 44 epidemics in 16 years caused by individual influenza strains (i.e., seasonal influenza A(H1N1), pandemic A(H1N1), A(H3N2), and B), as well as 19 aggregate epidemics caused by one or more of these influenza strains. Average forecast accuracies were 37% (for both peak timing and magnitude) at 1-3 week leads, and 51% (peak timing) and 50% (peak magnitude) at 0 lead. Forecast accuracy increased as the spread of a given forecast ensemble decreased; the forecast accuracy for peak timing (peak magnitude) increased up to 43% (45%) for H1N1, 93% (89%) for H3N2, and 53% (68%) for influenza B at 1-3 week leads. These findings suggest that accurate forecasts can be made at least 3 weeks in advance for subtropical and tropical regions. PMID:26226185

Addressing population heterogeneity and distribution in epidemics models using a cellular automata approach

PubMed Central

2014-01-01

Background The spread of an infectious disease is determined by biological and social factors. Models based on cellular automata are adequate to describe such natural systems consisting of a massive collection of simple interacting objects. They characterize the time evolution of the global system as the emergent behaviour resulting from the interaction of the objects, whose behaviour is defined through a set of simple rules that encode the individual behaviour and the transmission dynamic. Methods An epidemic is characterized trough an individual–based–model built upon cellular automata. In the proposed model, each individual of the population is represented by a cell of the automata. This way of modeling an epidemic situation allows to individually define the characteristic of each individual, establish different scenarios and implement control strategies. Results A cellular automata model to study the time evolution of a heterogeneous populations through the various stages of disease was proposed, allowing the inclusion of individual heterogeneity, geographical characteristics and social factors that determine the dynamic of the desease. Different assumptions made to built the classical model were evaluated, leading to following results: i) for low contact rate (like in quarantine process or low density population areas) the number of infective individuals is lower than other areas where the contact rate is higher, and ii) for different initial spacial distributions of infected individuals different epidemic dynamics are obtained due to its influence on the transition rate and the reproductive ratio of disease. Conclusions The contact rate and spatial distributions have a central role in the spread of a disease. For low density populations the spread is very low and the number of infected individuals is lower than in highly populated areas. The spacial distribution of the population and the disease focus as well as the geographical characteristic of the area

Addressing population heterogeneity and distribution in epidemics models using a cellular automata approach.

PubMed

López, Leonardo; Burguerner, Germán; Giovanini, Leonardo

2014-04-12

The spread of an infectious disease is determined by biological and social factors. Models based on cellular automata are adequate to describe such natural systems consisting of a massive collection of simple interacting objects. They characterize the time evolution of the global system as the emergent behaviour resulting from the interaction of the objects, whose behaviour is defined through a set of simple rules that encode the individual behaviour and the transmission dynamic. An epidemic is characterized trough an individual-based-model built upon cellular automata. In the proposed model, each individual of the population is represented by a cell of the automata. This way of modeling an epidemic situation allows to individually define the characteristic of each individual, establish different scenarios and implement control strategies. A cellular automata model to study the time evolution of a heterogeneous populations through the various stages of disease was proposed, allowing the inclusion of individual heterogeneity, geographical characteristics and social factors that determine the dynamic of the desease. Different assumptions made to built the classical model were evaluated, leading to following results: i) for low contact rate (like in quarantine process or low density population areas) the number of infective individuals is lower than other areas where the contact rate is higher, and ii) for different initial spacial distributions of infected individuals different epidemic dynamics are obtained due to its influence on the transition rate and the reproductive ratio of disease. The contact rate and spatial distributions have a central role in the spread of a disease. For low density populations the spread is very low and the number of infected individuals is lower than in highly populated areas. The spacial distribution of the population and the disease focus as well as the geographical characteristic of the area play a central role in the dynamics of the

Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model

NASA Astrophysics Data System (ADS)

Speidel, Leo; Klemm, Konstantin; Eguíluz, Víctor M.; Masuda, Naoki

2016-07-01

Data of physical contacts and face-to-face communications suggest temporally varying networks as the media on which infections take place among humans and animals. Epidemic processes on temporal networks are complicated by complexity of both network structure and temporal dimensions. Theoretical approaches are much needed for identifying key factors that affect dynamics of epidemics. In particular, what factors make some temporal networks stronger media of infection than other temporal networks is under debate. We develop a theory to understand the susceptible-infected-susceptible epidemic model on arbitrary temporal networks, where each contact is used for a finite duration. We show that temporality of networks lessens the epidemic threshold such that infections persist more easily in temporal networks than in their static counterparts. We further show that the Lie commutator bracket of the adjacency matrices at different times is a key determinant of the epidemic threshold in temporal networks. The effect of temporality on the epidemic threshold, which depends on a data set, is approximately predicted by the magnitude of a commutator norm.

Influence of Media on Seasonal Influenza Epidemic Curves.

PubMed

Saito, Satoshi; Saito, Norihiro; Itoga, Masamichi; Ozaki, Hiromi; Kimura, Toshiyuki; Okamura, Yuji; Murakami, Hiroshi; Kayaba, Hiroyuki

2016-09-01

Theoretical investigations predicting the epidemic curves of seasonal influenza have been demonstrated so far; however, there is little empirical research using ever accumulated epidemic curves. The effects of vaccine coverage and information distribution on influenza epidemics were evaluated. Four indices for epidemics (i.e., onset-peak duration, onset-end duration, ratio of the onset-peak duration to onset-end duration and steepness of epidemic curves) were defined, and the correlations between these indices and anti-flu drug prescription dose, vaccine coverage, the volume of media and search trend on influenza through internet were analyzed. Epidemiological data on seasonal influenza epidemics from 2002/2003 to 2013/2014 excluding 2009/2010 season were collected from National Institute of Infectious Diseases of Japan. The onset-peak duration and its ratio to onset-end duration correlated inversely with the volume of anti-flu drug prescription. Onset-peak duration correlated positively with media information volume on influenza. The steepness of the epidemic curve, and anti-flu drug prescription dose inversely correlated with the volume of media information. Pre-epidemic search trend and media volume on influenza correlated with the vaccine coverage in the season. Vaccine coverage had no strong effect on epidemic curve. Education through media has an effect on the epidemic curve of seasonal influenza. Copyright © 2016 The Author(s). Published by Elsevier Ltd.. All rights reserved.

Comparing functional responses in predator-infected eco-epidemics models.

PubMed

Haque, Mainul; Rahman, Md Sabiar; Venturino, Ezio

2013-11-01

The current paper deals with the mathematical models of predator-prey system where a transmissible disease spreads among the predator species only. Four mathematical models are proposed and analysed with several popular predator functional responses in order to show the influence of functional response on eco-epidemic models. The existence, boundedness, uniqueness of solutions of all the models are established. Mathematical analysis including stability and bifurcation are observed. Comparison among the results of these models allows the general conclusion that relevant behaviour of the eco-epidemic predator-prey system, including switching of stability, extinction, persistence and oscillations for any species depends on four important parameters viz. the rate of infection, predator interspecies competition and the attack rate on susceptible predator. The paper ends with a discussion of the biological implications of the analytical and numerical results. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Dynamic malware containment under an epidemic model with alert

NASA Astrophysics Data System (ADS)

Zhang, Tianrui; Yang, Lu-Xing; Yang, Xiaofan; Wu, Yingbo; Tang, Yuan Yan

2017-03-01

Alerting at the early stage of malware invasion turns out to be an important complement to malware detection and elimination. This paper addresses the issue of how to dynamically contain the prevalence of malware at a lower cost, provided alerting is feasible. A controlled epidemic model with alert is established, and an optimal control problem based on the epidemic model is formulated. The optimality system for the optimal control problem is derived. The structure of an optimal control for the proposed optimal control problem is characterized under some conditions. Numerical examples show that the cost-efficiency of an optimal control strategy can be enhanced by adjusting the upper and lower bounds on admissible controls.

Reproduction numbers for epidemic models with households and other social structures. I. Definition and calculation of R0

PubMed Central

Pellis, Lorenzo; Ball, Frank; Trapman, Pieter

2012-01-01

The basic reproduction number R0 is one of the most important quantities in epidemiology. However, for epidemic models with explicit social structure involving small mixing units such as households, its definition is not straightforward and a wealth of other threshold parameters has appeared in the literature. In this paper, we use branching processes to define R0, we apply this definition to models with households or other more complex social structures and we provide methods for calculating it. PMID:22085761

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.

Model of epidemic control based on quarantine and message delivery

NASA Astrophysics Data System (ADS)

Wang, Xingyuan; Zhao, Tianfang; Qin, Xiaomeng

2016-09-01

The model provides two novel strategies for the preventive control of epidemic diseases. One approach is related to the different isolating rates in latent period and invasion period. Experiments show that the increasing of isolating rates in invasion period, as long as over 0.5, contributes little to the preventing of epidemic; the improvement of isolation rate in latent period is key to control the disease spreading. Another is a specific mechanism of message delivering and forwarding. Information quality and information accumulating process are also considered there. Macroscopically, diseases are easy to control as long as the immune messages reach a certain quality. Individually, the accumulating messages bring people with certain immunity to the disease. Also, the model is performed on the classic complex networks like scale-free network and small-world network, and location-based social networks. Results show that the proposed measures demonstrate superior performance and significantly reduce the negative impact of epidemic disease.

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

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

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.

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.

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.

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.

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

Modelling virus- and host-limitation in vectored plant disease epidemics.

PubMed

Jeger, M J; van den Bosch, F; Madden, L V

2011-08-01

Models of plant virus epidemics have received less attention than those caused by fungal pathogens. Intuitively, the fact that virus diseases are systemic means that the individual diseased plant can be considered as the population unit which simplifies modelling. However, the fact that a vector is required in the vast majority of cases for virus transmission, means that explicit consideration must be taken of the vector, or, the involvement of the vector in the transmission process must be considered implicitly. In the latter case it is also important that within-plant processes, such as virus multiplication and systemic movement, are taken into account. In this paper we propose an approach based on the linking of transmission at the population level with virus multiplication within plants. The resulting models are parameter-sparse and hence simplistic. However, the range of model outcomes is representative of field observations relating to the apparent limitation of epidemic development in populations of healthy susceptible plants. We propose that epidemic development can be constrained by virus limitation in the early stages of an epidemic when the availability of healthy susceptible hosts is not limiting. There is an inverse relationship between levels of transmission in the population and the mean virus titre/infected plant. In the case of competition between viruses, both virus and host limitation are likely to be important in determining whether one virus can displace another or whether both viruses can co-exist in a plant population. Lotka-Volterra type equations are derived to describe density-dependent competition between two viruses multiplying within plants, embedded within a population level epidemiological model. Explicit expressions determining displacement or co-existence of the viruses are obtained. Unlike the classical Lotka-Volterra competition equations, the co-existence requirement for the competition coefficients to be both less than 1 can be

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

Estimation of the reproduction number of dengue fever from spatial epidemic data.

PubMed

Chowell, G; Diaz-Dueñas, P; Miller, J C; Alcazar-Velazco, A; Hyman, J M; Fenimore, P W; Castillo-Chavez, C

2007-08-01

Dengue, a vector-borne disease, thrives in tropical and subtropical regions worldwide. A retrospective analysis of the 2002 dengue epidemic in Colima located on the Mexican central Pacific coast is carried out. We estimate the reproduction number from spatial epidemic data at the level of municipalities using two different methods: (1) Using a standard dengue epidemic model and assuming pure exponential initial epidemic growth and (2) Fitting a more realistic epidemic model to the initial phase of the dengue epidemic curve. Using Method I, we estimate an overall mean reproduction number of 3.09 (95% CI: 2.34,3.84) as well as local reproduction numbers whose values range from 1.24 (1.15,1.33) to 4.22 (2.90,5.54). Using Method II, the overall mean reproduction number is estimated to be 2.0 (1.75,2.23) and local reproduction numbers ranging from 0.49 (0.0,1.0) to 3.30 (1.63,4.97). Method I systematically overestimates the reproduction number relative to the refined Method II, and hence it would overestimate the intensity of interventions required for containment. Moreover, optimal intervention with defined resources demands different levels of locally tailored mitigation. Local epidemic peaks occur between the 24th and 35th week of the year, and correlate positively with the final local epidemic sizes (rho=0.92, P-value<0.001). Moreover, final local epidemic sizes are found to be linearly related to the local population size (P-value<0.001). This observation supports a roughly constant number of female mosquitoes per person across urban and rural regions.

Understanding viral video dynamics through an epidemic modelling approach

NASA Astrophysics Data System (ADS)

Sachak-Patwa, Rahil; Fadai, Nabil T.; Van Gorder, Robert A.

2018-07-01

Motivated by the hypothesis that the spread of viral videos is analogous to the spread of a disease epidemic, we formulate a novel susceptible-exposed-infected-recovered-susceptible (SEIRS) delay differential equation epidemic model to describe the popularity evolution of viral videos. Our models incorporate time-delay, in order to accurately describe the virtual contact process between individuals and the temporary immunity of individuals to videos after they have grown tired of watching them. We validate our models by fitting model parameters to viewing data from YouTube music videos, in order to demonstrate that the model solutions accurately reproduce real behaviour seen in this data. We use an SEIR model to describe the initial growth and decline of daily views, and an SEIRS model to describe the long term behaviour of the popularity of music videos. We also analyse the decay rates in the daily views of videos, determining whether they follow a power law or exponential distribution. Although we focus on viral videos, the modelling approach may be used to understand dynamics emergent from other areas of science which aim to describe consumer behaviour.

Local immunization program for susceptible-infected-recovered network epidemic model

NASA Astrophysics Data System (ADS)

Wu, Qingchu; Lou, Yijun

2016-02-01

The immunization strategies through contact tracing on the susceptible-infected-recovered framework in social networks are modelled to evaluate the cost-effectiveness of information-based vaccination programs with particular focus on the scenario where individuals belonging to a specific set can get vaccinated due to the vaccine shortages and other economic or humanity constraints. By using the block heterogeneous mean-field approach, a series of discrete-time dynamical models is formulated and the condition for epidemic outbreaks can be established which is shown to be not only dependent on the network structure but also closely related to the immunization control parameters. Results show that increasing the immunization strength can effectively raise the epidemic threshold, which is different from the predictions obtained through the susceptible-infected-susceptible network framework, where epidemic threshold is independent of the vaccination strength. Furthermore, a significant decrease of vaccine use to control the infectious disease is observed for the local vaccination strategy, which shows the promising applications of the local immunization programs to disease control while calls for accurate local information during the process of disease 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

2014-11-06

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.

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

The global dynamics for a stochastic SIS epidemic model with isolation

NASA Astrophysics Data System (ADS)

Chen, Yiliang; Wen, Buyu; Teng, Zhidong

2018-02-01

In this paper, we investigate the dynamical behavior for a stochastic SIS epidemic model with isolation which is as an important strategy for the elimination of infectious diseases. It is assumed that the stochastic effects manifest themselves mainly as fluctuation in the transmission coefficient, the death rate and the proportional coefficient of the isolation of infective. It is shown that the extinction and persistence in the mean of the model are determined by a threshold value R0S . That is, if R0S < 1, then disease dies out with probability one, and if R0S > 1, then the disease is stochastic persistent in the means with probability one. Furthermore, the existence of a unique stationary distribution is discussed, and the sufficient conditions are established by using the Lyapunov function method. Finally, some numerical examples are carried out to confirm the analytical results.

Assessment of yellow fever epidemic risk: an original multi-criteria modeling approach.

PubMed

Briand, Sylvie; Beresniak, Ariel; Nguyen, Tim; Yonli, Tajoua; Duru, Gerard; Kambire, Chantal; Perea, William

2009-07-14

Yellow fever (YF) virtually disappeared in francophone West African countries as a result of YF mass vaccination campaigns carried out between 1940 and 1953. However, because of the failure to continue mass vaccination campaigns, a resurgence of the deadly disease in many African countries began in the early 1980s. We developed an original modeling approach to assess YF epidemic risk (vulnerability) and to prioritize the populations to be vaccinated. We chose a two-step assessment of vulnerability at district level consisting of a quantitative and qualitative assessment per country. Quantitative assessment starts with data collection on six risk factors: five risk factors associated with "exposure" to virus/vector and one with "susceptibility" of a district to YF epidemics. The multiple correspondence analysis (MCA) modeling method was specifically adapted to reduce the five exposure variables to one aggregated exposure indicator. Health districts were then projected onto a two-dimensional graph to define different levels of vulnerability. Districts are presented on risk maps for qualitative analysis in consensus groups, allowing the addition of factors, such as population migrations or vector density, that could not be included in MCA. The example of rural districts in Burkina Faso show five distinct clusters of risk profiles. Based on this assessment, 32 of 55 districts comprising over 7 million people were prioritized for preventive vaccination campaigns. This assessment of yellow fever epidemic risk at the district level includes MCA modeling and consensus group modification. MCA provides a standardized way to reduce complexity. It supports an informed public health decision-making process that empowers local stakeholders through the consensus group. This original approach can be applied to any disease with documented risk factors.

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.

HIV epidemic control-a model for optimal allocation of prevention and treatment resources.

PubMed

Alistar, Sabina S; Long, Elisa F; Brandeau, Margaret L; Beck, Eduard J

2014-06-01

With 33 million people living with human immunodeficiency virus (HIV) worldwide and 2.7 million new infections occurring annually, additional HIV prevention and treatment efforts are urgently needed. However, available resources for HIV control are limited and must be used efficiently to minimize the future spread of the epidemic. We develop a model to determine the appropriate resource allocation between expanded HIV prevention and treatment services. We create an epidemic model that incorporates multiple key populations with different transmission modes, as well as production functions that relate investment in prevention and treatment programs to changes in transmission and treatment rates. The goal is to allocate resources to minimize R 0, the reproductive rate of infection. We first develop a single-population model and determine the optimal resource allocation between HIV prevention and treatment. We extend the analysis to multiple independent populations, with resource allocation among interventions and populations. We then include the effects of HIV transmission between key populations. We apply our model to examine HIV epidemic control in two different settings, Uganda and Russia. As part of these applications, we develop a novel approach for estimating empirical HIV program production functions. Our study provides insights into the important question of resource allocation for a country's optimal response to its HIV epidemic and provides a practical approach for decision makers. Better decisions about allocating limited HIV resources can improve response to the epidemic and increase access to HIV prevention and treatment services for millions of people worldwide.

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

Heroin epidemics, treatment and ODE modelling.

PubMed

White, Emma; Comiskey, Catherine

2007-07-01

The UN [United Nations Office on Drugs and Crime (UNODC): World Drug Report, 2005, vol. 1: Analysis. UNODC, 2005.], EU [European Monitoring Centre for Drugs and Drug Addiction (EMCDDA): Annual Report, 2005.http://annualreport.emcdda.eu.int/en/home-en.html.] and WHO [World Health Organisation (WHO): Biregional Strategy for Harm Reduction, 2005-2009. HIV and Injecting Drug Use. WHO, 2005.] have consistently highlighted in recent years the ongoing and persistent nature of opiate and particularly heroin use on a global scale. While this is a global phenomenon, authors have emphasised the significant impact such an epidemic has on individual lives and on society. National prevalence studies have indicated the scale of the problem, but the drug-using career, typically consisting of initiation, habitual use, a treatment-relapse cycle and eventual recovery, is not well understood. This paper presents one of the first ODE models of opiate addiction, based on the principles of mathematical epidemiology. The aim of this model is to identify parameters of interest for further study, with a view to informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness. An epidemic threshold value, R(0), is proposed for the drug-using career. Sensitivity analysis is performed on R(0) and it is then used to examine the stability of the system. A condition under which a backward bifurcation may exist is found, as are conditions that permit the existence of one or more endemic equilibria. A key result arising from this model is that prevention is indeed better than cure.

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.

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects.

PubMed

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity.

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.

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.

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.

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

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

Epidemic spreading in multiplex networks influenced by opinion exchanges on vaccination.

PubMed

Alvarez-Zuzek, Lucila G; La Rocca, Cristian E; Iglesias, José R; Braunstein, Lidia A

2017-01-01

Through years, the use of vaccines has always been a controversial issue. People in a society may have different opinions about how beneficial the vaccines are and as a consequence some of those individuals decide to vaccinate or not themselves and their relatives. This attitude in face of vaccines has clear consequences in the spread of diseases and their transformation in epidemics. Motivated by this scenario, we study, in a simultaneous way, the changes of opinions about vaccination together with the evolution of a disease. In our model we consider a multiplex network consisting of two layers. One of the layers corresponds to a social network where people share their opinions and influence others opinions. The social model that rules the dynamic is the M-model, which takes into account two different processes that occurs in a society: persuasion and compromise. This two processes are related through a parameter r, r < 1 describes a moderate and committed society, for r > 1 the society tends to have extremist opinions, while r = 1 represents a neutral society. This social network may be of real or virtual contacts. On the other hand, the second layer corresponds to a network of physical contacts where the disease spreading is described by the SIR-Model. In this model the individuals may be in one of the following four states: Susceptible (S), Infected(I), Recovered (R) or Vaccinated (V). A Susceptible individual can: i) get vaccinated, if his opinion in the other layer is totally in favor of the vaccine, ii) get infected, with probability β if he is in contact with an infected neighbor. Those I individuals recover after a certain period tr = 6. Vaccinated individuals have an extremist positive opinion that does not change. We consider that the vaccine has a certain effectiveness ω and as a consequence vaccinated nodes can be infected with probability β(1 - ω) if they are in contact with an infected neighbor. In this case, if the infection process is

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

Adopting epidemic model to optimize medication and surgical intervention of excess weight

NASA Astrophysics Data System (ADS)

Sun, Ruoyan

2017-01-01

We combined an epidemic model with an objective function to minimize the weighted sum of people with excess weight and the cost of a medication and surgical intervention in the population. The epidemic model is consisted of ordinary differential equations to describe three subpopulation groups based on weight. We introduced an intervention using medication and surgery to deal with excess weight. An objective function is constructed taking into consideration the cost of the intervention as well as the weight distribution of the population. Using empirical data, we show that fixed participation rate reduces the size of obese population but increases the size for overweight. An optimal participation rate exists and decreases with respect to time. Both theoretical analysis and empirical example confirm the existence of an optimal participation rate, u*. Under u*, the weighted sum of overweight (S) and obese (O) population as well as the cost of the program is minimized. This article highlights the existence of an optimal participation rate that minimizes the number of people with excess weight and the cost of the intervention. The time-varying optimal participation rate could contribute to designing future public health interventions of excess weight.

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

Assessment of Yellow Fever Epidemic Risk: An Original Multi-criteria Modeling Approach

PubMed Central

Briand, Sylvie; Beresniak, Ariel; Nguyen, Tim; Yonli, Tajoua; Duru, Gerard; Kambire, Chantal; Perea, William

2009-01-01

Background Yellow fever (YF) virtually disappeared in francophone West African countries as a result of YF mass vaccination campaigns carried out between 1940 and 1953. However, because of the failure to continue mass vaccination campaigns, a resurgence of the deadly disease in many African countries began in the early 1980s. We developed an original modeling approach to assess YF epidemic risk (vulnerability) and to prioritize the populations to be vaccinated. Methods and Findings We chose a two-step assessment of vulnerability at district level consisting of a quantitative and qualitative assessment per country. Quantitative assessment starts with data collection on six risk factors: five risk factors associated with “exposure” to virus/vector and one with “susceptibility” of a district to YF epidemics. The multiple correspondence analysis (MCA) modeling method was specifically adapted to reduce the five exposure variables to one aggregated exposure indicator. Health districts were then projected onto a two-dimensional graph to define different levels of vulnerability. Districts are presented on risk maps for qualitative analysis in consensus groups, allowing the addition of factors, such as population migrations or vector density, that could not be included in MCA. The example of rural districts in Burkina Faso show five distinct clusters of risk profiles. Based on this assessment, 32 of 55 districts comprising over 7 million people were prioritized for preventive vaccination campaigns. Conclusion This assessment of yellow fever epidemic risk at the district level includes MCA modeling and consensus group modification. MCA provides a standardized way to reduce complexity. It supports an informed public health decision-making process that empowers local stakeholders through the consensus group. This original approach can be applied to any disease with documented risk factors. PMID:19597548

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.

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

Comparing the epidemic in U.S. and Britain.

PubMed

Harmon, K S

1999-01-01

Cultural differences between the United States and Britain influence how the AIDS/HIV epidemic is being addressed and why AIDS rates are smaller in the United Kingdom. The author proposes that highly diverse and racist societies, like in the United States, may cause distrust among different groups in the effort to challenge the spread of HIV/AIDS, leaving people to fend for themselves. Because of racism and distrust between ethnic and racial groups, as well as differences in financial resources between groups, the AIDS epidemic in the United States is being fought on too many fronts without the benefit of a uniform response. Ironically, this problem has also spurred a greater ability among US AIDS service providers to work with diverse communities during the course of the epidemic.

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.

Bayesian conditional-independence modeling of the AIDS epidemic in England and Wales

NASA Astrophysics Data System (ADS)

Gilks, Walter R.; De Angelis, Daniela; Day, Nicholas E.

We describe the use of conditional-independence modeling, Bayesian inference and Markov chain Monte Carlo, to model and project the HIV-AIDS epidemic in homosexual/bisexual males in England and Wales. Complexity in this analysis arises through selectively missing data, indirectly observed underlying processes, and measurement error. Our emphasis is on presentation and discussion of the concepts, not on the technicalities of this analysis, which can be found elsewhere [D. De Angelis, W.R. Gilks, N.E. Day, Bayesian projection of the the acquired immune deficiency syndrome epidemic (with discussion), Applied Statistics, in press].

Be-CoDiS: A Mathematical Model to Predict the Risk of Human Diseases Spread Between Countries--Validation and Application to the 2014-2015 Ebola Virus Disease Epidemic.

PubMed

Ivorra, Benjamin; Ngom, Diène; Ramos, Ángel M

2015-09-01

Ebola virus disease is a lethal human and primate disease that currently requires a particular attention from the international health authorities due to important outbreaks in some Western African countries and isolated cases in the UK, the USA and Spain. Regarding the emergency of this situation, there is a need for the development of decision tools, such as mathematical models, to assist the authorities to focus their efforts in important factors to eradicate Ebola. In this work, we propose a novel deterministic spatial-temporal model, called Between-Countries Disease Spread (Be-CoDiS), to study the evolution of human diseases within and between countries. The main interesting characteristics of Be-CoDiS are the consideration of the movement of people between countries, the control measure effects and the use of time-dependent coefficients adapted to each country. First, we focus on the mathematical formulation of each component of the model and explain how its parameters and inputs are obtained. Then, in order to validate our approach, we consider two numerical experiments regarding the 2014-2015 Ebola epidemic. The first one studies the ability of the model in predicting the EVD evolution between countries starting from the index cases in Guinea in December 2013. The second one consists of forecasting the evolution of the epidemic by using some recent data. The results obtained with Be-CoDiS are compared to real data and other model outputs found in the literature. Finally, a brief parameter sensitivity analysis is done. A free MATLAB version of Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htm.

Structured Modeling and Analysis of Stochastic Epidemics with Immigration and Demographic Effects

PubMed Central

Baumann, Hendrik; Sandmann, Werner

2016-01-01

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these epidemics as level-dependent quasi-birth-and-death processes enables efficient computations of the equilibrium distributions by matrix-analytic methods. Numerical examples for specific parameter sets are provided, which demonstrates that this approach is particularly well-suited for studying the impact of varying rates for immigration, births, deaths, infection, recovery from infection, and loss of immunity. PMID:27010993

Rainfall mediations in the spreading of epidemic cholera

NASA Astrophysics Data System (ADS)

Righetto, L.; Bertuzzo, E.; Mari, L.; Schild, E.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.

2013-10-01

Following the empirical evidence of a clear correlation between rainfall events and cholera resurgence that was observed in particular during the recent outbreak in Haiti, a spatially explicit model of epidemic cholera is re-examined. Specifically, we test a multivariate Poisson rainfall generator, with parameters varying in space and time, as a driver of enhanced disease transmission. The relevance of the issue relates to the key insight that predictive mathematical models may provide into the course of an ongoing cholera epidemic aiding emergency management (say, in allocating life-saving supplies or health care staff) or in evaluating alternative management strategies. Our model consists of a set of dynamical equations (SIRB-like i.e. subdivided into the compartments of Susceptible, Infected and Recovered individuals, and including a balance of Bacterial concentrations in the water reservoir) describing a connected network of human communities where the infection results from the exposure to excess concentrations of pathogens in the water. These, in turn, are driven by rainfall washout of open-air defecation sites or cesspool overflows, hydrologic transport through waterways and by mobility of susceptible and infected individuals. We perform an a posteriori analysis (from the beginning of the epidemic in October 2010 until December 2011) to test the model reliability in predicting cholera cases and in testing control measures, involving vaccination and sanitation campaigns, for the ongoing epidemic. Even though predicting reliably the timing of the epidemic resurgence proves difficult due to rainfall inter-annual variability, we find that the model can reasonably quantify the total number of reported infection cases in the selected time-span. We then run a multi-seasonal prediction of the course of the epidemic until December 2015, to investigate conditions for further resurgences and endemicity of cholera in the region with a view to policies which may bring to

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.

Viral epidemics in a cell culture: novel high resolution data and their interpretation by a percolation theory based model.

PubMed

Gönci, Balázs; Németh, Valéria; Balogh, Emeric; Szabó, Bálint; Dénes, Ádám; Környei, Zsuzsanna; Vicsek, Tamás

2010-12-20

Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent large scale observations have resulted in major discoveries concerning the overall features of the spreading process in systems with highly mobile susceptible units, but virtually no data are available about observations of infection spreading for a very large number of immobile units. Here we present the first detailed quantitative documentation of percolation-type viral epidemics in a highly reproducible in vitro system consisting of tens of thousands of virtually motionless cells. We use a confluent astroglial monolayer in a Petri dish and induce productive infection in a limited number of cells with a genetically modified herpesvirus strain. This approach allows extreme high resolution tracking of the spatio-temporal development of the epidemic. We show that a simple model is capable of reproducing the basic features of our observations, i.e., the observed behaviour is likely to be applicable to many different kinds of systems. Statistical physics inspired approaches to our data, such as fractal dimension of the infected clusters as well as their size distribution, seem to fit into a percolation theory based interpretation. We suggest that our observations may be used to model epidemics in more complex systems, which are difficult to study in isolation.

Viral Epidemics in a Cell Culture: Novel High Resolution Data and Their Interpretation by a Percolation Theory Based Model

PubMed Central

Gönci, Balázs; Németh, Valéria; Balogh, Emeric; Szabó, Bálint; Dénes, Ádám; Környei, Zsuzsanna; Vicsek, Tamás

2010-01-01

Because of its relevance to everyday life, the spreading of viral infections has been of central interest in a variety of scientific communities involved in fighting, preventing and theoretically interpreting epidemic processes. Recent large scale observations have resulted in major discoveries concerning the overall features of the spreading process in systems with highly mobile susceptible units, but virtually no data are available about observations of infection spreading for a very large number of immobile units. Here we present the first detailed quantitative documentation of percolation-type viral epidemics in a highly reproducible in vitro system consisting of tens of thousands of virtually motionless cells. We use a confluent astroglial monolayer in a Petri dish and induce productive infection in a limited number of cells with a genetically modified herpesvirus strain. This approach allows extreme high resolution tracking of the spatio-temporal development of the epidemic. We show that a simple model is capable of reproducing the basic features of our observations, i.e., the observed behaviour is likely to be applicable to many different kinds of systems. Statistical physics inspired approaches to our data, such as fractal dimension of the infected clusters as well as their size distribution, seem to fit into a percolation theory based interpretation. We suggest that our observations may be used to model epidemics in more complex systems, which are difficult to study in isolation. PMID:21187920

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.

[Spatial epidemiological study on malaria epidemics in Hainan province].

PubMed

Wen, Liang; Shi, Run-He; Fang, Li-Qun; Xu, De-Zhong; Li, Cheng-Yi; Wang, Yong; Yuan, Zheng-Quan; Zhang, Hui

2008-06-01

To better understand the characteristics of spatial distribution of malaria epidemics in Hainan province and to explore the relationship between malaria epidemics and environmental factors, as well to develop prediction model on malaria epidemics. Data on Malaria and meteorological factors were collected in all 19 counties in Hainan province from May to Oct., 2000, and the proportion of land use types of these counties in this period were extracted from digital map of land use in Hainan province. Land surface temperatures (LST) were extracted from MODIS images and elevations of these counties were extracted from DEM of Hainan province. The coefficients of correlation of malaria incidences and these environmental factors were then calculated with SPSS 13.0, and negative binomial regression analysis were done using SAS 9.0. The incidence of malaria showed (1) positive correlations to elevation, proportion of forest land area and grassland area; (2) negative correlations to the proportion of cultivated area, urban and rural residents and to industrial enterprise area, LST; (3) no correlations to meteorological factors, proportion of water area, and unemployed land area. The prediction model of malaria which came from negative binomial regression analysis was: I (monthly, unit: 1/1,000,000) = exp (-1.672-0.399xLST). Spatial distribution of malaria epidemics was associated with some environmental factors, and prediction model of malaria epidemic could be developed with indexes which extracted from satellite remote sensing images.

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.

A spatially explicit model for the future progression of the current Haiti cholera epidemic

NASA Astrophysics Data System (ADS)

Bertuzzo, E.; Mari, L.; Righetto, L.; Gatto, M.; Casagrandi, R.; Rodriguez-Iturbe, I.; Rinaldo, A.

2011-12-01

As a major cholera epidemic progresses in Haiti, and the figures of the infection, up to July 2011, climb to 385,000 cases and 5,800 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 textit{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 texttrademark project). The model directly account 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. 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

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.

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

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

Evolution of pathogen virulence across space during an epidemic

USGS Publications Warehouse

Osnas, Erik; Hurtado, Paul J.; Dobson, Andrew P.

2015-01-01

We explore pathogen virulence evolution during the spatial expansion of an infectious disease epidemic in the presence of a novel host movement trade-off, using a simple, spatially explicit mathematical model. This work is motivated by empirical observations of the Mycoplasma gallisepticum invasion into North American house finch (Haemorhous mexicanus) populations; however, our results likely have important applications to other emerging infectious diseases in mobile hosts. We assume that infection reduces host movement and survival and that across pathogen strains the severity of these reductions increases with pathogen infectiousness. Assuming these trade-offs between pathogen virulence (host mortality), pathogen transmission, and host movement, we find that pathogen virulence levels near the epidemic front (that maximize wave speed) are lower than those that have a short-term growth rate advantage or that ultimately prevail (i.e., are evolutionarily stable) near the epicenter and where infection becomes endemic (i.e., that maximize the pathogen basic reproductive ratio). We predict that, under these trade-offs, less virulent pathogen strains will dominate the periphery of an epidemic and that more virulent strains will increase in frequency after invasion where disease is endemic. These results have important implications for observing and interpreting spatiotemporal epidemic data and may help explain transient virulence dynamics of emerging infectious diseases.

Renaissance model of an epidemic with quarantine.

PubMed

Dobay, Akos; Gall, Gabriella E C; Rankin, Daniel J; Bagheri, Homayoun C

2013-01-21

Quarantine is one possible solution to limit the propagation of an emerging infectious disease. Typically, infected individuals are removed from the population by avoiding physical contact with healthy individuals. A key factor for the success of a quarantine strategy is the carrying capacity of the facility. This is often a known parameter, while other parameters such as those defining the population structure are more difficult to assess. Here we develop a model where we explicitly introduce the carrying capacity of the quarantine facility into a susceptible-infected-recovered (SIR) framework. We show how the model can address the propagation and control of contact and sexually transmitted infections. We illustrate this by a case study of the city of Zurich during the 16th century, when it had to face an epidemic of syphilis. After Swiss mercenaries came back from a war in Naples in 1495, the authorities of the city addressed subsequent epidemics by, among others, placing infected members of the population in quarantine. Our results suggest that a modestly sized quarantine facility can successfully prevent or reduce an epidemic. However, false detection can present a real impediment for this solution. Indiscriminate quarantine of individuals can lead to the overfilling of the facility, and prevent the intake of infected individuals. This results in the failure of the quarantine policy. Hence, improving the rate of true over false detection becomes the key factor for quarantine strategies. Moreover, in the case of sexually transmitted infections, asymmetries in the male to female ratio, and the force of infection pertaining to each sex and class of sexual encounter can alter the effectiveness of quarantine measures. For example, a heterosexually transmitted disease that mainly affects one sex is harder to control in a population with more individuals of the opposite sex. Hence an imbalance in the sex ratios as seen in situations such as mining colonies, or

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.

Forecasting Disease Risk for Increased Epidemic Preparedness in Public Health

PubMed Central

Myers, M.F.; Rogers, D.J.; Cox, J.; Flahault, A.; Hay, S.I.

2011-01-01

Emerging infectious diseases pose a growing threat to human populations. Many of the world’s epidemic diseases (particularly those transmitted by intermediate hosts) are known to be highly sensitive to long-term changes in climate and short-term fluctuations in the weather. The application of environmental data to the study of disease offers the capability to demonstrate vector–environment relationships and potentially forecast the risk of disease outbreaks or epidemics. Accurate disease forecasting models would markedly improve epidemic prevention and control capabilities. This chapter examines the potential for epidemic forecasting and discusses the issues associated with the development of global networks for surveillance and prediction. Existing global systems for epidemic preparedness focus on disease surveillance using either expert knowledge or statistical modelling of disease activity and thresholds to identify times and areas of risk. Predictive health information systems would use monitored environmental variables, linked to a disease system, to be observed and provide prior information of outbreaks. The components and varieties of forecasting systems are discussed with selected examples, along with issues relating to further development. PMID:10997211

Epidemic spreading on preferred degree adaptive networks.

PubMed

Jolad, Shivakumar; Liu, Wenjia; Schmittmann, B; Zia, R K P

2012-01-01

We study the standard SIS model of epidemic spreading on networks where individuals have a fluctuating number of connections around a preferred degree κ. Using very simple rules for forming such preferred degree networks, we find some unusual statistical properties not found in familiar Erdös-Rényi or scale free networks. By letting κ depend on the fraction of infected individuals, we model the behavioral changes in response to how the extent of the epidemic is perceived. In our models, the behavioral adaptations can be either 'blind' or 'selective'--depending on whether a node adapts by cutting or adding links to randomly chosen partners or selectively, based on the state of the partner. For a frozen preferred network, we find that the infection threshold follows the heterogeneous mean field result λ(c)/μ = <κ>/<κ2> and the phase diagram matches the predictions of the annealed adjacency matrix (AAM) approach. With 'blind' adaptations, although the epidemic threshold remains unchanged, the infection level is substantially affected, depending on the details of the adaptation. The 'selective' adaptive SIS models are most interesting. Both the threshold and the level of infection changes, controlled not only by how the adaptations are implemented but also how often the nodes cut/add links (compared to the time scales of the epidemic spreading). A simple mean field theory is presented for the selective adaptations which capture the qualitative and some of the quantitative features of the infection phase diagram.

An online spatiotemporal prediction model for dengue fever epidemic in Kaohsiung (Taiwan).

PubMed

Yu, Hwa-Lung; Angulo, José M; Cheng, Ming-Hung; Wu, Jiaping; Christakos, George

2014-05-01

The emergence and re-emergence of disease epidemics is a complex question that may be influenced by diverse factors, including the space-time dynamics of human populations, environmental conditions, and associated uncertainties. This study proposes a stochastic framework to integrate space-time dynamics in the form of a Susceptible-Infected-Recovered (SIR) model, together with uncertain disease observations, into a Bayesian maximum entropy (BME) framework. The resulting model (BME-SIR) can be used to predict space-time disease spread. Specifically, it was applied to obtain a space-time prediction of the dengue fever (DF) epidemic that took place in Kaohsiung City (Taiwan) during 2002. In implementing the model, the SIR parameters were continually updated and information on new cases of infection was incorporated. The results obtained show that the proposed model is rigorous to user-specified initial values of unknown model parameters, that is, transmission and recovery rates. In general, this model provides a good characterization of the spatial diffusion of the DF epidemic, especially in the city districts proximal to the location of the outbreak. Prediction performance may be affected by various factors, such as virus serotypes and human intervention, which can change the space-time dynamics of disease diffusion. The proposed BME-SIR disease prediction model can provide government agencies with a valuable reference for the timely identification, control, and prevention of DF spread in space and time. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

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.

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 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.

Rabies epidemic model with uncertainty in parameters: crisp and fuzzy approaches

NASA Astrophysics Data System (ADS)

Ndii, M. Z.; Amarti, Z.; Wiraningsih, E. D.; Supriatna, A. K.

2018-03-01

A deterministic mathematical model is formulated to investigate the transmission dynamics of rabies. In particular, we investigate the effects of vaccination, carrying capacity and the transmission rate on the rabies epidemics and allow for uncertainty in the parameters. We perform crisp and fuzzy approaches. We find that, in the case of crisp parameters, rabies epidemics may be interrupted when the carrying capacity and the transmission rate are not high. Our findings suggest that limiting the growth of dog population and reducing the potential contact between susceptible and infectious dogs may aid in interrupting rabies epidemics. We extend the work by considering a fuzzy carrying capacity and allow for low, medium, and high level of carrying capacity. The result confirms the results obtained by using crisp carrying capacity, that is, when the carrying capacity is not too high, the vaccination could confine the disease effectively.

Suppression of epidemic spreading in complex networks by local information based behavioral responses

NASA Astrophysics Data System (ADS)

Zhang, Hai-Feng; Xie, Jia-Rong; Tang, Ming; Lai, Ying-Cheng

2014-12-01

The interplay between individual behaviors and epidemic dynamics in complex networks is a topic of recent interest. In particular, individuals can obtain different types of information about the disease and respond by altering their behaviors, and this can affect the spreading dynamics, possibly in a significant way. We propose a model where individuals' behavioral response is based on a generic type of local information, i.e., the number of neighbors that has been infected with the disease. Mathematically, the response can be characterized by a reduction in the transmission rate by a factor that depends on the number of infected neighbors. Utilizing the standard susceptible-infected-susceptible and susceptible-infected-recovery dynamical models for epidemic spreading, we derive a theoretical formula for the epidemic threshold and provide numerical verification. Our analysis lays on a solid quantitative footing the intuition that individual behavioral response can in general suppress epidemic spreading. Furthermore, we find that the hub nodes play the role of "double-edged sword" in that they can either suppress or promote outbreak, depending on their responses to the epidemic, providing additional support for the idea that these nodes are key to controlling epidemic spreading in complex networks.

Suppression of epidemic spreading in complex networks by local information based behavioral responses.

PubMed

Zhang, Hai-Feng; Xie, Jia-Rong; Tang, Ming; Lai, Ying-Cheng

2014-12-01

The interplay between individual behaviors and epidemic dynamics in complex networks is a topic of recent interest. In particular, individuals can obtain different types of information about the disease and respond by altering their behaviors, and this can affect the spreading dynamics, possibly in a significant way. We propose a model where individuals' behavioral response is based on a generic type of local information, i.e., the number of neighbors that has been infected with the disease. Mathematically, the response can be characterized by a reduction in the transmission rate by a factor that depends on the number of infected neighbors. Utilizing the standard susceptible-infected-susceptible and susceptible-infected-recovery dynamical models for epidemic spreading, we derive a theoretical formula for the epidemic threshold and provide numerical verification. Our analysis lays on a solid quantitative footing the intuition that individual behavioral response can in general suppress epidemic spreading. Furthermore, we find that the hub nodes play the role of "double-edged sword" in that they can either suppress or promote outbreak, depending on their responses to the epidemic, providing additional support for the idea that these nodes are key to controlling epidemic spreading in complex networks.

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.

Mathematical models of the AIDS epidemic: An historical perspective

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

Stanley, E.A.

1988-01-01

Researchers developing mathematical models of the spreading of HIV, the Human Immunodeficiency Virus that causes AIDS, hope to achieve a number of goals. These goals may be classified rather broadly into three categories: understanding, prediction, and control. Understanding which are the key biological and sociological processes spreading this epidemic and leading to the deaths of those infected will allow AIDS researchers to collect better data and to identify ways of slowing the epidemic. Predicting the groups at risk and future numbers of ill people will allow an appropriate allocation of health-care resources. Analysis and comparison of proposed control methods willmore » point out unexpected consequences and allow a better design of these programs. The processes which lead to the spread of HIV are biologically and sociologically complex. Mathematical models allow us to organize our knowledge into a coherent picture and examine the logical consequences, therefore they have the potential to be extremely useful in the search to control this disease. 24 refs., 3 figs.« less

The 2017 plague outbreak in Madagascar: Data descriptions and epidemic modelling.

PubMed

Nguyen, Van Kinh; Parra-Rojas, César; Hernandez-Vargas, Esteban A

2018-06-01

From August to November 2017, Madagascar endured an outbreak of plague. A total of 2417 cases of plague were confirmed, causing a death toll of 209. Public health intervention efforts were introduced and successfully stopped the epidemic at the end of November. The plague, however, is endemic in the region and occurs annually, posing the risk of future outbreaks. To understand the plague transmission, we collected real-time data from official reports, described the outbreak's characteristics, and estimated transmission parameters using statistical and mathematical models. The pneumonic plague epidemic curve exhibited multiple peaks, coinciding with sporadic introductions of new bubonic cases. Optimal climate conditions for rat flea to flourish were observed during the epidemic. Estimate of the plague basic reproduction number during the large wave of the epidemic was high, ranging from 5 to 7 depending on model assumptions. The incubation and infection periods for bubonic and pneumonic plague were 4.3 and 3.4 days and 3.8 and 2.9 days, respectively. Parameter estimation suggested that even with a small fraction of the population exposed to infected rat fleas (1/10,000) and a small probability of transition from a bubonic case to a secondary pneumonic case (3%), the high human-to-human transmission rate can still generate a large outbreak. Controlling rodent and fleas can prevent new index cases, but managing human-to-human transmission is key to prevent large-scale outbreaks. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.

Spatially explicit modelling of cholera epidemics

NASA Astrophysics Data System (ADS)

Finger, F.; Bertuzzo, E.; Mari, L.; Knox, A. C.; Gatto, M.; Rinaldo, A.

2013-12-01

Epidemiological models can provide crucial understanding about the dynamics of infectious diseases. Possible applications range from real-time forecasting and allocation of health care resources to testing alternative intervention mechanisms such as vaccines, antibiotics or the improvement of sanitary conditions. We apply a spatially explicit model to the cholera epidemic that struck Haiti in October 2010 and is still ongoing. The dynamics of susceptibles as well as symptomatic and asymptomatic infectives are modelled at the scale of local human communities. Dissemination of Vibrio cholerae through hydrological transport and human mobility along the road network is explicitly taken into account, as well as the effect of rainfall as a driver of increasing disease incidence. The model is calibrated using a dataset of reported cholera cases. We further model the long term impact of several types of interventions on the disease dynamics by varying parameters appropriately. Key epidemiological mechanisms and parameters which affect the efficiency of treatments such as antibiotics are identified. Our results lead to conclusions about the influence of different intervention strategies on the overall epidemiological dynamics.

Epidemic Spreading in a Multi-compartment System

NASA Astrophysics Data System (ADS)

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

2012-02-01

We introduce the variant rate and white noise into the susceptible-infected-removed (SIR) model for epidemics, discuss the epidemic dynamics of a multiple-compartment system, and describe this system by using master equations. For both the local epidemic spreading system and the whole multiple-compartment system, we find that a threshold could be useful in forecasting when the epidemic vanishes. Furthermore, numerical simulations show that a model with the variant infection rate and white noise can improve fitting with real SARS data.

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.

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.

Reversible Parallel Discrete-Event Execution of Large-scale Epidemic Outbreak Models

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

Perumalla, Kalyan S; Seal, Sudip K

2010-01-01

The spatial scale, runtime speed and behavioral detail of epidemic outbreak simulations together require the use of large-scale parallel processing. In this paper, an optimistic parallel discrete event execution of a reaction-diffusion simulation model of epidemic outbreaks is presented, with an implementation over themore » $$\\mu$$sik simulator. Rollback support is achieved with the development of a novel reversible model that combines reverse computation with a small amount of incremental state saving. Parallel speedup and other runtime performance metrics of the simulation are tested on a small (8,192-core) Blue Gene / P system, while scalability is demonstrated on 65,536 cores of a large Cray XT5 system. Scenarios representing large population sizes (up to several hundred million individuals in the largest case) are exercised.« less

Modeling historical tuberculosis epidemics among Canadian First Nations: effects of malnutrition and genetic variation

PubMed Central

Ackley, Sarah F.; Liu, Fengchen; Porco, Travis C.

2015-01-01

Late 19th century epidemics of tuberculosis (TB) in Western Canadian First Nations resulted in peak TB mortality rates more than six times the highest rates recorded in Europe. Using a mathematical modeling approach and historical TB mortality time series, we investigate potential causes of high TB mortality and rapid epidemic decline in First Nations from 1885 to 1940. We explore two potential causes of dramatic epidemic dynamics observed in this setting: first, we explore effects of famine prior to 1900 on both TB and population dynamics. Malnutrition is recognized as an individual-level risk factor for TB progression and mortality; its population-level effects on TB epidemics have not been explored previously. Second, we explore effects of heterogeneity in susceptibility to TB in two ways: modeling heterogeneity in susceptibility to infection, and heterogeneity in risk of developing disease once infected. Our results indicate that models lacking famine-related changes in TB parameters or heterogeneity result in an implausibly poor fit to both the TB mortality time series and census data; the inclusion of these features allows for the characteristic decline and rise in population observed in First Nations during this time period and confers improved fits to TB mortality data. PMID:26421237

Stability of differential susceptibility and infectivity epidemic models

PubMed Central

Bonzi, B.; Fall, A. A.; Iggidr, Abderrahman; Sallet, Gauthier

2011-01-01

We introduce classes of differential susceptibility and infectivity epidemic models. These models address the problem of flows between the different susceptible, infectious and infected compartments and differential death rates as well. We prove the global stability of the disease free equilibrium when the basic reproduction ratio ≤ 1 and the existence and uniqueness of an endemic equilibrium when > 1. We also prove the global asymptotic stability of the endemic equilibrium for a differential susceptibility and staged progression infectivity model, when > 1. Our results encompass and generalize those of [18, 22]. AMS Subject Classification : 34A34,34D23,34D40,92D30 PMID:20148330

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.

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.

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.

Bi-Hamiltonian structure of the Kermack-McKendrick model for epidemics

NASA Astrophysics Data System (ADS)

Nutku, Y.

1990-11-01

The dynamical system proposed by Kermack and McKendrick (1933) to model the spread of epidemics is shown to admit bi-Hamiltonian structure without any restrictions on the rate constants. These two inequivalent Hamiltonian structures are compatible.

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.

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

Periodic re-emergence of endemic strains with strong epidemic potential-a proposed explanation for the 2004 Indonesian dengue epidemic.

PubMed

Ong, Swee Hoe; Yip, Jin Teen; Chen, Yen Liang; Liu, Wei; Harun, Syahrial; Lystiyaningsih, Erlin; Heriyanto, Bambang; Beckett, Charmagne G; Mitchell, Wayne P; Hibberd, Martin L; Suwandono, Agus; Vasudevan, Subhash G; Schreiber, Mark J

2008-03-01

Indonesia experienced a severe dengue epidemic in the first quarter of 2004 with 58,301 cases and 658 deaths reported to the WHO. All four dengue virus (DENV) serotypes were detected, with DENV-3 the predominant strain. To ascertain the molecular epidemiology of the DENV associated with the epidemic, complete genomes of 15 isolates were sequenced from patient serum collected in Jakarta during the epidemic, and two historical DENV-3 isolates from previous epidemics in 1988 and 1998 were selectively sequenced for comparative studies. Phylogenetic trees for all four serotypes indicate the viruses are endemic strains that have been circulating in Indonesia for a few decades. Whole-genome phylogeny showed the 2004 DENV-3 isolates share high similarity with those isolated in 1998 during a major epidemic in Sumatra. Together these subtype I DENV-3 strains form a Sumatran-Javan clade with demonstrated epidemic potential. No newly-acquired amino acid mutations were found while comparing genomes from the two epidemics. This suggests re-emergence of little-changed endemic strains as causative agents of the epidemic in 2004. Notably, the molecular evidence rules out change in the viral genomes as the trigger of the epidemic.

Epidemic processes in complex networks

NASA Astrophysics Data System (ADS)

Pastor-Satorras, Romualdo; Castellano, Claudio; Van Mieghem, Piet; Vespignani, Alessandro

2015-07-01

In recent years the research community has accumulated overwhelming evidence for the emergence of complex and heterogeneous connectivity patterns in a wide range of biological and sociotechnical systems. The complex properties of real-world networks have a profound impact on the behavior of equilibrium and nonequilibrium phenomena occurring in various systems, and the study of epidemic spreading is central to our understanding of the unfolding of dynamical processes in complex networks. The theoretical analysis of epidemic spreading in heterogeneous networks requires the development of novel analytical frameworks, and it has produced results of conceptual and practical relevance. A coherent and comprehensive review of the vast research activity concerning epidemic processes is presented, detailing the successful theoretical approaches as well as making their limits and assumptions clear. Physicists, mathematicians, epidemiologists, computer, and social scientists share a common interest in studying epidemic spreading and rely on similar models for the description of the diffusion of pathogens, knowledge, and innovation. For this reason, while focusing on the main results and the paradigmatic models in infectious disease modeling, the major results concerning generalized social contagion processes are also presented. Finally, the research activity at the forefront in the study of epidemic spreading in coevolving, coupled, and time-varying networks is reported.

Modelling cholera epidemics: the role of waterways, human mobility and sanitation

PubMed Central

Mari, L.; Bertuzzo, E.; Righetto, L.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.

2012-01-01

We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000–2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies. PMID:21752809

Modelling cholera epidemics: the role of waterways, human mobility and sanitation.

PubMed

Mari, L; Bertuzzo, E; Righetto, L; Casagrandi, R; Gatto, M; Rodriguez-Iturbe, I; Rinaldo, A

2012-02-07

We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000-2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies.

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.

Modeling the dynamical interaction between epidemics on overlay networks

NASA Astrophysics Data System (ADS)

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

2011-08-01

Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. By exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytical approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g., the spread of preventive information in the context of an emerging infectious disease).

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

Bifurcation analysis in SIR epidemic model with treatment

NASA Astrophysics Data System (ADS)

Balamuralitharan, S.; Radha, M.

2018-04-01

We investigated the bifurcation analysis of nonlinear system of SIR epidemic model with treatment. It is accepted that the treatment is corresponding to the quantity of infective which is below the limit and steady when the quantity of infective achieves the limit. We analyze about the Transcritical bifurcation which occurs at the disease free equilibrium point and Hopf bifurcation which occurs at endemic equilibrium point. Using MATLAB we show the picture of bifurcation at the disease free equilibrium point.

Implementation and validation of an economic module in the Be-FAST model to predict costs generated by livestock disease epidemics: Application to classical swine fever epidemics in Spain.

PubMed

Fernández-Carrión, E; Ivorra, B; Martínez-López, B; Ramos, A M; Sánchez-Vizcaíno, J M

2016-04-01

Be-FAST is a computer program based on a time-spatial stochastic spread mathematical model for studying the transmission of infectious livestock diseases within and between farms. The present work describes a new module integrated into Be-FAST to model the economic consequences of the spreading of classical swine fever (CSF) and other infectious livestock diseases within and between farms. CSF is financially one of the most damaging diseases in the swine industry worldwide. Specifically in Spain, the economic costs in the two last CSF epidemics (1997 and 2001) reached jointly more than 108 million euros. The present analysis suggests that severe CSF epidemics are associated with significant economic costs, approximately 80% of which are related to animal culling. Direct costs associated with control measures are strongly associated with the number of infected farms, while indirect costs are more strongly associated with epidemic duration. The economic model has been validated with economic information around the last outbreaks in Spain. These results suggest that our economic module may be useful for analysing and predicting economic consequences of livestock disease epidemics. Copyright © 2016 Elsevier B.V. All rights reserved.

Dynamics of a network-based SIS epidemic model with nonmonotone incidence rate

NASA Astrophysics Data System (ADS)

Li, Chun-Hsien

2015-06-01

This paper studies the dynamics of a network-based SIS epidemic model with nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological effect of certain diseases spread in a contact network at high infective levels. We first find a threshold value for the transmission rate. This value completely determines the dynamics of the model and interestingly, the threshold is not dependent on the functional form of the nonlinear incidence rate. Furthermore, if the transmission rate is less than or equal to the threshold value, the disease will die out. Otherwise, it will be permanent. Numerical experiments are given to illustrate the theoretical results. We also consider the effect of the nonlinear incidence on the epidemic dynamics.

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.

Effects of local and global network connectivity on synergistic epidemics

NASA Astrophysics Data System (ADS)

Broder-Rodgers, David; Pérez-Reche, Francisco J.; Taraskin, Sergei N.

2015-12-01

Epidemics in networks can be affected by cooperation in transmission of infection and also connectivity between nodes. An interplay between these two properties and their influence on epidemic spread are addressed in the paper. A particular type of cooperative effects (called synergy effects) is considered, where the transmission rate between a pair of nodes depends on the number of infected neighbors. The connectivity effects are studied by constructing networks of different topology, starting with lattices with only local connectivity and then with networks that have both local and global connectivity obtained by random bond-rewiring to nodes within a certain distance. The susceptible-infected-removed epidemics were found to exhibit several interesting effects: (i) for epidemics with strong constructive synergy spreading in networks with high local connectivity, the bond rewiring has a negative role in epidemic spread, i.e., it reduces invasion probability; (ii) in contrast, for epidemics with destructive or weak constructive synergy spreading on networks of arbitrary local connectivity, rewiring helps epidemics to spread; (iii) and, finally, rewiring always enhances the spread of epidemics, independent of synergy, if the local connectivity is low.

Effects of local and global network connectivity on synergistic epidemics.

PubMed

Broder-Rodgers, David; Pérez-Reche, Francisco J; Taraskin, Sergei N

2015-12-01

Epidemics in networks can be affected by cooperation in transmission of infection and also connectivity between nodes. An interplay between these two properties and their influence on epidemic spread are addressed in the paper. A particular type of cooperative effects (called synergy effects) is considered, where the transmission rate between a pair of nodes depends on the number of infected neighbors. The connectivity effects are studied by constructing networks of different topology, starting with lattices with only local connectivity and then with networks that have both local and global connectivity obtained by random bond-rewiring to nodes within a certain distance. The susceptible-infected-removed epidemics were found to exhibit several interesting effects: (i) for epidemics with strong constructive synergy spreading in networks with high local connectivity, the bond rewiring has a negative role in epidemic spread, i.e., it reduces invasion probability; (ii) in contrast, for epidemics with destructive or weak constructive synergy spreading on networks of arbitrary local connectivity, rewiring helps epidemics to spread; (iii) and, finally, rewiring always enhances the spread of epidemics, independent of synergy, if the local connectivity is low.

Epidemic spread on interconnected metapopulation networks

NASA Astrophysics Data System (ADS)

Wang, Bing; Tanaka, Gouhei; Suzuki, Hideyuki; Aihara, Kazuyuki

2014-09-01

Numerous real-world networks have been observed to interact with each other, resulting in interconnected networks that exhibit diverse, nontrivial behavior with dynamical processes. Here we investigate epidemic spreading on interconnected networks at the level of metapopulation. Through a mean-field approximation for a metapopulation model, we find that both the interaction network topology and the mobility probabilities between subnetworks jointly influence the epidemic spread. Depending on the interaction between subnetworks, proper controls of mobility can efficiently mitigate epidemics, whereas an extremely biased mobility to one subnetwork will typically cause a severe outbreak and promote the epidemic spreading. Our analysis provides a basic framework for better understanding of epidemic behavior in related transportation systems as well as for better control of epidemics by guiding human mobility patterns.

Optical Coherence Tomographic Comparison of Cuban Epidemic and Leber’s Hereditary Optic Neuropathy

PubMed Central

Santiesteban-Freixas, Rosaralis; Pola-Alvarado, Lester; Columbie-Garbey, Yannara; Gonzalez-Quevedo, Alina; Juvier-Riesgo, Tamara; Hernandez-Echevarria, Odelaisys; Hedges, Thomas R.; Mendoza-Santiesteban, Carlos

2015-01-01

Abstract Following the epidemic of optic and peripheral neuropathy, which occurred in Cuba between 1991 and 1993, a number of patients have been re-evaluated, including testing with optical coherence tomography (OCT) and electrophysiology. At the same time, a number of patients with Leber’s hereditary optic neuropathy have also been evaluated. The purpose of this study was to detect residual loss of retinal nerve fibre layer (RNFL) in patients who suffered Cuban epidemic optic neuropathy (CEON), and to compare these findings with those in patients with Leber’s hereditary optic neuropathy (LHON). Optical coherence tomography as well as clinical examinations were performed on 11 patients diagnosed with CEON 15 years following the epidemic and 14 patients with LHON. OCT in CEON patients showed thinning of the RNFL in the temporal sector and normal thickness in other quadrants. However, patients with chronic LHON had more diffuse RNFL loss throughout the retina. OCT findings corresponded with clinical findings in CEON and LHON. There was drop out of the papillomacular bundle in both diseases. Two patients in the acute stages of LHON and three LHON carriers showed thinning of the temporal RNFL only. This is the first report of OCT in CEON that shows residual damage in the papillomacular bundle compared with chronic LHON where there is more diffuse and progressive loss of the RNFL. The importance of OCT for the diagnosis and evaluation of similar optic neuropathies is emphasised. PMID:27928368

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

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

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).

The politics of pathology: how obesity became an epidemic disease.

PubMed

Oliver, J Eric

2006-01-01

Americans' recent weight gains have been widely described as an "obesity epidemic." Such a characterization, however, has many problems: the average American weight gain has been relatively low (eight to 12 pounds over the last 20 years), and the causal linkages between adiposity, morbidity, and mortality are unclear. Nevertheless, the media and numerous health officials continue to sound dire warnings that obesity has become an epidemic disease. In this article, I examine how and why America's growing weight became an "obesity epidemic." I find the disease characterization has less to do with the health consequences of excess weight and more with the various financial and political incentives of the weight loss industry, medical profession, and public health bureaucracy. This epidemic image was also assisted by the method of displaying information about weight gain with maps in PowerPoint slides. Such characterizations, I argue, are problematic. Given the inconclusive scientific evidence and the absence of a safe and effective weight loss regimen, calling America's growing weight an epidemic disease is likely to cause more harm than good.

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.

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 analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks.

PubMed

Zhang, Juping; Yang, Chan; Jin, Zhen; Li, Jia

2018-07-14

In this paper, the correlation coefficients between nodes in states are used as dynamic variables, and we construct SIR epidemic dynamic models with correlation coefficients by using the pair approximation method in static networks and dynamic networks, respectively. Considering the clustering coefficient of the network, we analytically investigate the existence and the local asymptotic stability of each equilibrium of these models and derive threshold values for the prevalence of diseases. Additionally, we obtain two equivalent epidemic thresholds in dynamic networks, which are compared with the results of the mean field equations. Copyright © 2018 Elsevier Ltd. All rights reserved.

Epidemic cholera spreads like wildfire

NASA Astrophysics Data System (ADS)

Roy, Manojit; Zinck, Richard D.; Bouma, Menno J.; Pascual, Mercedes

2014-01-01

Cholera is on the rise globally, especially epidemic cholera which is characterized by intermittent and unpredictable outbreaks that punctuate periods of regional disease fade-out. These epidemic dynamics remain however poorly understood. Here we examine records for epidemic cholera over both contemporary and historical timelines, from Africa (1990-2006) and former British India (1882-1939). We find that the frequency distribution of outbreak size is fat-tailed, scaling approximately as a power-law. This pattern which shows strong parallels with wildfires is incompatible with existing cholera models developed for endemic regions, as it implies a fundamental role for stochastic transmission and local depletion of susceptible hosts. Application of a recently developed forest-fire model indicates that epidemic cholera dynamics are located above a critical phase transition and propagate in similar ways to aggressive wildfires. These findings have implications for the effectiveness of control measures and the mechanisms that ultimately limit the size of outbreaks.

Epidemic cholera spreads like wildfire

PubMed Central

Roy, Manojit; Zinck, Richard D.; Bouma, Menno J.; Pascual, Mercedes

2014-01-01

Cholera is on the rise globally, especially epidemic cholera which is characterized by intermittent and unpredictable outbreaks that punctuate periods of regional disease fade-out. These epidemic dynamics remain however poorly understood. Here we examine records for epidemic cholera over both contemporary and historical timelines, from Africa (1990–2006) and former British India (1882–1939). We find that the frequency distribution of outbreak size is fat-tailed, scaling approximately as a power-law. This pattern which shows strong parallels with wildfires is incompatible with existing cholera models developed for endemic regions, as it implies a fundamental role for stochastic transmission and local depletion of susceptible hosts. Application of a recently developed forest-fire model indicates that epidemic cholera dynamics are located above a critical phase transition and propagate in similar ways to aggressive wildfires. These findings have implications for the effectiveness of control measures and the mechanisms that ultimately limit the size of outbreaks. PMID:24424273

Epidemic cholera spreads like wildfire.

PubMed

Roy, Manojit; Zinck, Richard D; Bouma, Menno J; Pascual, Mercedes

2014-01-15

Cholera is on the rise globally, especially epidemic cholera which is characterized by intermittent and unpredictable outbreaks that punctuate periods of regional disease fade-out. These epidemic dynamics remain however poorly understood. Here we examine records for epidemic cholera over both contemporary and historical timelines, from Africa (1990-2006) and former British India (1882-1939). We find that the frequency distribution of outbreak size is fat-tailed, scaling approximately as a power-law. This pattern which shows strong parallels with wildfires is incompatible with existing cholera models developed for endemic regions, as it implies a fundamental role for stochastic transmission and local depletion of susceptible hosts. Application of a recently developed forest-fire model indicates that epidemic cholera dynamics are located above a critical phase transition and propagate in similar ways to aggressive wildfires. These findings have implications for the effectiveness of control measures and the mechanisms that ultimately limit the size of outbreaks.

On Spatially Explicit Models of Cholera Epidemics: Hydrologic controls, environmental drivers, human-mediated transmissions (Invited)

NASA Astrophysics Data System (ADS)

Rinaldo, A.; Bertuzzo, E.; Mari, L.; Righetto, L.; Gatto, M.; Casagrandi, R.; Rodriguez-Iturbe, I.

2010-12-01

A recently proposed model for cholera epidemics is examined. The model accounts for local communities of susceptibles and infectives in a spatially explicit arrangement of nodes linked by networks having different topologies. The vehicle of infection (Vibrio cholerae) is transported through the network links which are thought of as hydrological connections among susceptible communities. The mathematical tools used are borrowed from general schemes of reactive transport on river networks acting as the environmental matrix for the circulation and mixing of water-borne pathogens. The results of a large-scale application to the Kwa Zulu (Natal) epidemics of 2001-2002 will be discussed. Useful theoretical results derived in the spatially-explicit context will also be reviewed (like e.g. the exact derivation of the speed of propagation for traveling fronts of epidemics on regular lattices endowed with uniform population density). Network effects will be discussed. The analysis of the limit case of uniformly distributed population density proves instrumental in establishing the overall conditions for the relevance of spatially explicit models. To that extent, it is shown that the ratio between spreading and disease outbreak timescales proves the crucial parameter. The relevance of our results lies in the major differences potentially arising between the predictions of spatially explicit models and traditional compartmental models of the SIR-like type. Our results suggest that in many cases of real-life epidemiological interest timescales of disease dynamics may trigger outbreaks that significantly depart from the predictions of compartmental models. Finally, a view on further developments includes: hydrologically improved aquatic reservoir models for pathogens; human mobility patterns affecting disease propagation; double-peak emergence and seasonality in the spatially explicit epidemic context.

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

Metapopulation epidemic models with heterogeneous mixing and travel behaviour

PubMed Central

2014-01-01

Background Determining the pandemic potential of an emerging infectious disease and how it depends on the various epidemic and population aspects is critical for the preparation of an adequate response aimed at its control. The complex interplay between population movements in space and non-homogeneous mixing patterns have so far hindered the fundamental understanding of the conditions for spatial invasion through a general theoretical framework. To address this issue, we present an analytical modelling approach taking into account such interplay under general conditions of mobility and interactions, in the simplifying assumption of two population classes. Methods We describe a spatially structured population with non-homogeneous mixing and travel behaviour through a multi-host stochastic epidemic metapopulation model. Different population partitions, mixing patterns and mobility structures are considered, along with a specific application for the study of the role of age partition in the early spread of the 2009 H1N1 pandemic influenza. Results We provide a complete mathematical formulation of the model and derive a semi-analytical expression of the threshold condition for global invasion of an emerging infectious disease in the metapopulation system. A rich solution space is found that depends on the social partition of the population, the pattern of contacts across groups and their relative social activity, the travel attitude of each class, and the topological and traffic features of the mobility network. Reducing the activity of the less social group and reducing the cross-group mixing are predicted to be the most efficient strategies for controlling the pandemic potential in the case the less active group constitutes the majority of travellers. If instead traveling is dominated by the more social class, our model predicts the existence of an optimal across-groups mixing that maximises the pandemic potential of the disease, whereas the impact of variations in

Metapopulation epidemic models with heterogeneous mixing and travel behaviour.

PubMed

Apolloni, Andrea; Poletto, Chiara; Ramasco, José J; Jensen, Pablo; Colizza, Vittoria

2014-01-13

Determining the pandemic potential of an emerging infectious disease and how it depends on the various epidemic and population aspects is critical for the preparation of an adequate response aimed at its control. The complex interplay between population movements in space and non-homogeneous mixing patterns have so far hindered the fundamental understanding of the conditions for spatial invasion through a general theoretical framework. To address this issue, we present an analytical modelling approach taking into account such interplay under general conditions of mobility and interactions, in the simplifying assumption of two population classes. We describe a spatially structured population with non-homogeneous mixing and travel behaviour through a multi-host stochastic epidemic metapopulation model. Different population partitions, mixing patterns and mobility structures are considered, along with a specific application for the study of the role of age partition in the early spread of the 2009 H1N1 pandemic influenza. We provide a complete mathematical formulation of the model and derive a semi-analytical expression of the threshold condition for global invasion of an emerging infectious disease in the metapopulation system. A rich solution space is found that depends on the social partition of the population, the pattern of contacts across groups and their relative social activity, the travel attitude of each class, and the topological and traffic features of the mobility network. Reducing the activity of the less social group and reducing the cross-group mixing are predicted to be the most efficient strategies for controlling the pandemic potential in the case the less active group constitutes the majority of travellers. If instead traveling is dominated by the more social class, our model predicts the existence of an optimal across-groups mixing that maximises the pandemic potential of the disease, whereas the impact of variations in the activity of each group

Heterogeneity in geographical trends of HIV epidemics among key populations in Pakistan: a mathematical modeling study of survey data.

PubMed

Melesse, Dessalegn Y; Shafer, Leigh Anne; Emmanuel, Faran; Reza, Tahira; Achakzai, Baseer K; Furqan, Sofia; Blanchard, James F

2018-06-01

Assessing patterns and trends in new infections is key to better understanding of HIV epidemics, and is best done through monitoring changes in incidence over time. In this study, we examined disparities in geographical trends of HIV epidemics among people who inject drugs (PWIDs), female sex workers (FSWs) and hijra /transgender/male sex workers (H/MSWs), in Pakistan. The UNAIDS Estimation and Projection Package (EPP) mathematical model was used to explore geographical trends in HIV epidemics. Four rounds of mapping and surveillance data collected among key populations (KPs) across 20 cities in Pakistan between 2005-2011 was used for modeling. Empirical estimates of HIV prevalence of each KP in each city were used to fit the model to estimate prevalence and incidence over time. HIV incidence among PWIDs in Pakistan reached its peak in 2011, estimated at 45.3 per 1000 person-years. Incidence was projected to continue to rise from 18.9 in 2015 to 24.3 in 2020 among H/MSWs and from 3.2 in 2015 to 6.3 in 2020 among FSWs. The number of people living with HIV in Pakistan was estimated to steadily increase through at least 2020. HIV incidence peak among PWIDs ranged from 16.2 in 1997 in Quetta to 71.0 in 2010 in Faisalabad (per 1000 person-years). Incidence among H/MSWs may continue to rise through 2020 in all the cities, except in Larkana where it peaked in the early 2000s. In 2015, model estimated incidence among FSWs was 8.1 in Karachi, 6.6 in Larkana, 2.0 in Sukkur and 1.2 in Lahore (per 1000 person-years). There exists significant geographical heterogeneity in patterns and trends of HIV sub-epidemics in Pakistan. Focused interventions and service delivery approaches, different by KP and city, are recommended.

Heterogeneity in geographical trends of HIV epidemics among key populations in Pakistan: a mathematical modeling study of survey data

PubMed Central

Melesse, Dessalegn Y; Shafer, Leigh Anne; Emmanuel, Faran; Reza, Tahira; Achakzai, Baseer K; Furqan, Sofia; Blanchard, James F

2018-01-01

Background Assessing patterns and trends in new infections is key to better understanding of HIV epidemics, and is best done through monitoring changes in incidence over time. In this study, we examined disparities in geographical trends of HIV epidemics among people who inject drugs (PWIDs), female sex workers (FSWs) and hijra/transgender/male sex workers (H/MSWs), in Pakistan. Methods The UNAIDS Estimation and Projection Package (EPP) mathematical model was used to explore geographical trends in HIV epidemics. Four rounds of mapping and surveillance data collected among key populations (KPs) across 20 cities in Pakistan between 2005-2011 was used for modeling. Empirical estimates of HIV prevalence of each KP in each city were used to fit the model to estimate prevalence and incidence over time. Results HIV incidence among PWIDs in Pakistan reached its peak in 2011, estimated at 45.3 per 1000 person-years. Incidence was projected to continue to rise from 18.9 in 2015 to 24.3 in 2020 among H/MSWs and from 3.2 in 2015 to 6.3 in 2020 among FSWs. The number of people living with HIV in Pakistan was estimated to steadily increase through at least 2020. HIV incidence peak among PWIDs ranged from 16.2 in 1997 in Quetta to 71.0 in 2010 in Faisalabad (per 1000 person-years). Incidence among H/MSWs may continue to rise through 2020 in all the cities, except in Larkana where it peaked in the early 2000s. In 2015, model estimated incidence among FSWs was 8.1 in Karachi, 6.6 in Larkana, 2.0 in Sukkur and 1.2 in Lahore (per 1000 person-years). Conclusions There exists significant geographical heterogeneity in patterns and trends of HIV sub-epidemics in Pakistan. Focused interventions and service delivery approaches, different by KP and city, are recommended. PMID:29770215

Epidemics, Exponential Functions, and Modeling

ERIC Educational Resources Information Center

Bush, Sarah B.; Gibbons, Katie; Karp, Karen S.; Dillon, Fred

2015-01-01

The phenomenon of outbreaks of dangerous diseases is both intriguing to students and of mathematical significance, which is exactly why the authors engaged eighth graders in an introductory activity on the growth that occurs as an epidemic spreads. Various contexts can set the stage for such an exploration. Reading adolescent literature like…

Modelling dengue epidemic spreading with human mobility

NASA Astrophysics Data System (ADS)

Barmak, D. H.; Dorso, C. O.; Otero, M.

2016-04-01

We explored the effect of human mobility on the spatio-temporal dynamics of Dengue with a stochastic model that takes into account the epidemiological dynamics of the infected mosquitoes and humans, with different mobility patterns of the human population. We observed that human mobility strongly affects the spread of infection by increasing the final size and by changing the morphology of the epidemic outbreaks. When the spreading of the disease is driven only by mosquito dispersal (flight), a main central focus expands diffusively. On the contrary, when human mobility is taken into account, multiple foci appear throughout the evolution of the outbreaks. These secondary foci generated throughout the outbreaks could be of little importance according to their mass or size compared with the largest main focus. However, the coalescence of these foci with the main one generates an effect, through which the latter develops a size greater than the one obtained in the case driven only by mosquito dispersal. This increase in growth rate due to human mobility and the coalescence of the foci are particularly relevant in temperate cities such as the city of Buenos Aires, since they give more possibilities to the outbreak to grow before the arrival of the low-temperature season. The findings of this work indicate that human mobility could be the main driving force in the dynamics of vector epidemics.

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 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.

Reverse-feeding effect of epidemic by propagators in two-layered networks

NASA Astrophysics Data System (ADS)

Dayu, Wu; Yanping, Zhao; Muhua, Zheng; Jie, Zhou; Zonghua, Liu

2016-02-01

Epidemic spreading has been studied for a long time and is currently focused on the spreading of multiple pathogens, especially in multiplex networks. However, little attention has been paid to the case where the mutual influence between different pathogens comes from a fraction of epidemic propagators, such as bisexual people in two separated groups of heterosexual and homosexual people. We here study this topic by presenting a network model of two layers connected by impulsive links, in contrast to the persistent links in each layer. We let each layer have a distinct pathogen and their interactive infection is implemented by a fraction of propagators jumping between the corresponding pairs of nodes in the two layers. By this model we show that (i) the propagators take the key role to transmit pathogens from one layer to the other, which significantly influences the stabilized epidemics; (ii) the epidemic thresholds will be changed by the propagators; and (iii) a reverse-feeding effect can be expected when the infective rate is smaller than its threshold of isolated spreading. A theoretical analysis is presented to explain the numerical results. Project supported by the National Natural Science Foundation of China (Grant Nos. 11135001, 11375066, and 11405059) and the National Basic Key Program of China (Grant No. 2013CB834100).

Dynamic Patterns of Modern Epidemics

NASA Astrophysics Data System (ADS)

Brockmann, Dirk; Hufnagel, Lars; Geisel, Theo

2004-03-01

We investigate the effects of scale-free travelling of humans and their inhomogeneous geographic distribution on the dynamic patterns of spreading epidemics. Our approach combines the susceptible/infected/recovered paradigm for the infection dynamics with superdiffusive dispersion of individuals and their inhomogeneous spatial distribution. We show that scale-free motion of individuals and their variable spatial distribution leads to the absence of wavefronts in dynamic epidemic patterns which are typical for the limiting cases of ordinary diffusion and spatially homogeneous populations. Instead, patterns emerge with isolated hotspots on highly populated areas from which regional epidemic outbursts are triggered. Hotspot sizes are independent of the correlation length in the spatial distribution of individuals and occur on all scales. Our theory predicts that highly populated areas are reached by an epidemic in advance and must receive special attention in control measure strategies. Furthermore, our analysis predicts strong fluctuations in the time course of the total infection which cannot be accounted for by ordinary reaction-diffusion models for epidemics.

Estimation of sickness absenteeism among Italian healthcare workers during seasonal influenza epidemics

PubMed Central

Politano, Gianfranco; Scarmozzino, Antonio; Charrier, Lorena; Testa, Marco; Giacomelli, Sebastian; Benso, Alfredo; Zotti, Carla Maria

2017-01-01

Objectives To analyze absenteeism among healthcare workers (HCWs) at a large Italian hospital and to estimate the increase in absenteeism that occurred during seasonal flu periods. Design Retrospective observational study. Methods The absenteeism data were divided into three “epidemic periods,” starting at week 42 of one year and terminating at week 17 of the following year (2010–2011, 2011–2012, 2012–2013), and three “non-epidemic periods,” defined as week 18 to week 41 and used as baseline data. The excess of the absenteeism occurring among HCWs during periods of epidemic influenza in comparison with baseline was estimated. All data, obtained from Hospital’s databases, were collected for each of the following six job categories: medical doctors, technical executives (i.e., pharmacists), nurses and allied health professionals (i.e., radiographers), other executives (i.e., engineers), nonmedical support staff, and administrative staff. The HCWs were classified by: in and no-contact; vaccinated and unvaccinated. Results 5,544, 5,369, and 5,291 workers in three years were studied. The average duration of absenteeism during the epidemic periods increased among all employees by +2.07 days/person (from 2.99 to 5.06), and the relative increase ranged from 64–94% among the different job categories. Workers not in contact with patients experienced a slightly greater increase in absenteeism (+2.28 days/person, from 2.73 to 5.01) than did employees in contact with patients (+2.04, from 3.04 to 5.08). The vaccination rate among HCWs was below 3%, however the higher excess of absenteeism rate among unvaccinated in comparison with vaccinated workers was observed during the epidemic periods (2.09 vs 1.45 days/person). Conclusion The influenza-related absenteeism during epidemic periods was quantified as totaling more than 11,000 days/year at the Italian hospital studied. This result confirms the economic impact of sick leave on healthcare systems and stresses

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.

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.

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

R Factors in Strains of Salmonella typhi and Shigella dysenteriae 1 Isolated During Epidemics in Mexico: Classification by Compatibility

PubMed Central

Datta, Naomi; Olarte, J.

1974-01-01

All 17 Salmonella typhi strains tested from the epidemic in Mexico carried R factors of compatibility group H, conferring resistance to chloramphenicol, streptomycin, tetracycline, and sulfonamides. Some S. typhi strains carried, in addition, non-conjugative, ampicillin resistance plasmids and R factors of the I or A–C complex. All 20 Shigella dysenteriae 1 strains tested of epidemic origin carried O-group R factors. Ampicillin resistance in S. dysenteriae 1 was not proved to be plasmid borne. R factors of group H were not identified in any of the tested Mexican isolates other than S. typhi, but R factors of group O were identified in Escherichia coli, Shigella flexneri, and one strain of S. typhi, as well as in the epidemic S. dysenteriae. An R factor was identified which seemed to have two compatibility specificities, groups Iω and O. PMID:4599123

An epidemic model of rumor diffusion in online social networks

NASA Astrophysics Data System (ADS)

Cheng, Jun-Jun; Liu, Yun; Shen, Bo; Yuan, Wei-Guo

2013-01-01

So far, in some standard rumor spreading models, the transition probability from ignorants to spreaders is always treated as a constant. However, from a practical perspective, the case that individual whether or not be infected by the neighbor spreader greatly depends on the trustiness of ties between them. In order to solve this problem, we introduce a stochastic epidemic model of the rumor diffusion, in which the infectious probability is defined as a function of the strength of ties. Moreover, we investigate numerically the behavior of the model on a real scale-free social site with the exponent γ = 2.2. We verify that the strength of ties plays a critical role in the rumor diffusion process. Specially, selecting weak ties preferentially cannot make rumor spread faster and wider, but the efficiency of diffusion will be greatly affected after removing them. Another significant finding is that the maximum number of spreaders max( S) is very sensitive to the immune probability μ and the decay probability v. We show that a smaller μ or v leads to a larger spreading of the rumor, and their relationships can be described as the function ln(max( S)) = Av + B, in which the intercept B and the slope A can be fitted perfectly as power-law functions of μ. Our findings may offer some useful insights, helping guide the application in practice and reduce the damage brought by the rumor.

Mathematical modeling of Avian Influenza epidemic with bird vaccination in constant population

NASA Astrophysics Data System (ADS)

Kharis, M.; Amidi

2018-03-01

The development of the industrial world and human life is increasingly modern and less attention to environmental sustainability causes the virus causes the epidemic has a high tendency to mutate so that the virus that initially only attack animals, is also found to have the ability to attack humans. The epidemics that lasted some time were bird flu epidemics and swine flu epidemics. The flu epidemic led to several deaths and many people admitted to the hospital. Strain (derivatives) of H5N1 virus was identified as the cause of the bird flu epidemic while the H1N1 strain of the virus was identified as the cause of the swine flu epidemic. The symptoms are similar to seasonal flu caused by H3N2 strain of the virus. Outbreaks of bird flu and swine flu initially only attacked animals, but over time some people were found to be infected with the virus.

Dynamical analysis of the avian-human influenza epidemic model using the semi-analytical method

NASA Astrophysics Data System (ADS)

Jabbari, Azizeh; Kheiri, Hossein; Bekir, Ahmet

2015-03-01

In this work, we present a dynamic behavior of the avian-human influenza epidemic model by using efficient computational algorithm, namely the multistage differential transform method(MsDTM). The MsDTM is used here as an algorithm for approximating the solutions of the avian-human influenza epidemic model in a sequence of time intervals. In order to show the efficiency of the method, the obtained numerical results are compared with the fourth-order Runge-Kutta method (RK4M) and differential transform method(DTM) solutions. It is shown that the MsDTM has the advantage of giving an analytical form of the solution within each time interval which is not possible in purely numerical techniques like RK4M.

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.

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.

Oscillations in epidemic models with spread of awareness.

PubMed

Just, Winfried; Saldaña, Joan; Xin, Ying

2018-03-01

We study ODE models of epidemic spreading with a preventive behavioral response that is triggered by awareness of the infection. Previous studies of such models have mostly focused on the impact of the response on the initial growth of an outbreak and the existence and location of endemic equilibria. Here we study the question whether this type of response is sufficient to prevent future flare-ups from low endemic levels if awareness is assumed to decay over time. In the ODE context, such flare-ups would translate into sustained oscillations with significant amplitudes. Our results show that such oscillations are ruled out in Susceptible-Aware-Infectious-Susceptible models with a single compartment of aware hosts, but can occur if we consider two distinct compartments of aware hosts who differ in their willingness to alert other susceptible hosts.

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

Epidemics of panic during a bioterrorist attack--a mathematical model.

PubMed

Radosavljevic, Vladan; Radunovic, Desanka; Belojevic, Goran

2009-09-01

A bioterrorist attacks usually cause epidemics of panic in a targeted population. We have presented epidemiologic aspect of this phenomenon as a three-component model--host, information on an attack and social network. We have proposed a mathematical model of panic and counter-measures as the function of time in a population exposed to a bioterrorist attack. The model comprises ordinary differential equations and graphically presented combinations of the equations parameters. Clinically, we have presented a model through a sequence of psychic conditions and disorders initiated by an act of bioterrorism. This model might be helpful for an attacked community to timely and properly apply counter-measures and to minimize human mental suffering during a bioterrorist attack.

Smoking uptake among Saudi adolescents: tobacco epidemic indicators and preventive actions needed.

PubMed

Mohammed, Mutaz; Eggers, Sander Matthijs; Alotaiby, Fahad Falah; de Vries, Nanne; de Vries, Hein

2014-11-25

The aim of this cross-sectional school-based study was to assess smoking prevalence, indicators for the smoking epidemic and determinants of smoking among Saudi adolescents. The study included 695 male adolescents from 11 to 16 years of age who filled out self-report questionnaires based on the European Smoking Framework Approach questionnaire, which uses the I-Change model to assess attitude, social influence and the self-efficacy of the participants. Smokers were 275 (39.6%) adolescents. Smokers tended to receive more daily pocket money, live in more affluent families and show lower academic performance. Non-smokers were inclined to believe that smoking may help people to feel relaxed and confident, encountered less social influences to smoke than smokers, but reported low self-efficacy not to smoke when with smoker friends and when offered a cigarette. Smokers reported the lowest self-efficacy not to smoke in all situations assessed. The results suggest the smoking epidemic among male Saudi adolescents may still be in the early stages, providing ample opportunity for preventive actions aimed at halting the further progress of this epidemic. Secondly, smoking prevention programs in Saudi Arabia need to reinforce non-smoking attitudes, address how to resist pressure to smoke, and how to develop high self-efficacy towards non-smoking in various situations. © The Author(s) 2014.

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

MOSES: A Matlab-based open-source stochastic epidemic simulator.

PubMed

Varol, Huseyin Atakan

2016-08-01

This paper presents an open-source stochastic epidemic simulator. Discrete Time Markov Chain based simulator is implemented in Matlab. The simulator capable of simulating SEQIJR (susceptible, exposed, quarantined, infected, isolated and recovered) model can be reduced to simpler models by setting some of the parameters (transition probabilities) to zero. Similarly, it can be extended to more complicated models by editing the source code. It is designed to be used for testing different control algorithms to contain epidemics. The simulator is also designed to be compatible with a network based epidemic simulator and can be used in the network based scheme for the simulation of a node. Simulations show the capability of reproducing different epidemic model behaviors successfully in a computationally efficient manner.

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

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.

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

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

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].

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).

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.

Spatiotemporal modelling and mapping of the bubonic plague epidemic in India.

PubMed

Yu, Hwa-Lung; Christakos, George

2006-03-17

This work studies the spatiotemporal evolution of bubonic plague in India during 1896-1906 using stochastic concepts and geographical information science techniques. In the past, most investigations focused on selected cities to conduct different kinds of studies, such as the ecology of rats. No detailed maps existed incorporating the space-time dependence structure and uncertainty sources of the epidemic system and providing a composite space-time picture of the disease propagation characteristics. Informative spatiotemporal maps were generated that represented mortality rates and geographical spread of the disease, and epidemic indicator plots were derived that offered meaningful characterizations of the spatiotemporal disease distribution. The bubonic plague in India exhibited strong seasonal and geographical features. During its entire duration, the plague continued to invade new geographical areas, while it followed a re-emergence pattern at many localities; its rate changed significantly during each year and the mortality distribution exhibited space-time heterogeneous patterns; prevalence usually occurred in the autumn and spring, whereas the plague stopped moving towards new locations during the summers. Modern stochastic modelling and geographical information science provide powerful means to study the spatiotemporal distribution of the bubonic plague epidemic under conditions of uncertainty and multi-sourced databases; to account for various forms of interdisciplinary knowledge; and to generate informative space-time maps of mortality rates and propagation patterns. To the best of our knowledge, this kind of plague maps and plots become available for the first time, thus providing novel perspectives concerning the distribution and space-time propagation of the deadly epidemic. Furthermore, systematic maps and indicator plots make possible the comparison of the spatial-temporal propagation patterns of different diseases.

Spatiotemporal modelling and mapping of the bubonic plague epidemic in India

PubMed Central

Yu, Hwa-Lung; Christakos, George

2006-01-01

Background This work studies the spatiotemporal evolution of bubonic plague in India during 1896–1906 using stochastic concepts and geographical information science techniques. In the past, most investigations focused on selected cities to conduct different kinds of studies, such as the ecology of rats. No detailed maps existed incorporating the space-time dependence structure and uncertainty sources of the epidemic system and providing a composite space-time picture of the disease propagation characteristics. Results Informative spatiotemporal maps were generated that represented mortality rates and geographical spread of the disease, and epidemic indicator plots were derived that offered meaningful characterizations of the spatiotemporal disease distribution. The bubonic plague in India exhibited strong seasonal and geographical features. During its entire duration, the plague continued to invade new geographical areas, while it followed a re-emergence pattern at many localities; its rate changed significantly during each year and the mortality distribution exhibited space-time heterogeneous patterns; prevalence usually occurred in the autumn and spring, whereas the plague stopped moving towards new locations during the summers. Conclusion Modern stochastic modelling and geographical information science provide powerful means to study the spatiotemporal distribution of the bubonic plague epidemic under conditions of uncertainty and multi-sourced databases; to account for various forms of interdisciplinary knowledge; and to generate informative space-time maps of mortality rates and propagation patterns. To the best of our knowledge, this kind of plague maps and plots become available for the first time, thus providing novel perspectives concerning the distribution and space-time propagation of the deadly epidemic. Furthermore, systematic maps and indicator plots make possible the comparison of the spatial-temporal propagation patterns of different diseases

Epidemic predictions in an imperfect world: modelling disease spread with partial data

PubMed Central

Dawson, Peter M.; Werkman, Marleen; Brooks-Pollock, Ellen; Tildesley, Michael J.

2015-01-01

‘Big-data’ epidemic models are being increasingly used to influence government policy to help with control and eradication of infectious diseases. In the case of livestock, detailed movement records have been used to parametrize realistic transmission models. While livestock movement data are readily available in the UK and other countries in the EU, in many countries around the world, such detailed data are not available. By using a comprehensive database of the UK cattle trade network, we implement various sampling strategies to determine the quantity of network data required to give accurate epidemiological predictions. It is found that by targeting nodes with the highest number of movements, accurate predictions on the size and spatial spread of epidemics can be made. This work has implications for countries such as the USA, where access to data is limited, and developing countries that may lack the resources to collect a full dataset on livestock movements. PMID:25948687

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

Toxic Epidemics: Agent Orange Sickness in Vietnam and the United States.

PubMed

Uesugi, Tak

2016-01-01

Social scientists studying toxic epidemics have often endeavored to shed light on the differences between scientists' and nonscientists' epistemic perspectives. Yet, little attention has been paid to the processes through which a toxic epidemic emerges as a phenomenon. A Luoi Valley of Central Vietnam was extensively sprayed with chemical defoliants (including Agent Orange) during the Vietnam War. The latent toxic effects of these chemicals, however, went largely unnoticed until the late 1990s. By juxtaposing the history through which the notion of "Agent Orange Sickness" emerged in the United States with an ethnographic study of A Luoi, I explore the notion of poison under which Agent Orange became recognizable as a poison.

Household demographic determinants of Ebola epidemic risk.

PubMed

Adams, Ben

2016-03-07

A salient characteristic of Ebola, and some other infectious diseases such as Tuberculosis, is intense transmission among small groups of cohabitants and relatively limited indiscriminate transmission in the wider population. Here we consider a mathematical model for an Ebola epidemic in a population structured into households of equal size. We show that household size, a fundamental demographic unit, is a critical factor that determines the vulnerability of a community to epidemics, and the effort required to control them. Our analysis is based on the household reproduction number, but we also consider the basic reproduction number, intrinsic growth rate and final epidemic size. We show that, when other epidemiological parameters are kept the same, all of these quantifications of epidemic growth and size are increased by larger households and more intense within-household transmission. We go on to model epidemic control by case detection and isolation followed by household quarantine. We show that, if household quarantine is ineffective, the critical probability with which cases must be detected to halt an epidemic increases significantly with each increment in household size and may be a very challenging target for communities composed of large households. Effective quarantine may, however, mitigate the detrimental impact of large household sizes. We conclude that communities composed of large households are fundamentally more vulnerable to epidemics of infectious diseases primarily transmitted by close contact, and any assessment of control strategies for these epidemics should take into account the demographic structure of the population. Copyright © 2015 Elsevier Ltd. All rights reserved.

Legislative epidemics: the role of model law in the transnational trend to criminalise HIV transmission.

PubMed

Grace, Daniel

2013-12-01

HIV-related state laws are being created transnationally though the use of omnibus model laws. In 2004, the US Agency for International Development (USAID) funded the creation of one such guidance text known as the USAID/Action for West Africa Region Model Law, or N'Djamena Model Law, which led to the rapid spread of HIV/AIDS laws, including the criminalisation of HIV transmission, across much of West and Central Africa (2005-2010). In this article, I explicate how an epidemic of highly problematic legislation spread across the region as a result of a text-mediated work process enabled through model laws. I theorise the textual genre of model laws arguing that these texts are best understood as 'preoperative documents' which, when activated, can lead to swift legislative reform in and beyond the field of HIV/AIDS governance. The legislative process being investigated was made visible through participant observation, archival research, textual analysis and informant interviews with national and international stakeholders (n=32). This involved ethnographic research in Canada, the USA, Switzerland, Austria, South Africa and Senegal (2010-2011). The untold policy processes and narratives explored in this article make evident how the work of contesting problematic HIV/AIDS model laws and newly drafted state laws involves both creating new texts and contesting the legitimacy and efficacy of others.

On Spatially Explicit Models of Epidemic and Endemic Cholera: The Haiti and Lake Kivu Case Studies.

NASA Astrophysics Data System (ADS)

Rinaldo, A.; Bertuzzo, E.; Mari, L.; Finger, F.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.

2014-12-01

The first part of the Lecture deals with the predictive ability of mechanistic models for the Haitian cholera epidemic. Predictive models of epidemic cholera need to resolve at suitable aggregation levels spatial data pertaining to local communities, epidemiological records, hydrologic drivers, waterways, patterns of human mobility and proxies of exposure rates. A formal model comparison framework provides a quantitative assessment of the explanatory and predictive abilities of various model settings with different spatial aggregation levels. Intensive computations and objective model comparisons show that parsimonious spatially explicit models accounting for spatial connections have superior explanatory power than spatially disconnected ones for short-to intermediate calibration windows. In general, spatially connected models show better predictive ability than disconnected ones. We suggest limits and validity of the various approaches and discuss the pathway towards the development of case-specific predictive tools in the context of emergency management. The second part deals with approaches suitable to describe patterns of endemic cholera. Cholera outbreaks have been reported in the Democratic Republic of the Congo since the 1970s. Here we employ a spatially explicit, inhomogeneous Markov chain model to describe cholera incidence in eight health zones on the shore of lake Kivu. Remotely sensed datasets of chlorophyll a concentration in the lake, precipitation and indices of global climate anomalies are used as environmental drivers in addition to baseline seasonality. The effect of human mobility is also modelled mechanistically. We test several models on a multi-year dataset of reported cholera cases. Fourteen models, accounting for different environmental drivers, are selected in calibration. Among these, the one accounting for seasonality, El Nino Southern Oscillation, precipitation and human mobility outperforms the others in cross-validation.

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

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.

Bacteriocin from epidemic Listeria strains alters the host intestinal microbiota to favor infection

PubMed Central

Quereda, Juan J.; Dussurget, Olivier; Nahori, Marie-Anne; Ghozlane, Amine; Volant, Stevenn; Dillies, Marie-Agnès; Regnault, Béatrice; Kennedy, Sean; Mondot, Stanislas; Villoing, Barbara; Cossart, Pascale; Pizarro-Cerda, Javier

2016-01-01

Listeria monocytogenes is responsible for gastroenteritis in healthy individuals and for a severe invasive disease in immunocompromised patients. Among the three identified L. monocytogenes evolutionary lineages, lineage I strains are overrepresented in epidemic listeriosis outbreaks, but the mechanisms underlying the higher virulence potential of strains of this lineage remain elusive. Here, we demonstrate that Listeriolysin S (LLS), a virulence factor only present in a subset of lineage I strains, is a bacteriocin highly expressed in the intestine of orally infected mice that alters the host intestinal microbiota and promotes intestinal colonization by L. monocytogenes, as well as deeper organ infection. To our knowledge, these results therefore identify LLS as the first bacteriocin described in L. monocytogenes and associate modulation of host microbiota by L. monocytogenes epidemic strains to increased virulence. PMID:27140611

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.

Epidemics in interconnected small-world networks.

PubMed

Liu, Meng; Li, Daqing; Qin, Pengju; Liu, Chaoran; Wang, Huijuan; Wang, Feilong

2015-01-01

Networks can be used to describe the interconnections among individuals, which play an important role in the spread of disease. Although the small-world effect has been found to have a significant impact on epidemics in single networks, the small-world effect on epidemics in interconnected networks has rarely been considered. Here, we study the susceptible-infected-susceptible (SIS) model of epidemic spreading in a system comprising two interconnected small-world networks. We find that the epidemic threshold in such networks decreases when the rewiring probability of the component small-world networks increases. When the infection rate is low, the rewiring probability affects the global steady-state infection density, whereas when the infection rate is high, the infection density is insensitive to the rewiring probability. Moreover, epidemics in interconnected small-world networks are found to spread at different velocities that depend on the rewiring probability.

Outbreak or Epidemic? How Obama's Language Choice Transformed the Ebola Outbreak Into an Epidemic.

PubMed

Gesser-Edelsburg, Anat; Shir-Raz, Yaffa; Bar-Lev, Oshrat Sassoni; James, James J; Green, Manfred S

2016-08-01

Our aim was to examine in what terms leading newspapers' online sites described the current Ebola crisis. We employed a quantitative content analysis of terms attributed to Ebola. We found and analyzed 582 articles published between March 23 and September 30, 2014, on the online websites of 3 newspapers: The New York Times, Daily Mail, and Ynet. Our theoretical framework drew from the fields of health communication and emerging infectious disease communication, including such concepts as framing media literacy, risk signatures, and mental models. We found that outbreak and epidemic were used interchangeably in the articles. From September 16, 2014, onward, epidemic predominated, corresponding to when President Barack Obama explicitly referred to Ebola as an epidemic. Prior to Obama's speech, 86.8% of the articles (323) used the term outbreak and only 8.6% (32) used the term epidemic. Subsequently, both terms were used almost the same amount: 53.8% of the articles (113) used the term outbreak and 53.3% (112) used the term epidemic. Effective communication is crucial during public health emergencies such as Ebola, because language framing affects the decision-making process of social judgments and actions. The choice of one term (outbreak) over another (epidemic) can create different conceptualizations of the disease, thereby influencing the risk signature. (Disaster Med Public Health Preparedness. 2016;10:669-673).

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.

Molecular Phylodynamic Analysis Indicates Lineage Displacement Occurred in Chinese Rabies Epidemics between 1949 to 2010

PubMed Central

Tao, Xiao-Yan; Tang, Qing; Rayner, Simon; Guo, Zhen-Yang; Li, Hao; Lang, Shu-Lin; Yin, Cui-Ping; Han, Na; Fang, Wei; Adams, James; Song, Miao; Liang, Guo-Dong

2013-01-01

Rabies remains a serious problem in China with three epidemics since 1949 and the country in the midst of the third epidemic. Significantly, the control of each outbreak has been followed by a rapid reemergence of the disease. In 2005, the government implemented a rabies national surveillance program that included the collection and screening of almost 8,000 samples. In this work, we analyzed a Chinese dataset comprising 320 glycoprotein sequences covering 23 provinces and eight species, spanning the second and third epidemics. Specifically, we investigated whether the three epidemics are associated with a single reemerging lineage or a different lineage was responsible for each epidemic. Consistent with previous results, phylogenetic analysis identified six lineages, China I to VI. Analysis of the geographical composition of these lineages revealed they are consistent with human case data and reflect the gradual emergence of China I in the third epidemic. Initially, China I was restricted to south China and China II was dominant. However, as the epidemic began to spread into new areas, China I began to emerge, whereas China II remained confined to south China. By the latter part of the surveillance period, almost all isolates were China I and contributions from the remaining lineages were minimal. The prevalence of China II in the early stages of the third epidemic and its established presence in wildlife suggests that it too replaced a previously dominant lineage during the second epidemic. This lineage replacement may be a consequence of control programs that were dominated by dog culling efforts as the primary control method in the first two epidemics. This had the effect of reducing dominant strains to levels comparable with other localized background stains. Our results indicate the importance of effective control strategies for long term control of the disease. PMID:23875035

State Injury Programs’ Response to the Opioid Epidemic: The Role of CDC’s Core Violence and Injury Prevention Program

PubMed Central

Deokar, Angela J.; Dellapenna, Alan; DeFiore-Hyrmer, Jolene; Laidler, Matt; Millet, Lisa; Morman, Sara; Myers, Lindsey

2018-01-01

The Centers for Disease Control and Prevention’s (CDC’s) Core Violence and Injury Prevention Program (Core) supports capacity of state violence and injury prevention programs to implement evidence-based interventions. Several Core-funded states prioritized prescription drug overdose (PDO) and leveraged their systems to identify and respond to the epidemic before specific PDO prevention funding was available through CDC. This article describes activities employed by Core-funded states early in the epidemic. Four case examples illustrate states’ approaches within the context of their systems and partners. While Core funding is not sufficient to support a comprehensive PDO prevention program, having Core in place at the beginning of the emerging epidemic had critical implications for identifying the problem and developing systems that were later expanded as additional resources became available. Important components included staffing support to bolster programmatic and epidemiological capacity; diverse and collaborative partnerships; and use of surveillance and evidence-informed best practices to prioritize decision-making. PMID:29189501

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.

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

Listeriolysin S: A bacteriocin from epidemic Listeria monocytogenes strains that targets the gut microbiota.

PubMed

Quereda, Juan J; Meza-Torres, Jazmín; Cossart, Pascale; Pizarro-Cerdá, Javier

2017-07-04

Listeria monocytogenes is a Gram-positive food-borne pathogen that in humans may traverse the intestinal, placental and blood/brain barriers, causing gastroenteritis, abortions and meningitis. Crossing of these barriers is dependent on the bacterial ability to enter host cells, and several L. monocytogenes surface and secreted virulence factors are known to facilitate entry and the intracellular lifecycle. The study of L. monocytogenes strains associated to human listeriosis epidemics has revealed the presence of novel virulence factors. One such factor is Listeriolysin S, a thiazole/oxazole modified microcin that displays bactericidal activity and modifies the host microbiota during infection. Our recent results therefore highlight the interaction of L. monocytogenes with gut microbes as a crucial step in epidemic listeriosis. In this article, we will discuss novel implications for this family of toxins in the pathogenesis of diverse medically relevant microorganisms.

Listeriolysin S: A bacteriocin from epidemic Listeria monocytogenes strains that targets the gut microbiota

PubMed Central

Quereda, Juan J.; Meza-Torres, Jazmín; Cossart, Pascale; Pizarro-Cerdá, Javier

2017-01-01

ABSTRACT Listeria monocytogenes is a Gram-positive food-borne pathogen that in humans may traverse the intestinal, placental and blood/brain barriers, causing gastroenteritis, abortions and meningitis. Crossing of these barriers is dependent on the bacterial ability to enter host cells, and several L. monocytogenes surface and secreted virulence factors are known to facilitate entry and the intracellular lifecycle. The study of L. monocytogenes strains associated to human listeriosis epidemics has revealed the presence of novel virulence factors. One such factor is Listeriolysin S, a thiazole/oxazole modified microcin that displays bactericidal activity and modifies the host microbiota during infection. Our recent results therefore highlight the interaction of L. monocytogenes with gut microbes as a crucial step in epidemic listeriosis. In this article, we will discuss novel implications for this family of toxins in the pathogenesis of diverse medically relevant microorganisms. PMID:28156183

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.

Detection of severe respiratory disease epidemic outbreaks by CUSUM-based overcrowd-severe-respiratory-disease-index model.

PubMed

Polanco, Carlos; Castañón-González, Jorge Alberto; Macías, Alejandro E; Samaniego, José Lino; Buhse, Thomas; Villanueva-Martínez, Sebastián

2013-01-01

A severe respiratory disease epidemic outbreak correlates with a high demand of specific supplies and specialized personnel to hold it back in a wide region or set of regions; these supplies would be beds, storage areas, hemodynamic monitors, and mechanical ventilators, as well as physicians, respiratory technicians, and specialized nurses. We describe an online cumulative sum based model named Overcrowd-Severe-Respiratory-Disease-Index based on the Modified Overcrowd Index that simultaneously monitors and informs the demand of those supplies and personnel in a healthcare network generating early warnings of severe respiratory disease epidemic outbreaks through the interpretation of such variables. A post hoc historical archive is generated, helping physicians in charge to improve the transit and future allocation of supplies in the entire hospital network during the outbreak. The model was thoroughly verified in a virtual scenario, generating multiple epidemic outbreaks in a 6-year span for a 13-hospital network. When it was superimposed over the H1N1 influenza outbreak census (2008-2010) taken by the National Institute of Medical Sciences and Nutrition Salvador Zubiran in Mexico City, it showed that it is an effective algorithm to notify early warnings of severe respiratory disease epidemic outbreaks with a minimal rate of false alerts.

Detection of Severe Respiratory Disease Epidemic Outbreaks by CUSUM-Based Overcrowd-Severe-Respiratory-Disease-Index Model

PubMed Central

Castañón-González, Jorge Alberto; Macías, Alejandro E.; Samaniego, José Lino; Buhse, Thomas; Villanueva-Martínez, Sebastián

2013-01-01

A severe respiratory disease epidemic outbreak correlates with a high demand of specific supplies and specialized personnel to hold it back in a wide region or set of regions; these supplies would be beds, storage areas, hemodynamic monitors, and mechanical ventilators, as well as physicians, respiratory technicians, and specialized nurses. We describe an online cumulative sum based model named Overcrowd-Severe-Respiratory-Disease-Index based on the Modified Overcrowd Index that simultaneously monitors and informs the demand of those supplies and personnel in a healthcare network generating early warnings of severe respiratory disease epidemic outbreaks through the interpretation of such variables. A post hoc historical archive is generated, helping physicians in charge to improve the transit and future allocation of supplies in the entire hospital network during the outbreak. The model was thoroughly verified in a virtual scenario, generating multiple epidemic outbreaks in a 6-year span for a 13-hospital network. When it was superimposed over the H1N1 influenza outbreak census (2008–2010) taken by the National Institute of Medical Sciences and Nutrition Salvador Zubiran in Mexico City, it showed that it is an effective algorithm to notify early warnings of severe respiratory disease epidemic outbreaks with a minimal rate of false alerts. PMID:24069063

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.

Clustering model for transmission of the SARS virus: application to epidemic control and risk assessment

NASA Astrophysics Data System (ADS)

Small, Michael; Tse, C. K.

2005-06-01

We propose a new four state model for disease transmission and illustrate the model with data from the 2003 SARS epidemic in Hong Kong. The critical feature of this model is that the community is modelled as a small-world network of interconnected nodes. Each node is linked to a fixed number of immediate neighbors and a random number of geographically remote nodes. Transmission can only propagate between linked nodes. This model exhibits two features typical of SARS transmission: geographically localized outbreaks and “super-spreaders”. Neither of these features are evident in standard susceptible-infected-removed models of disease transmission. Our analysis indicates that “super-spreaders” may occur even if the infectiousness of all infected individuals is constant. Moreover, we find that nosocomial transmission in Hong Kong directly contributed to the severity of the outbreak and that by limiting individual exposure time to 3-5 days the extent of the SARS epidemic would have been minimal.

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.

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.

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.

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.

Two approaches to forecast Ebola synthetic epidemics.

PubMed

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

2018-03-01

We use two modelling approaches to forecast synthetic Ebola epidemics in the context of the RAPIDD Ebola Forecasting Challenge. The first approach is a standard stochastic compartmental model that aims to forecast incidence, hospitalization and deaths among both the general population and health care workers. The second is a model based on the renewal equation with latent variables that forecasts incidence in the whole population only. We describe fitting and forecasting procedures for each model and discuss their advantages and drawbacks. We did not find that one model was consistently better in forecasting than the other. Copyright © 2017 The Author(s). Published by Elsevier B.V. All rights reserved.

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.

Effect of climatological factors on respiratory syncytial virus epidemics

PubMed Central

NOYOLA, D. E.; MANDEVILLE, P. B.

2008-01-01

SUMMARY Respiratory syncytial virus (RSV) presents as yearly epidemics in temperate climates. We analysed the association of atmospheric conditions to RSV epidemics in San Luis Potosí, S.L.P., Mexico. The weekly number of RSV detections between October 2002 and May 2006 were correlated to ambient temperature, barometric pressure, relative humidity, vapour tension, dew point, precipitation, and hours of light using time-series and regression analyses. Of the variation in RSV cases, 49·8% was explained by the study variables. Of the explained variation in RSV cases, 32·5% was explained by the study week and 17·3% was explained by meteorological variables (average daily temperature, maximum daily temperature, temperature at 08:00 hours, and relative humidity at 08:00 hours). We concluded that atmospheric conditions, particularly temperature, partly explain the year to year variability in RSV activity. Identification of additional factors that affect RSV seasonality may help develop a model to predict the onset of RSV epidemics. PMID:18177520

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.

How Uganda Reversed Its HIV Epidemic

PubMed Central

Okware, Sam; Naamara, Warren; Sutherland, Don; Flanagan, Donna; Carael, Michel; Blas, Erik; Delay, Paul; Tarantola, Daniel

2006-01-01

Uganda is one of only two countries in the world that has successfully reversed the course of its HIV epidemic. There remains much controversy about how Uganda's HIV prevalence declined in the 1990s. This article describes the prevention programs and activities that were implemented in Uganda during critical years in its HIV epidemic, 1987 to 1994. Multiple resources were aggregated to fuel HV prevention campaigns at multiple levels to a far greater degree than in neighboring countries. We conclude that the reversed direction of the HIV epidemic in Uganda was the direct result of these interventions and that other countries in the developing world could similarly prevent or reverse the escalation of HIV epidemics with greater availability of HIV prevention resources, and well designed programs that take efforts to a critical breadth and depth of effort. PMID:16858635

Hamiltonian Analysis of Subcritical Stochastic Epidemic Dynamics

PubMed Central

2017-01-01

We extend a technique of approximation of the long-term behavior of a supercritical stochastic epidemic model, using the WKB approximation and a Hamiltonian phase space, to the subcritical case. The limiting behavior of the model and approximation are qualitatively different in the subcritical case, requiring a novel analysis of the limiting behavior of the Hamiltonian system away from its deterministic subsystem. This yields a novel, general technique of approximation of the quasistationary distribution of stochastic epidemic and birth-death models and may lead to techniques for analysis of these models beyond the quasistationary distribution. For a classic SIS model, the approximation found for the quasistationary distribution is very similar to published approximations but not identical. For a birth-death process without depletion of susceptibles, the approximation is exact. Dynamics on the phase plane similar to those predicted by the Hamiltonian analysis are demonstrated in cross-sectional data from trachoma treatment trials in Ethiopia, in which declining prevalences are consistent with subcritical epidemic dynamics. PMID:28932256

The “Cuban Epidemic Neuropathy” of the 1990s: A glimpse from inside a totalitarian disease

PubMed Central

Coutin-Churchman, Pedro

2014-01-01

During the 1990s, Cuba was struck by a rare epidemic disease. Up to 50,000 people were affected by a pathology compromising primarily the optic nerve but also peripheral nerves and even spinal cord. This is a testimony from a direct witness and participant in the initial study of the epidemics showing that in spite of claims of a “multifactorial” etiology, still in the literature, the root cause of this disease is just result of the deliberate deprivation of the most elementary economic rights by extreme Government control over a population left unable to tend to its elementary survival by itself, in spite of a thorough Government-sponsored, universally celebrated Universal Healthcare System. PMID:25024884

Influence of Average Income on Epidemics of Seasonal Influenza.

PubMed

Seike, Issei; Saito, Norihiro; Saito, Satoshi; Itoga, Masamichi; Kayaba, Hiroyuki

2016-11-22

Understanding the local factors influencing the transmission of communicable diseases is important to minimize social damage. The aim of this study was to investigate local factors influencing seasonal influenza epidemics in Aomori prefecture consisting of 6 regions, i.e., Seihoku, Chunan, and Tosei on the west side, and Sanpachi, Kamikita, and Shimokita on the east side. Four indices (epidemic onset, duration, scale, and steepness of epidemic curves) were defined, and their correlations with regional characteristics and meteorological factors were investigated. Data for influenza seasons from 2006-2007 to 2014-2015 were collected. The 2009-2010 season was excluded because of the pandemic of A (H1N1)pdm09. Average income was strongly correlated with epidemic onset, duration, and scale. The ratio of children aged ≤5 years to the total population was strongly correlated with epidemic duration and scale. Low temperature in January showed moderate correlation with epidemic duration and scale. Cluster analysis showed that 2 isolated regions, Seihoku and Chunan, belonged to the same cluster in the 4 indices of epidemic curves, and other 2 relatively urbanized regions formed another cluster in 3 of the 4 indices. This study highlights important local factors that influence seasonal influenza epidemics and may help in implementation of preventive measures.

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.

The epidemic of Tuberculosis on vaccinated population

NASA Astrophysics Data System (ADS)

Syahrini, Intan; Sriwahyuni; Halfiani, Vera; Meurah Yuni, Syarifah; Iskandar, Taufiq; Rasudin; Ramli, Marwan

2017-09-01

Tuberculosis is an infectious disease which has caused a large number of mortality in Indonesia. This disease is caused by Mycrobacterium tuberculosis. Besides affecting lung, this disease also affects other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. This article discusses the epidemic of tuberculosis through employing the SEIR model. Here, the population is divided into four compartments which are susceptible, exposed, infected and recovered. The susceptible population is further grouped into two which are vaccinated group and unvaccinated group. The behavior of the epidemic is investigated through analysing the equilibrium of the model. The result shows that administering vaccine to the susceptible population contributes to the reduction of the tuberculosis epidemic rate.

A murine model of infection with Rickettsia prowazekii: implications for pathogenesis of epidemic typhus.

PubMed

Bechah, Yassina; Capo, Christian; Grau, Georges E; Raoult, Didier; Mege, Jean-Louis

2007-06-01

Epidemic typhus remains a major disease threat, furthermore, its etiologic agent, Rickettsia prowazekii, is classified as a bioterrorism agent. We describe here a murine model of epidemic typhus that reproduced some features of the human disease. When BALB/c mice were inoculated intravenously with R. prowazekii (Breinl strain), they survived but did not clear R. prowazekii infection. Immunohistological analysis of tissues and quantitative PCR showed that R. prowazekii was present in blood, liver, lungs and brain 1 day after infection and persisted for at least 9 days. Importantly, infected mice developed interstitial pneumonia, with consolidation of the alveoli, hemorrhages in lungs, multifocal granulomas in liver, and hemorrhages in brain, as seen in humans. Circulating antibodies directed against R. prowazekii were detected at day 4 post-infection and steadily increased for up to 21 days, demonstrating that R. prowazekii lesions were independent of humoral immune response. R. prowazekii-induced lesions were associated with inflammatory response, as demonstrated by elevated levels of inflammatory cytokines including interferon-gamma, tumor necrosis factor and the CC chemokine RANTES in the lesions. We concluded that the BALB/c mouse strain provides a useful model for studying the pathogenic mechanisms of epidemic typhus and its control by the immune system.

[The mathematical modelling of the possible morbidity from epidemic louse-borne typhus under current conditions].

PubMed

Lukin, E P; Mikhaĭlov, V V; Oleĭchik, V L; Solodiankin, A I

1996-01-01

On the basis of their earlier formula for modeling the possible development of the epidemic process of louse-borne exanthematous typhus the authors have calculated the probability of the development of such process for high indices (10 -- 12 % of convalescents with louse contamination rate among them reaching 20 -- 40 %) characterizing this process. The number of sources of this infection (primary patients), as well as the rate of increase and scale of louse contamination of the population, are of prime importance for the prognostication of the development of the epidemic.

Impact of early treatment programs on HIV epidemics: An immunity-based mathematical model.

PubMed

Rahman, S M Ashrafur; Vaidya, Naveen K; Zou, Xingfu

2016-10-01

While studies on pre-exposure prophylaxis (PrEP) and post-exposure prophylaxis (PEP) have demonstrated substantial advantages in controlling HIV transmission, the overall benefits of the programs with early initiation of antiretroviral therapy (ART) have not been fully understood and are still on debate. Here, we develop an immunity-based (CD4+ T cell count based) mathematical model to study the impacts of early treatment programs on HIV epidemics and the overall community-level immunity. The model is parametrized using the HIV prevalence data from South Africa and fully analyzed for stability of equilibria and infection persistence criteria. Using our model, we evaluate the effects of early treatment on the new infection transmission, disease death, basic reproduction number, HIV prevalence, and the community-level immunity. Our model predicts that the programs with early treatments significantly reduce the new infection transmission and increase the community-level immunity, but the treatments alone may not be enough to eliminate HIV epidemics. These findings, including the community-level immunity, might provide helpful information for proper implementation of HIV treatment programs. Copyright © 2016 Elsevier Inc. All rights reserved.

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

Epidemic threshold of the susceptible-infected-susceptible model on complex networks

NASA Astrophysics Data System (ADS)

Lee, Hyun Keun; Shim, Pyoung-Seop; Noh, Jae Dong

2013-06-01

We demonstrate that the susceptible-infected-susceptible (SIS) model on complex networks can have an inactive Griffiths phase characterized by a slow relaxation dynamics. It contrasts with the mean-field theoretical prediction that the SIS model on complex networks is active at any nonzero infection rate. The dynamic fluctuation of infected nodes, ignored in the mean field approach, is responsible for the inactive phase. It is proposed that the question whether the epidemic threshold of the SIS model on complex networks is zero or not can be resolved by the percolation threshold in a model where nodes are occupied in degree-descending order. Our arguments are supported by the numerical studies on scale-free network models.

THE TRANSMISSION AND PERSISTENCE OF ‘URBAN LEGENDS’: SOCIOLOGICAL APPLICATION OF AGE-STRUCTURED EPIDEMIC MODELS

PubMed Central

NOYMER, ANDREW

2009-01-01

This paper describes two related epidemic models of rumor transmission in an age-structured population. Rumors share with communicable disease certain basic aspects, which means that formal models of epidemics may be applied to the transmission of rumors. The results show that rumors may become entrenched very quickly and persist for a long time, even when skeptics are modeled to take an active role in trying to convince others that the rumor is false. This is a macrophenomeon, because individuals eventually cease to believe the rumor, but are replaced by new recruits. This replacement of former believers by new ones is an aspect of all the models, but the approach to stability is quicker, and involves smaller chance of extinction, in the model where skeptics actively try to counter the rumor, as opposed to the model where interest is naturally lost by believers. Skeptics hurt their own cause. The result shows that including age, or a variable for which age is a proxy (e.g., experience), can improve model fidelity and yield important insights. PMID:20351799

Epidemic model for information diffusion in web forums: experiments in marketing exchange and political dialog.

PubMed

Woo, Jiyoung; Chen, Hsinchun

2016-01-01

As social media has become more prevalent, its influence on business, politics, and society has become significant. Due to easy access and interaction between large numbers of users, information diffuses in an epidemic style on the web. Understanding the mechanisms of information diffusion through these new publication methods is important for political and marketing purposes. Among social media, web forums, where people in online communities disseminate and receive information, provide a good environment for examining information diffusion. In this paper, we model topic diffusion in web forums using the epidemiology model, the susceptible-infected-recovered (SIR) model, frequently used in previous research to analyze both disease outbreaks and knowledge diffusion. The model was evaluated on a large longitudinal dataset from the web forum of a major retail company and from a general political discussion forum. The fitting results showed that the SIR model is a plausible model to describe the diffusion process of a topic. This research shows that epidemic models can expand their application areas to topic discussion on the web, particularly social media such as web forums.

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.

Could the Recent Zika Epidemic Have Been Predicted?

NASA Astrophysics Data System (ADS)

Vecchi, G. A.; Munoz, A. G.; Thomson, M. C.; Stewart-Ibarra, A. M.; Chourio, X.; Nájera, P.; Moran, Z.; Yang, X.

2017-12-01

Given knowledge at the time, the recent 2015-2016 zika virus (ZIKV) epidemic probably could not have been predicted. Without the prior knowledge of ZIKV being already present in South America, and given the lack of understanding of key epidemiologic processes and long-term records of ZIKV cases in the continent, the best related prediction could be carried out for the potential risk of a generic Aedes-borne disease epidemic. Here we use a recently published two-vector basic reproduction number model to assess the predictability of the conditions conducive to epidemics of diseases like zika, chikungunya, or dengue, transmitted by the independent or concurrent presence of Aedes aegypti and Aedes albopictus. We compare the potential risk of transmission forcing the model with the observed climate and with state-of-the-art operational forecasts from the North American Multi Model Ensemble (NMME), finding that the predictive skill of this new seasonal forecast system is highest for multiple countries in Latin America and the Caribbean during the December-February and March-May seasons, and slightly lower—but still of potential use to decision-makers—for the rest of the year. In particular, we find that above-normal suitable conditions for the occurrence of the zika epidemic at the beginning of 2015 could have been successfully predicted at least 1 month in advance for several zika hotspots, and in particular for Northeast Brazil: the heart of the epidemic. Nonetheless, the initiation and spread of an epidemic depends on the effect of multiple factors beyond climate conditions, and thus this type of approach must be considered as a guide and not as a formal predictive tool of vector-borne epidemics.

Could the Recent Zika Epidemic Have Been Predicted?

PubMed

Muñoz, Ángel G; Thomson, Madeleine C; Stewart-Ibarra, Anna M; Vecchi, Gabriel A; Chourio, Xandre; Nájera, Patricia; Moran, Zelda; Yang, Xiaosong

2017-01-01

Given knowledge at the time, the recent 2015-2016 zika virus (ZIKV) epidemic probably could not have been predicted. Without the prior knowledge of ZIKV being already present in South America, and given the lack of understanding of key epidemiologic processes and long-term records of ZIKV cases in the continent, the best related prediction could be carried out for the potential risk of a generic Aedes -borne disease epidemic. Here we use a recently published two-vector basic reproduction number model to assess the predictability of the conditions conducive to epidemics of diseases like zika, chikungunya, or dengue, transmitted by the independent or concurrent presence of Aedes aegypti and Aedes albopictus . We compare the potential risk of transmission forcing the model with the observed climate and with state-of-the-art operational forecasts from the North American Multi Model Ensemble (NMME), finding that the predictive skill of this new seasonal forecast system is highest for multiple countries in Latin America and the Caribbean during the December-February and March-May seasons, and slightly lower-but still of potential use to decision-makers-for the rest of the year. In particular, we find that above-normal suitable conditions for the occurrence of the zika epidemic at the beginning of 2015 could have been successfully predicted at least 1 month in advance for several zika hotspots, and in particular for Northeast Brazil: the heart of the epidemic. Nonetheless, the initiation and spread of an epidemic depends on the effect of multiple factors beyond climate conditions, and thus this type of approach must be considered as a guide and not as a formal predictive tool of vector-borne epidemics.

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.

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

Research Spotlight: Model suggests path to ending the ongoing Haitian cholera epidemic

NASA Astrophysics Data System (ADS)

Schultz, Colin

2011-05-01

Since early November 2010 a deadly cholera epidemic has been spreading across the Caribbean nation of Haiti, killing thousands of people and infecting hundreds of thousands. While infection rates are being actively monitored, health organizations have been left without a clear understanding of exactly how the disease has spread across Haiti. Cholera can spread through exposure to contaminated water, and the disease travels over long distances if an infected individual moves around the country. Using representations of these two predominant dispersion mechanisms, along with information on the size of the susceptible population, the number of infected individuals, and the aquatic concentration of the cholera-causing bacteria for more than 500 communities, Bertuzzo et al. designed a model that was able to accurately reproduce the progression of the Haitian cholera epidemic. (Geophysical Research Letters, doi:10.1029/2011GL046823, 2011)

Dynamics of epidemics outbreaks in heterogeneous populations

NASA Astrophysics Data System (ADS)

Brockmann, Dirk; Morales-Gallardo, Alejandro; Geisel, Theo

2007-03-01

The dynamics of epidemic outbreaks have been investigated in recent years within two alternative theoretical paradigms. The key parameter of mean field type of models such as the SIR model is the basic reproduction number R0, the average number of secondary infections caused by one infected individual. Recently, scale free network models have received much attention as they account for the high variability in the number of social contacts involved. These models predict an infinite basic reproduction number in some cases. We investigate the impact of heterogeneities of contact rates in a generic model for epidemic outbreaks. We present a system in which both the time periods of being infectious and the time periods between transmissions are Poissonian processes. The heterogeneities are introduced by means of strongly variable contact rates. In contrast to scale free network models we observe a finite basic reproduction number and, counterintuitively a smaller overall epidemic outbreak as compared to the homogeneous system. Our study thus reveals that heterogeneities in contact rates do not necessarily facilitate the spread to infectious disease but may well attenuate it.

The importance of including dynamic social networks when modeling epidemics of airborne infections: does increasing complexity increase accuracy?

PubMed

Blower, Sally; Go, Myong-Hyun

2011-07-19

Mathematical models are useful tools for understanding and predicting epidemics. A recent innovative modeling study by Stehle and colleagues addressed the issue of how complex models need to be to ensure accuracy. The authors collected data on face-to-face contacts during a two-day conference. They then constructed a series of dynamic social contact networks, each of which was used to model an epidemic generated by a fast-spreading airborne pathogen. Intriguingly, Stehle and colleagues found that increasing model complexity did not always increase accuracy. Specifically, the most detailed contact network and a simplified version of this network generated very similar results. These results are extremely interesting and require further exploration to determine their generalizability.

IS THE U.S. EXPERIENCING AN INCIPIENT EPIDEMIC OF HALLUCINOGEN USE?

PubMed Central

Golub, Andrew; Johnson, Bruce D.; Sifaneck, Stephen J.; Chesluk, Benjamin; Parker, Howard

2008-01-01

NHSDA and MTF survey data indicate “epidemic”-like growth in hallucinogen use from 1992-1996 and associated increases in cocaine, crack, heroin and amphetamine use. These trends might have resulted from a proliferation of raves and dance clubs in the U.S. as occurred in Europe and elsewhere, although in contrast to evidence regarding European experiences the American epidemic involves primarily teens as opposed to persons in their twenties and involves primarily use of LSD as opposed to MDMA. This analysis highlights the need for further research into the context, significance, and consequences of these recently popular American drug use practices. PMID:11758819

Equilibria of an epidemic game with piecewise linear social distancing cost.

PubMed

Reluga, Timothy C

2013-10-01

Around the world, infectious disease epidemics continue to threaten people's health. When epidemics strike, we often respond by changing our behaviors to reduce our risk of infection. This response is sometimes called "social distancing." Since behavior changes can be costly, we would like to know the optimal social distancing behavior. But the benefits of changes in behavior depend on the course of the epidemic, which itself depends on our behaviors. Differential population game theory provides a method for resolving this circular dependence. Here, I present the analysis of a special case of the differential SIR epidemic population game with social distancing when the relative infection rate is linear, but bounded below by zero. Equilibrium solutions are constructed in closed-form for an open-ended epidemic. Constructions are also provided for epidemics that are stopped by the deployment of a vaccination that becomes available a fixed-time after the start of the epidemic. This can be used to anticipate a window of opportunity during which mass vaccination can significantly reduce the cost of an epidemic.

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

Negligible Risk for Epidemics after Geophysical Disasters

PubMed Central

Floret, Nathalie; Viel, Jean-François; Mauny, Frédéric; Hoen, Bruno

2006-01-01

After geophysical disasters (i.e., earthquakes, volcanic eruptions, tsunamis), media reports almost always stress the risk for epidemics; whether this risk is genuine has been debated. We analyzed the medical literature and data from humanitarian agencies and the World Health Organization from 1985 to 2004. Of >600 geophysical disasters recorded, we found only 3 reported outbreaks related to these disasters: 1 of measles after the eruption of Pinatubo in Philippines, 1 of coccidioidomycosis after an earthquake in California, and 1 of Plasmodium vivax malaria in Costa Rica related to an earthquake and heavy rainfall. Even though the humanitarian response may play a role in preventing epidemics, our results lend support to the epidemiologic evidence that short-term risk for epidemics after a geophysical disaster is very low. PMID:16704799

Genome Structural Diversity among 31 Bordetella pertussis Isolates from Two Recent U.S. Whooping Cough Statewide Epidemics.

PubMed

Bowden, Katherine E; Weigand, Michael R; Peng, Yanhui; Cassiday, Pamela K; Sammons, Scott; Knipe, Kristen; Rowe, Lori A; Loparev, Vladimir; Sheth, Mili; Weening, Keeley; Tondella, M Lucia; Williams, Margaret M

2016-01-01

level, previously undetectable by traditional sequence analysis using short-read technologies. For the first time, we combine short- and long-read sequencing platforms with restriction optical mapping for single-contig, de novo assembly of 31 isolates to investigate two geographically and temporally independent U.S. pertussis epidemics. These complete genomes reshape our understanding of B. pertussis evolution and strengthen molecular epidemiology toward one day understanding the resurgence of pertussis.

The "childhood obesity epidemic": health crisis or social construction?

PubMed

Moffat, Tina

2010-03-01

There has been a meteoric rise over the past two decades in the medical research and media coverage of the so-called global childhood obesity epidemic. Recently, in response to this phenomenon, there has been a spate of books and articles in the fields of critical sociology and cultural studies that have argued that this "epidemic" is socially constructed, what Natalie Boero (2007) dubs a "postmodern epidemic." As an anthropologist who has studied child nutrition and obesity in relation to poverty and the school environment, I am concerned about both the lack of reflexivity among medical researchers as well as critical scholars' treatment of the problem as entirely socially constructed. In this article I present both sides of this debate and then discuss how wee can attempt to navigate a middle course that recognizes this health issue but also offers alternative approaches to those set by the biomedical agenda.

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.

Influence of non-homogeneous mixing on final epidemic size in a meta-population model.

PubMed

Cui, Jingan; Zhang, Yanan; Feng, Zhilan

2018-06-18

In meta-population models for infectious diseases, the basic reproduction number [Formula: see text] can be as much as 70% larger in the case of preferential mixing than that in homogeneous mixing [J.W. Glasser, Z. Feng, S.B. Omer, P.J. Smith, and L.E. Rodewald, The effect of heterogeneity in uptake of the measles, mumps, and rubella vaccine on the potential for outbreaks of measles: A modelling study, Lancet ID 16 (2016), pp. 599-605. doi: 10.1016/S1473-3099(16)00004-9 ]. This suggests that realistic mixing can be an important factor to consider in order for the models to provide a reliable assessment of intervention strategies. The influence of mixing is more significant when the population is highly heterogeneous. In this paper, another quantity, the final epidemic size ([Formula: see text]) of an outbreak, is considered to examine the influence of mixing and population heterogeneity. Final size relation is derived for a meta-population model accounting for a general mixing. The results show that [Formula: see text] can be influenced by the pattern of mixing in a significant way. Another interesting finding is that, heterogeneity in various sub-population characteristics may have the opposite effect on [Formula: see text] and [Formula: see text].

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.

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.

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

Recent results on the spatiotemporal modelling and comparative analysis of Black Death and bubonic plague epidemics.

PubMed

Christakos, G; Olea, R A; Yu, H-L

2007-09-01

This work demonstrates the importance of spatiotemporal stochastic modelling in constructing maps of major epidemics from fragmentary information, assessing population impacts, searching for possible etiologies, and performing comparative analysis of epidemics. Based on the theory previously published by the authors and incorporating new knowledge bases, informative maps of the composite space-time distributions were generated for important characteristics of two major epidemics: Black Death (14th century Western Europe) and bubonic plague (19th-20th century Indian subcontinent). The comparative spatiotemporal analysis of the epidemics led to a number of interesting findings: (1) the two epidemics exhibited certain differences in their spatiotemporal characteristics (correlation structures, trends, occurrence patterns and propagation speeds) that need to be explained by means of an interdisciplinary effort; (2) geographical epidemic indicators confirmed in a rigorous quantitative manner the partial findings of isolated reports and time series that Black Death mortality was two orders of magnitude higher than that of bubonic plague; (3) modern bubonic plague is a rural disease hitting harder the small villages in the countryside whereas Black Death was a devastating epidemic that indiscriminately attacked large urban centres and the countryside, and while the epidemic in India lasted uninterruptedly for five decades, in Western Europe it lasted three and a half years; (4) the epidemics had reverse areal extension features in response to annual seasonal variations. Temperature increase at the end of winter led to an expansion of infected geographical area for Black Death and a reduction for bubonic plague, reaching a climax at the end of spring when the infected area in Western Europe was always larger than in India. Conversely, without exception, the infected area during winter was larger for the Indian bubonic plague; (5) during the Indian epidemic, the disease

Recent results on the spatiotemporal modelling and comparative analysis of Black Death and bubonic plague epidemics

USGS Publications Warehouse

Christakos, G.; Olea, R.A.; Yu, H.-L.

2007-01-01

Background: This work demonstrates the importance of spatiotemporal stochastic modelling in constructing maps of major epidemics from fragmentary information, assessing population impacts, searching for possible etiologies, and performing comparative analysis of epidemics. Methods: Based on the theory previously published by the authors and incorporating new knowledge bases, informative maps of the composite space-time distributions were generated for important characteristics of two major epidemics: Black Death (14th century Western Europe) and bubonic plague (19th-20th century Indian subcontinent). Results: The comparative spatiotemporal analysis of the epidemics led to a number of interesting findings: (1) the two epidemics exhibited certain differences in their spatiotemporal characteristics (correlation structures, trends, occurrence patterns and propagation speeds) that need to be explained by means of an interdisciplinary effort; (2) geographical epidemic indicators confirmed in a rigorous quantitative manner the partial findings of isolated reports and time series that Black Death mortality was two orders of magnitude higher than that of bubonic plague; (3) modern bubonic plague is a rural disease hitting harder the small villages in the countryside whereas Black Death was a devastating epidemic that indiscriminately attacked large urban centres and the countryside, and while the epidemic in India lasted uninterruptedly for five decades, in Western Europe it lasted three and a half years; (4) the epidemics had reverse areal extension features in response to annual seasonal variations. Temperature increase at the end of winter led to an expansion of infected geographical area for Black Death and a reduction for bubonic plague, reaching a climax at the end of spring when the infected area in Western Europe was always larger than in India. Conversely, without exception, the infected area during winter was larger for the Indian bubonic plague; (5) during the

A micro-epidemic model for primary dengue infection

NASA Astrophysics Data System (ADS)

Mishra, Arti; Gakkhar, Sunita

2017-06-01

In this paper, a micro-epidemic non-linear dynamical model has been proposed and analyzed for primary dengue infection. The model incorporates the effects of T cells immune response as well as humoral response during pathogenesis of dengue infection. The time delay has been accounted for production of antibodies from B cells. The basic reproduction number (R0) has been computed. Three equilibrium states are obtained. The existence and stability conditions for infection-free and ineffective cellular immune response state have been discussed. The conditions for existence of endemic state have been obtained. Further, the parametric region is obtained where system exhibits complex behavior. The threshold value of time delay has been computed which is critical for change in stability of endemic state. A threshold level for antibodies production rate has been obtained over which the infection will die out even though R0 > 1. The model is in line with the clinical observation that viral load decreases within 7-14 days from the onset of primary infection.

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

Connecting the obesity and the narcissism epidemics.

PubMed

Lemaitre, Bruno

2016-10-01

Obesity and metabolic syndromes are major threats to health in both developed and developing countries. This opinion article is a holistic attempt to understand the obesity epidemic, by connecting it to the widespread narcissism in society. The narcissism epidemic refers to an increased prevalence of status-striving individualism and a decreased sense of community, observed in Westerns populations and spreading worldwide. Based on social personality and evolutionary psychology approaches, I speculate that this rise of narcissism underlies a steep social hierarchy resulting in increase of social stress. This social stress markedly affects individuals who are sensitive to social hierarchy dominance due to their personality, yet are relegated at a lower social position. I speculate that over-eating is one major mechanism for coping with this stress, and discuss the possibility that visceral fat may constitute an adaptive behaviour to the lower social hierarchy position, which is perceived as unjust. Connecting the prevalence of obesity to the narcissism epidemic allows for a more thorough examination of factors, which contribute to obesity, which includes early difficult childhood experience, lower rank, and the overall competitive framework of the society. Copyright © 2016 The Author. Published by Elsevier Ltd.. All rights reserved.

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

Planning horizon affects prophylactic decision-making and epidemic dynamics

PubMed Central

Ridenhour, Benjamin J.; Krone, Stephen M.

2016-01-01

The spread of infectious diseases can be impacted by human behavior, and behavioral decisions often depend implicitly on a planning horizon—the time in the future over which options are weighed. We investigate the effects of planning horizons on epidemic dynamics. We developed an epidemiological agent-based model (along with an ODE analog) to explore the decision-making of self-interested individuals on adopting prophylactic behavior. The decision-making process incorporates prophylaxis efficacy and disease prevalence with the individuals’ payoffs and planning horizon. Our results show that for short and long planning horizons individuals do not consider engaging in prophylactic behavior. In contrast, individuals adopt prophylactic behavior when considering intermediate planning horizons. Such adoption, however, is not always monotonically associated with the prevalence of the disease, depending on the perceived protection efficacy and the disease parameters. Adoption of prophylactic behavior reduces the epidemic peak size while prolonging the epidemic and potentially generates secondary waves of infection. These effects can be made stronger by increasing the behavioral decision frequency or distorting an individual’s perceived risk of infection. PMID:27843714

Epidemic hecatomb in the New World.

PubMed

Naranjo, P

1992-01-01

The American population developed, during thousands of years, free of epidemics that had been attacking Europe, Asia and Africa. The European and African migrations, after Columbus's first trip, produced an epidemic invasion of influenza, smallpox, measles, yellow fever, malaria, diphtheria, typhus, and other diseases that attacked the immunologically virgin populations and produced a very high mortality, with a diminution of the indigenous population of more than 90% in many places. According to historical evidence, the first epidemic was influenza, produced by swine strain of virus, immediately followed by smallpox. The Spaniards mated freely with the Indians producing a mixed race called the Mestizo, who were immunologically more capable of defending themselves against various viruses, bacteria, and parasites brought over from the Old World. Marriage between the races also was sanctioned by Queen Isabella (1503) and Fernando I (1515). With these new genetic immunologic defenses against infections, the Mestizo eventually made up the majority of the population of Indians in the New World.

Complex dynamics of an SEIR epidemic model with saturated incidence rate and treatment

NASA Astrophysics Data System (ADS)

Khan, Muhammad Altaf; Khan, Yasir; Islam, Saeed

2018-03-01

In this paper, we describe the dynamics of an SEIR epidemic model with saturated incidence, treatment function, and optimal control. Rigorous mathematical results have been established for the model. The stability analysis of the model is investigated and found that the model is locally asymptotically stable when R0 < 1. The model is locally as well as globally asymptotically stable at endemic equilibrium when R0 > 1. The proposed model may possess a backward bifurcation. The optimal control problem is designed and obtained their necessary results. Numerical results have been presented for justification of theoretical results.

Forecasting fluctuating outbreaks in seasonally driven epidemics

NASA Astrophysics Data System (ADS)

Stone, Lewi

2009-03-01

Seasonality is a driving force that has major impact on the spatio-temporal dynamics of natural systems and their populations. This is especially true for the transmission of common infectious diseases such as influenza, measles, chickenpox, and pertussis. Here we gain new insights into the nonlinear dynamics of recurrent diseases through the analysis of the classical seasonally forced SIR epidemic model. Despite many efforts over the last decades, it has been difficult to gain general analytical insights because of the complex synchronization effects that can evolve between the external forcing and the model's natural oscillations. The analysis advanced here attempts to make progress in this direction by focusing on the dynamics of ``skips'' where we identify and predict years in which the epidemic is absent rather than outbreak years. Skipping events are intrinsic to the forced SIR model when parameterised in the chaotic regime. In fact, it is difficult if not impossible to locate realistic chaotic parameter regimes in which outbreaks occur regularly each year. This contrasts with the well known Rossler oscillator whose outbreaks recur regularly but whose amplitude vary chaotically in time (Uniform Phase Chaotic Amplitude oscillations). The goal of the present study is to develop a ``language of skips'' that makes it possible to predict under what conditions the next outbreak is likely to occur, and how many ``skips'' might be expected after any given outbreak. We identify a new threshold effect and give clear analytical conditions that allow accurate predictions. Moreover, the time of occurrence (i.e., phase) of an outbreak proves to be a useful new parameter that carries important epidemiological information. In forced systems, seasonal changes can prevent late-initiating outbreaks (i.e., having high phase) from running to completion. These principles yield forecasting tools that should have relevance for the study of newly emerging and reemerging diseases.

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.

Disease-induced resource constraints can trigger explosive epidemics

NASA Astrophysics Data System (ADS)

Böttcher, L.; Woolley-Meza, O.; Araújo, N. A. M.; Herrmann, H. J.; Helbing, D.

2015-11-01

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into “explosive” spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.

Disease-induced resource constraints can trigger explosive epidemics.

PubMed

Böttcher, L; Woolley-Meza, O; Araújo, N A M; Herrmann, H J; Helbing, D

2015-11-16

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into "explosive" spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process.

Disease-induced resource constraints can trigger explosive epidemics

PubMed Central

Böttcher, L.; Woolley-Meza, O.; Araújo, N. A. M.; Herrmann, H. J.; Helbing, D.

2015-01-01

Advances in mathematical epidemiology have led to a better understanding of the risks posed by epidemic spreading and informed strategies to contain disease spread. However, a challenge that has been overlooked is that, as a disease becomes more prevalent, it can limit the availability of the capital needed to effectively treat those who have fallen ill. Here we use a simple mathematical model to gain insight into the dynamics of an epidemic when the recovery of sick individuals depends on the availability of healing resources that are generated by the healthy population. We find that epidemics spiral out of control into “explosive” spread if the cost of recovery is above a critical cost. This can occur even when the disease would die out without the resource constraint. The onset of explosive epidemics is very sudden, exhibiting a discontinuous transition under very general assumptions. We find analytical expressions for the critical cost and the size of the explosive jump in infection levels in terms of the parameters that characterize the spreading process. Our model and results apply beyond epidemics to contagion dynamics that self-induce constraints on recovery, thereby amplifying the spreading process. PMID:26568377

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

A class of stochastic delayed SIR epidemic models with generalized nonlinear incidence rate and temporary immunity

NASA Astrophysics Data System (ADS)

Fan, Kuangang; Zhang, Yan; Gao, Shujing; Wei, Xiang

2017-09-01

A class of SIR epidemic model with generalized nonlinear incidence rate is presented in this paper. Temporary immunity and stochastic perturbation are also considered. The existence and uniqueness of the global positive solution is achieved. Sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established. Moreover, the threshold behavior is discussed, and the threshold value R0 is obtained. We show that if R0 < 1, the disease eventually becomes extinct with probability one, whereas if R0 > 1, then the system remains permanent in the mean.

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.

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.

Epidemic mitigation via awareness propagation in communication networks: the role of time scales

NASA Astrophysics Data System (ADS)

Wang, Huijuan; Chen, Chuyi; Qu, Bo; Li, Daqing; Havlin, Shlomo

2017-07-01

The participation of individuals in multi-layer networks allows for feedback between network layers, opening new possibilities to mitigate epidemic spreading. For instance, the spread of a biological disease such as Ebola in a physical contact network may trigger the propagation of the information related to this disease in a communication network, e.g. an online social network. The information propagated in the communication network may increase the awareness of some individuals, resulting in them avoiding contact with their infected neighbors in the physical contact network, which might protect the population from the infection. In this work, we aim to understand how the time scale γ of the information propagation (speed that information is spread and forgotten) in the communication network relative to that of the epidemic spread (speed that an epidemic is spread and cured) in the physical contact network influences such mitigation using awareness information. We begin by proposing a model of the interaction between information propagation and epidemic spread, taking into account the relative time scale γ. We analytically derive the average fraction of infected nodes in the meta-stable state for this model (i) by developing an individual-based mean-field approximation (IBMFA) method and (ii) by extending the microscopic Markov chain approach (MMCA). We show that when the time scale γ of the information spread relative to the epidemic spread is large, our IBMFA approximation is better compared to MMCA near the epidemic threshold, whereas MMCA performs better when the prevalence of the epidemic is high. Furthermore, we find that an optimal mitigation exists that leads to a minimal fraction of infected nodes. The optimal mitigation is achieved at a non-trivial relative time scale γ, which depends on the rate at which an infected individual becomes aware. Contrary to our intuition, information spread too fast in the communication network could reduce the

Epidemic spreading in a hierarchical social network.

PubMed

Grabowski, A; Kosiński, R A

2004-09-01

A model of epidemic spreading in a population with a hierarchical structure of interpersonal interactions is described and investigated numerically. The structure of interpersonal connections is based on a scale-free network. Spatial localization of individuals belonging to different social groups, and the mobility of a contemporary community, as well as the effectiveness of different interpersonal interactions, are taken into account. Typical relations characterizing the spreading process, like a range of epidemic and epidemic curves, are discussed. The influence of preventive vaccinations on the spreading process is investigated. The critical value of preventively vaccinated individuals that is sufficient for the suppression of an epidemic is calculated. Our results are compared with solutions of the master equation for the spreading process and good agreement of the character of this process is found.

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.

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.

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.

Teaching dental students how to deliver bad news: S-P-I-K-E-S model.

PubMed

Curtin, Sharon; McConnell, Mary

2012-03-01

Delivering bad news has traditionally been associated with life-threatening illness, the imminence of death, or communicating about the death of a loved one to a family member. The delivery of bad news in dentistry is rarely about life-threatening circumstances. However, the impact of the bad news such as the loss of an anterior tooth can be devastating for the patient. This article outlines the S-P-I-K-E-S protocol and discusses the teaching aims and methodology in applying the model in an undergraduate dental program in Ireland.

Food system consequences of a fungal disease epidemic in a major crop.

PubMed

Godfray, H Charles J; Mason-D'Croz, Daniel; Robinson, Sherman

2016-12-05

Fungal diseases are major threats to the most important crops upon which humanity depends. Were there to be a major epidemic that severely reduced yields, its effects would spread throughout the globalized food system. To explore these ramifications, we use a partial equilibrium economic model of the global food system (IMPACT) to study a hypothetical severe but short-lived epidemic that reduces rice yields in the countries affected by 80%. We modelled a succession of epidemic scenarios of increasing severity, starting with the disease in a single country in southeast Asia and ending with the pathogen present in most of eastern Asia. The epidemic and subsequent crop losses led to substantially increased global rice prices. However, as long as global commodity trade was unrestricted and able to respond fast enough, the effects on individual calorie consumption were, to a large part, mitigated. Some of the worse effects were projected to be experienced by poor net-rice importing countries in sub-Saharan Africa, which were not affected directly by the disease but suffered because of higher rice prices. We critique the assumptions of our models and explore political economic pressures to restrict trade at times of crisis. We finish by arguing for the importance of 'stress-testing' the resilience of the global food system to crop disease and other shocks.This article is part of the themed issue 'Tackling emerging fungal threats to animal health, food security and ecosystem resilience'. © 2016 The Author(s).

Evolutionary characterization of the emerging porcine epidemic diarrhea virus worldwide and 2014 epidemic in Taiwan.

PubMed

Sung, Ming-Hua; Deng, Ming-Chung; Chung, Yi-Hsuan; Huang, Yu-Liang; Chang, Chia-Yi; Lan, Yu-Ching; Chou, Hsin-Lin; Chao, Day-Yu

2015-12-01

Since 2010, a new variant of PEDV belonging to Genogroup 2 has been transmitting in China and further spreading to the Unites States and other Asian countries including Taiwan. In order to characterize in detail the temporal and geographic relationships among PEDV strains, the present study systematically evaluated the evolutionary patterns and phylogenetic resolution in each gene of the whole PEDV genome in order to determine which regions provided the maximal interpretative power. The result was further applied to identify the origin of PEDV that caused the 2014 epidemic in Taiwan. Thirty-four full genome sequences were downloaded from GenBank and divided into three non-mutually exclusive groups, namely, worldwide, Genogroup 2 and China, to cover different ranges of secular and spatial trends. Each dataset was then divided into different alignments by different genes for likelihood mapping and phylogenetic analysis. Our study suggested that both nsp3 and S genes contained the highest phylogenetic signal with substitution rate and phylogenetic topology similar to those obtained from the complete genome. Furthermore, the proportion of nodes with high posterior support (posterior probability >0.8) was similar between nsp3 and S genes. The nsp3 gene sequences from three clinical samples of swine with PEDV infections were aligned with other strains available from GenBank and the results suggested that the virus responsible for the 2014 PEDV outbreak in Taiwan clustered together with Clade I from the US within Genogroup 2. In conclusion, the current study identified the nsp3 gene as an alternative marker for a rapid and unequivocal classification of the circulating PEDV strains which provides complementary information to the S gene in identifying the emergence of epidemic strain resulting from recombination. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

Neoliberal science, Chinese style: Making and managing the 'obesity epidemic'.

PubMed

Greenhalgh, Susan

2016-08-01

Science and Technology Studies has seen a growing interest in the commercialization of science. In this article, I track the role of corporations in the construction of the obesity epidemic, deemed one of the major public health threats of the century. Focusing on China, a rising superpower in the midst of rampant, state-directed neoliberalization, I unravel the process, mechanisms, and broad effects of the corporate invention of an obesity epidemic. Largely hidden from view, Western firms were central actors at every stage in the creation, definition, and governmental management of obesity as a Chinese disease. Two industry-funded global health entities and the exploitation of personal ties enabled actors to nudge the development of obesity science and policy along lines beneficial to large firms, while obscuring the nudging. From Big Pharma to Big Food and Big Soda, transnational companies have been profiting from the 'epidemic of Chinese obesity', while doing little to effectively treat or prevent it. The China case suggests how obesity might have been constituted an 'epidemic threat' in other parts of the world and underscores the need for global frameworks to guide the study of neoliberal science and policymaking.

[A proposal for a new definition of excess mortality associated with influenza-epidemics and its estimation].

PubMed

Takahashi, M; Tango, T

2001-05-01

As methods for estimating excess mortality associated with influenza-epidemic, the Serfling's cyclical regression model and the Kawai and Fukutomi model with seasonal indices have been proposed. Excess mortality under the old definition (i.e., the number of deaths actually recorded in excess of the number expected on the basis of past seasonal experience) covers the random error for that portion of variation regarded as due to chance. In addition, it disregards the range of random variation of mortality with the season. In this paper, we propose a new definition of excess mortality associated with influenza-epidemics and a new estimation method, considering these questions with the Kawai and Fukutomi method. The new definition of excess mortality and a novel method for its estimation were generated as follows. Factors bringing about variation in mortality in months with influenza-epidemics may be divided into two groups: 1. Influenza itself, 2. others (practically random variation). The range of variation of mortality due to the latter (normal range) can be estimated from the range for months in the absence of influenza-epidemics. Excess mortality is defined as death over the normal range. A new definition of excess mortality associated with influenza-epidemics and an estimation method are proposed. The new method considers variation in mortality in months in the absence of influenza-epidemics. Consequently, it provides reasonable estimates of excess mortality by separating the portion of random variation. Further, it is a characteristic that the proposed estimate can be used as a criterion of statistical significance test.

The role of the airline transportation network in the prediction and predictability of global epidemics.

PubMed

Colizza, Vittoria; Barrat, Alain; Barthélemy, Marc; Vespignani, Alessandro

2006-02-14

The systematic study of large-scale networks has unveiled the ubiquitous presence of connectivity patterns characterized by large-scale heterogeneities and unbounded statistical fluctuations. These features affect dramatically the behavior of the diffusion processes occurring on networks, determining the ensuing statistical properties of their evolution pattern and dynamics. In this article, we present a stochastic computational framework for the forecast of global epidemics that considers the complete worldwide air travel infrastructure complemented with census population data. We address two basic issues in global epidemic modeling: (i) we study the role of the large scale properties of the airline transportation network in determining the global diffusion pattern of emerging diseases; and (ii) we evaluate the reliability of forecasts and outbreak scenarios with respect to the intrinsic stochasticity of disease transmission and traffic flows. To address these issues we define a set of quantitative measures able to characterize the level of heterogeneity and predictability of the epidemic pattern. These measures may be used for the analysis of containment policies and epidemic risk assessment.

A Simulation Optimization Approach to Epidemic Forecasting

PubMed Central

Nsoesie, Elaine O.; Beckman, Richard J.; Shashaani, Sara; Nagaraj, Kalyani S.; Marathe, Madhav V.

2013-01-01

Reliable forecasts of influenza can aid in the control of both seasonal and pandemic outbreaks. We introduce a simulation optimization (SIMOP) approach for forecasting the influenza epidemic curve. This study represents the final step of a project aimed at using a combination of simulation, classification, statistical and optimization techniques to forecast the epidemic curve and infer underlying model parameters during an influenza outbreak. The SIMOP procedure combines an individual-based model and the Nelder-Mead simplex optimization method. The method is used to forecast epidemics simulated over synthetic social networks representing Montgomery County in Virginia, Miami, Seattle and surrounding metropolitan regions. The results are presented for the first four weeks. Depending on the synthetic network, the peak time could be predicted within a 95% CI as early as seven weeks before the actual peak. The peak infected and total infected were also accurately forecasted for Montgomery County in Virginia within the forecasting period. Forecasting of the epidemic curve for both seasonal and pandemic influenza outbreaks is a complex problem, however this is a preliminary step and the results suggest that more can be achieved in this area. PMID:23826222

A Simulation Optimization Approach to Epidemic Forecasting.

PubMed

Nsoesie, Elaine O; Beckman, Richard J; Shashaani, Sara; Nagaraj, Kalyani S; Marathe, Madhav V

2013-01-01

Reliable forecasts of influenza can aid in the control of both seasonal and pandemic outbreaks. We introduce a simulation optimization (SIMOP) approach for forecasting the influenza epidemic curve. This study represents the final step of a project aimed at using a combination of simulation, classification, statistical and optimization techniques to forecast the epidemic curve and infer underlying model parameters during an influenza outbreak. The SIMOP procedure combines an individual-based model and the Nelder-Mead simplex optimization method. The method is used to forecast epidemics simulated over synthetic social networks representing Montgomery County in Virginia, Miami, Seattle and surrounding metropolitan regions. The results are presented for the first four weeks. Depending on the synthetic network, the peak time could be predicted within a 95% CI as early as seven weeks before the actual peak. The peak infected and total infected were also accurately forecasted for Montgomery County in Virginia within the forecasting period. Forecasting of the epidemic curve for both seasonal and pandemic influenza outbreaks is a complex problem, however this is a preliminary step and the results suggest that more can be achieved in this area.

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.

Effects of clustered transmission on epidemic growth Comment on "Mathematical models to characterize early epidemic growth: A review" by Gerardo Chowell et al.

NASA Astrophysics Data System (ADS)

Merler, Stefano

2016-09-01

Characterizing the early growth profile of an epidemic outbreak is key for predicting the likely trajectory of the number of cases and for designing adequate control measures. Epidemic profiles characterized by exponential growth have been widely observed in the past and a grounding theoretical framework for the analysis of infectious disease dynamics was provided by the pioneering work of Kermack and McKendrick [1]. In particular, exponential growth stems from the assumption that pathogens spread in homogeneous mixing populations; that is, individuals of the population mix uniformly and randomly with each other. However, this assumption was readily recognized as highly questionable [2], and sub-exponential profiles of epidemic growth have been observed in a number of epidemic outbreaks, including HIV/AIDS, foot-and-mouth disease, measles and, more recently, Ebola [3,4].

Epidemic spreading through direct and indirect interactions.

PubMed

Ganguly, Niloy; Krueger, Tyll; Mukherjee, Animesh; Saha, Sudipta

2014-09-01

In this paper we study the susceptible-infected-susceptible epidemic dynamics, considering a specialized setting where popular places (termed passive entities) are visited by agents (termed active entities). We consider two types of spreading dynamics: direct spreading, where the active entities infect each other while visiting the passive entities, and indirect spreading, where the passive entities act as carriers and the infection is spread via them. We investigate in particular the effect of selection strategy, i.e., the way passive entities are chosen, in the spread of epidemics. We introduce a mathematical framework to study the effect of an arbitrary selection strategy and derive formulas for prevalence, extinction probabilities, and epidemic thresholds for both indirect and direct spreading. We also obtain a very simple relationship between the extinction probability and the prevalence. We pay special attention to preferential selection and derive exact formulas. The analysis reveals that an increase in the diversity in the selection process lowers the epidemic thresholds. Comparing the direct and indirect spreading, we identify regions in the parameter space where the prevalence of the indirect spreading is higher than the direct one.

Epidemic spreading through direct and indirect interactions

NASA Astrophysics Data System (ADS)

Ganguly, Niloy; Krueger, Tyll; Mukherjee, Animesh; Saha, Sudipta

2014-09-01

In this paper we study the susceptible-infected-susceptible epidemic dynamics, considering a specialized setting where popular places (termed passive entities) are visited by agents (termed active entities). We consider two types of spreading dynamics: direct spreading, where the active entities infect each other while visiting the passive entities, and indirect spreading, where the passive entities act as carriers and the infection is spread via them. We investigate in particular the effect of selection strategy, i.e., the way passive entities are chosen, in the spread of epidemics. We introduce a mathematical framework to study the effect of an arbitrary selection strategy and derive formulas for prevalence, extinction probabilities, and epidemic thresholds for both indirect and direct spreading. We also obtain a very simple relationship between the extinction probability and the prevalence. We pay special attention to preferential selection and derive exact formulas. The analysis reveals that an increase in the diversity in the selection process lowers the epidemic thresholds. Comparing the direct and indirect spreading, we identify regions in the parameter space where the prevalence of the indirect spreading is higher than the direct one.

Phylodynamics of the HIV-1 epidemic in Cuba.

PubMed

Delatorre, Edson; Bello, Gonzalo

2013-01-01

Previous studies have shown that the HIV-1 epidemic in Cuba displayed a complex molecular epidemiologic profile with circulation of several subtypes and circulating recombinant forms (CRF); but the evolutionary and population history of those viral variants remains unknown. HIV-1 pol sequences of the most prevalent Cuban lineages (subtypes B, C and G, CRF18_cpx, CRF19_cpx, and CRFs20/23/24_BG) isolated between 1999 and 2011 were analyzed. Maximum-likelihood analyses revealed multiple introductions of subtype B (n≥66), subtype C (n≥10), subtype G (n≥8) and CRF18_cpx (n≥2) viruses in Cuba. The bulk of HIV-1 infections in this country, however, was caused by dissemination of a few founder strains probably introduced from North America/Europe (clades B(CU-I) and B(CU-II)), east Africa (clade C(CU-I)) and central Africa (clades G(CU), CRF18(CU) and CRF19(CU)), or locally generated (clades CRFs20/23/24_BG). Bayesian-coalescent analyses show that the major HIV-1 founder strains were introduced into Cuba during 1985-1995; whereas the CRFs_BG strains emerged in the second half of the 1990s. Most HIV-1 Cuban clades appear to have experienced an initial period of fast exponential spread during the 1990s and early 2000s, followed by a more recent decline in growth rate. The median initial growth rate of HIV-1 Cuban clades ranged from 0.4 year⁻¹ to 1.6 year⁻¹. Thus, the HIV-1 epidemic in Cuba has been a result of the successful introduction of a few viral strains that began to circulate at a rather late time of the AIDS pandemic, but then were rapidly disseminated through local transmission networks.

The epidemic of obesity and changes in food intake: the Fluoride Hypothesis.

PubMed

Bray, George A

2004-08-01

The epidemic of obesity is worldwide. It will be followed by an epidemic of diabetes. Although there is a genetic basis for obesity and diabetes, the current epidemic reflects the failure of our ancient genes to cope with a modern toxic environment. To put it another way, the genetic background loads the gun, but the environment pulls the trigger. Diet, lifestyle and exercise are the cornerstones of current approaches to treating obesity. However, these approaches that depend on individuals making lifestyle changes have been ineffective in preventing the epidemic. An alternative model views obesity as an epidemiological disease with food(s) and other environmental agents acting on the host to produce disease. The consumption patterns for many foods have changed over the past 30 years, but the increase in the consumption of high-fructose corn syrup (HFCS) for soft drinks is far and away the largest. Moreover, the rise in HFCS intake is an environmental insult that has occurred at exactly the same time as obesity began to increase in prevalence. Rising soft drink consumption is associated with a decrease in milk consumption and a decrease in calcium intake, which has an inverse relationship to body mass index (BMI). To combat the epidemic of obesity, we need new strategies that flow from the epidemiological model. The Fluoride Hypothesis for obesity proposes that we can make environmental changes that when made, will reduce the epidemic of obesity, in much the same way as fluoride reduced the incidence of dental disease. Fluoride-like strategies can work without the personal effort required by changes in lifestyle. In this context, fluoride is also an acronym for treatment and prevention of obesity: For Lowering Universal Obesity Rates are Implement ideas that Don't demand Effort (FLUORIDE).

Importance of exfoliatin toxin A production by Staphylococcus aureus strains isolated from clustered epidemics of neonatal pustulosis.

PubMed Central

Kaplan, M H; Chmel, H; Hsieh, H C; Stephens, A; Brinsko, V

1986-01-01

Clustered epidemics of pustulosis due to Staphylococcus aureus occurred in two geographically distant newborn nurseries. In nurseries A and B an attack rate of pustulosis of 0.8 and 2.0 cases per 100 live births occurred, respectively. Experimental phage type 1046/1116 belonging to phage group II dominated clustered epidemics in nursery A, while group II phage type 3A/3C/55/71 and 3A/3C/55 occurred in nursery B. Other group II strains also occasionally produced clustered epidemics. These epidemic strains were found to be making heat-stable dermal exfoliatin toxin A (ETA) which had a pI of 6.8 and a molecular weight of 32,000 and 33,000. ETA-bearing strains did not make bacteriocin. Children infected with ETA-producing strains developed extensive bullous pustulosis. Surveillance cultures of personnel revealed an ETA-bearing strain in only one person. This strain was not the same phage type as the epidemic cluster. In contrast, ETA-bearing epidemic strains were found in the inanimate environment of both nurseries. ETA protein acts as an important virulence factor in the production of neonatal pustulosis infection and appears to be linked with the ability of S. aureus organisms to stick to the inanimate environment. Images PMID:3700612

The dysentery epidemic in Poland in 1920-1921

PubMed

Wnęk, Jan

This article describes in general the issues related to the dysentery epidemic in 1920-1921. The current literature on the subject lacks publications presenting these issues fully. Based on historical sources from that period, including articles published in medical magazines, the incidence rate, the methods and results of the battle against that epidemic were depicted. The article represents an important contribution to a better insight in the struggle of Polish medical services with infectious diseases afflicting people in the first years following the end of World War I. It also sheds light on the development of Polish studies on infectious diseases in the Second Polish Republic, the scientists’ belief in the successful treatment of epidemic diseases and understanding of the need to educate people about the rules of hygiene and taking medicines.

Environmental Factors Influencing Epidemic Cholera

PubMed Central

Jutla, Antarpreet; Whitcombe, Elizabeth; Hasan, Nur; Haley, Bradd; Akanda, Ali; Huq, Anwar; Alam, Munir; Sack, R. Bradley; Colwell, Rita

2013-01-01

Cholera outbreak following the earthquake of 2010 in Haiti has reaffirmed that the disease is a major public health threat. Vibrio cholerae is autochthonous to aquatic environment, hence, it cannot be eradicated but hydroclimatology-based prediction and prevention is an achievable goal. Using data from the 1800s, we describe uniqueness in seasonality and mechanism of occurrence of cholera in the epidemic regions of Asia and Latin America. Epidemic regions are located near regional rivers and are characterized by sporadic outbreaks, which are likely to be initiated during episodes of prevailing warm air temperature with low river flows, creating favorable environmental conditions for growth of cholera bacteria. Heavy rainfall, through inundation or breakdown of sanitary infrastructure, accelerates interaction between contaminated water and human activities, resulting in an epidemic. This causal mechanism is markedly different from endemic cholera where tidal intrusion of seawater carrying bacteria from estuary to inland regions, results in outbreaks. PMID:23897993

Modeling Alzheimer’s disease with human induced pluripotent stem (iPS) cells

PubMed Central

Mungenast, Alison E.; Siegert, Sandra; Tsai, Li-Huei

2018-01-01

In the last decade, induced pluripotent stem (iPS) cells have revolutionized the utility of human in vitro models of neurological disease. The iPS-derived and differentiated cells allow researchers to study the impact of a distinct cell type in health and disease as well as performing therapeutic drug screens on a human genetic background. In particular, clinical trials for Alzheimer’s disease (AD) have been often failing. Two of the potential reasons are first, the species gap involved in proceeding from initial discoveries in rodent models to human studies, and second, an unsatisfying patient stratification, meaning subgrouping patients based on the disease severity due to the lack of phenotypic and genetic markers. iPS cells overcome this obstacles and will improve our understanding of disease subtypes in AD. They allow researchers conducting in depth characterization of neural cells from both familial and sporadic AD patients as well as preclinical screens on human cells. In this review, we briefly outline the status quo of iPS cell research in neurological diseases along with the general advantages and pitfalls of these models. We summarize how genome-editing techniques such as CRISPR/Cas will allow researchers to reduce the problem of genomic variability inherent to human studies, followed by recent iPS cell studies relevant to AD. We then focus on current techniques for the differentiation of iPS cells into neural cell types that are relevant to AD research. Finally, we discuss how the generation of three-dimensional cell culture systems will be important for understanding AD phenotypes in a complex cellular milieu, and how both two- and three-dimensional iPS cell models can provide platforms for drug discovery and translational studies into the treatment of AD. PMID:26657644

Effects of active links on epidemic transmission over social networks

NASA Astrophysics Data System (ADS)

Zhu, Guanghu; Chen, Guanrong; Fu, Xinchu

2017-02-01

A new epidemic model with two infection periods is developed to account for the human behavior in social network, where newly infected individuals gradually restrict most of future contacts or are quarantined, causing infectivity change from a degree-dependent form to a constant. The corresponding dynamics are formulated by a set of ordinary differential equations (ODEs) via mean-field approximation. The effects of diverse infectivity on the epidemic dynamics ​are examined, with a behavioral interpretation of the basic reproduction number. Results show that such simple adaptive reactions largely determine the impact of network structure on epidemics. Particularly, a theorem proposed by Lajmanovich and Yorke in 1976 is generalized, so that it can be applied for the analysis of the epidemic models with multi-compartments especially network-coupled ODE systems.

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.

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

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

Modelling control of epidemics spreading by long-range interactions.

PubMed

Dybiec, Bartłomiej; Kleczkowski, Adam; Gilligan, Christopher A

2009-10-06

We have studied the spread of epidemics characterized by a mixture of local and non-local interactions. The infection spreads on a two-dimensional lattice with the fixed nearest neighbour connections. In addition, long-range dynamical links are formed by moving agents (vectors). Vectors perform random walks, with step length distributed according to a thick-tail distribution. Two distributions are considered in this paper, an alpha-stable distribution describing self-similar vector movement, yet characterized by an infinite variance and an exponential power characterized by a large but finite variance. Such long-range interactions are hard to track and make control of epidemics very difficult. We also allowed for cryptic infection, whereby an infected individual on the lattice can be infectious prior to showing any symptoms of infection or disease. To account for such cryptic spread, we considered a control strategy in which not only detected, i.e. symptomatic, individuals but also all individuals within a certain control neighbourhood are treated upon the detection of disease. We show that it is possible to eradicate the disease by using such purely local control measures, even in the presence of long-range jumps. In particular, we show that the success of local control and the choice of the optimal strategy depend in a non-trivial way on the dispersal patterns of the vectors. By characterizing these patterns using the stability index of the alpha-stable distribution to change the power-law behaviour or the exponent characterizing the decay of an exponential power distribution, we show that infection can be successfully contained using relatively small control neighbourhoods for two limiting cases for long-distance dispersal and for vectors that are much more limited in their dispersal range.

Epidemic spreading on dual-structure networks with mobile agents

NASA Astrophysics Data System (ADS)

Yao, Yiyang; Zhou, Yinzuo

2017-02-01

The rapid development of modern society continually transforms the social structure which leads to an increasingly distinct dual structure of higher population density in urban areas and lower density in rural areas. Such structure may induce distinctive spreading behavior of epidemics which does not happen in a single type structure. In this paper, we study the epidemic spreading of mobile agents on dual structure networks based on SIRS model. First, beyond the well known epidemic threshold for generic epidemic model that when the infection rate is below the threshold a pertinent infectious disease will die out, we find the other epidemic threshold which appears when the infection rate of a disease is relatively high. This feature of two thresholds for the SIRS model may lead to the elimination of infectious disease when social network has either high population density or low population density. Interestingly, however, we find that when a high density area is connected to a low density may cause persistent spreading of the infectious disease, even though the same disease will die out when it spreads in each single area. This phenomenon indicates the critical role of the connection between the two areas which could radically change the behavior of spreading dynamics. Our findings, therefore, provide new understanding of epidemiology pertinent to the characteristic modern social structure and have potential to develop controlling strategies accordingly.

Homo-psychologicus: Reactionary behavioural aspects of epidemics.

PubMed

Cherif, Alhaji; Barley, Kamal; Hurtado, Marcel

2016-03-01

We formulate an in silico model of pathogen avoidance mechanism and investigate its impact on defensive behavioural measures (e.g., spontaneous social exclusions and distancing, crowd avoidance and voluntary vaccination adaptation). In particular, we use SIR(B)S (e.g., susceptible-infected-recovered with additional behavioural component) model to investigate the impact of homo-psychologicus aspects of epidemics. We focus on reactionary behavioural changes, which apply to both social distancing and voluntary vaccination participations. Our analyses reveal complex relationships between spontaneous and uncoordinated behavioural changes, the emergence of its contagion properties, and mitigation of infectious diseases. We find that the presence of effective behavioural changes can impede the persistence of disease. Furthermore, it was found that under perfect effective behavioural change, there are three regions in the response factor (e.g., imitation and/or reactionary) and behavioural scale factor (e.g., global/local) factors ρ-α behavioural space. Mainly, (1) disease is always endemic even in the presence of behavioural change, (2) behavioural-prevalence plasticity is observed and disease can sometimes be eradication, and (3) elimination of endemic disease under permanence of permanent behavioural change is achieved. These results suggest that preventive behavioural changes (e.g., non-pharmaceutical prophylactic measures, social distancing and exclusion, crowd avoidance) are influenced by individual differences in perception of risks and are a salient feature of epidemics. Additionally, these findings indicates that care needs to be taken when considering the effect of adaptive behavioural change in predicting the course of epidemics, and as well as the interpretation and development of the public health measures that account for spontaneous behavioural changes. Copyright © 2015 The Authors. Published by Elsevier B.V. All rights reserved.

Impact of the infectious period on epidemics

NASA Astrophysics Data System (ADS)

Wilkinson, Robert R.; Sharkey, Kieran J.

2018-05-01

The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise, message passing, and spatial models as special cases. For this model, we prove a monotonic relationship between the variability of the infectious period (with fixed mean) and the probability that the infection will reach any given subset of the population by any given time. For certain families of distributions, this result implies that epidemic severity is decreasing with respect to the variance of the infectious period. The striking importance of this relationship is demonstrated numerically. We then prove, with a fixed basic reproductive ratio (R0), a monotonic relationship between the variability of the posterior transmission probability (which is a function of the infectious period) and the probability that the infection will reach any given subset of the population by any given time. Thus again, even when R0 is fixed, variability of the infectious period tends to dampen the epidemic. Numerical results illustrate this but indicate the relationship is weaker. We then show how our results apply to message passing, pairwise, and Kermack-McKendrick epidemic models, even when they are not exactly consistent with the stochastic dynamics. For Poissonian contact processes, and arbitrarily distributed infectious periods, we demonstrate how systems of delay differential equations and ordinary differential equations can provide upper and lower bounds, respectively, for the probability that any given individual has been infected by any given time.

Human Mobility Patterns and Cholera Epidemics: a Spatially Explicit Modeling Approach

NASA Astrophysics Data System (ADS)

Mari, L.; Bertuzzo, E.; Righetto, L.; Casagrandi, R.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.

2010-12-01

Cholera is an acute enteric disease caused by the ingestion of water or food contaminated by the bacterium Vibrio cholerae. Although most infected individuals do not develop severe symptoms, their stool may contain huge quantities of V.~cholerae cells. Therefore, while traveling or commuting, asymptomatic carriers can be responsible for the long-range dissemination of the disease. As a consequence, human mobility is an alternative and efficient driver for the spread of cholera, whose primary propagation pathway is hydrological transport through river networks. We present a multi-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of V.~cholerae due to human movement. In particular, building on top of state-of-the-art spatially explicit models for cholera spread through surface waters, we describe human movement and its effects on the propagation of the disease by means of a gravity-model approach borrowed from transportation theory. Gravity-like contact processes have been widely used in epidemiology, because they can satisfactorily depict human movement when data on actual mobility patterns are not available. We test our model against epidemiological data recorded during the cholera outbreak occurred in the KwaZulu-Natal province of South Africa during years 2000--2001. We show that human mobility does actually play an important role in the formation of the spatiotemporal patterns of cholera epidemics. In particular, long-range human movement may determine inter-catchment dissemination of V.~cholerae cells, thus in turn explaining the emergence of epidemic patterns that cannot be produced by hydrological transport alone. We also show that particular attention has to be devoted to study how heterogeneously distributed drinking water supplies and sanitation conditions may affect cholera transmission.

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.

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.

Dynamical response of multi-patch, flux-based models to the input of infected people: Epidemic response to initiated events

NASA Astrophysics Data System (ADS)

Rho, Young-Ah; Liebovitch, Larry S.; Schwartz, Ira B.

2008-07-01

The time course of an epidemic can be modeled using the differential equations that describe the spread of disease and by dividing people into “patches” of different sizes with the migration of people between these patches. We used these multi-patch, flux-based models to determine how the time course of infected and susceptible populations depends on the disease parameters, the geometry of the migrations between the patches, and the addition of infected people into a patch. We found that there are significantly longer lived transients and additional “ancillary” epidemics when the reproductive rate R is closer to 1, as would be typical of SARS (Severe Acute Respiratory Syndrome) and bird flu, than when R is closer to 10, as would be typical of measles. In addition we show, both analytical and numerical, how the time delay between the injection of infected people into a patch and the corresponding initial epidemic that it produces depends on R.

Mathematical model of tuberculosis epidemic with recovery time delay

NASA Astrophysics Data System (ADS)

Iskandar, Taufiq; Chaniago, Natasya Ayuningtia; Munzir, Said; Halfiani, Vera; Ramli, Marwan

2017-12-01

Tuberculosis (TB) is a contagious disease which can cause death. The disease is caused by Mycobacterium Tuberculosis which generally affects lungs and other organs such as lymph gland, intestine, kidneys, uterus, bone, and brain. The spread of TB occurs through the bacteria-contaminated air which is inhaled into the lungs. The symptoms of the TB patients are cough, chest pain, shortness of breath, appetite lose, weight lose, fever, cold, and fatigue. World Health Organization (WHO) reported that Indonesia placed the second in term of the most TB cases after India which has 23 % cases while China is reported to have 10 % cases in global. TB has become one of the greatest death threats in global. One way to countermeasure TB disease is by administering vaccination. However, a medication is needed when one has already infected. The medication can generally take 6 months of time which consists of two phases, inpatient and outpatient. Mathematical models to analyze the spread of TB have been widely developed. One of them is the SEIR type model. In this model the population is divided into four groups, which are suspectible (S), exposed (S), infected (I), recovered (R). In fact, a TB patient needs to undergo medication with a period of time in order to recover. This article discusses a model of TB spread with considering the term of recovery (time delay). The model is developed in SIR type where the population is divided into three groups, suspectible (S), infected (I), and recovered (R). Here, the vaccine is given to the susceptible group and the time delay is considered in the group undergoing the medication.

Impacts of clustering on interacting epidemics.

PubMed

Wang, Bing; Cao, Lang; Suzuki, Hideyuki; Aihara, Kazuyuki

2012-07-07

Since community structures in real networks play a major role for the epidemic spread, we therefore explore two interacting diseases spreading in networks with community structures. As a network model with community structures, we propose a random clique network model composed of different orders of cliques. We further assume that each disease spreads only through one type of cliques; this assumption corresponds to the issue that two diseases spread inside communities and outside them. Considering the relationship between the susceptible-infected-recovered (SIR) model and the bond percolation theory, we apply this theory to clique random networks under the assumption that the occupation probability is clique-type dependent, which is consistent with the observation that infection rates inside a community and outside it are different, and obtain a number of statistical properties for this model. Two interacting diseases that compete the same hosts are also investigated, which leads to a natural generalization of analyzing an arbitrary number of infectious diseases. For two-disease dynamics, the clustering effect is hypersensitive to the cohesiveness and concentration of cliques; this illustrates the impacts of clustering and the composition of subgraphs in networks on epidemic behavior. The analysis of coexistence/bistability regions provides significant insight into the relationship between the network structure and the potential epidemic prevalence. Copyright © 2012 Elsevier Ltd. All rights reserved.

Epidemic cycles driven by host behaviour

PubMed Central

Althouse, Benjamin M.; Hébert-Dufresne, Laurent

2014-01-01

Host immunity and demographics (the recruitment of susceptibles via birthrate) have been demonstrated to be a key determinant of the periodicity of measles, pertussis and dengue epidemics. However, not all epidemic cycles are from pathogens inducing sterilizing immunity or are driven by demographics. Many sexually transmitted infections are driven by sexual behaviour. We present a mathematical model of disease transmission where individuals can disconnect and reconnect depending on the infectious status of their contacts. We fit the model to historic syphilis (Treponema pallidum) and gonorrhea (Neisseria gonorrhoeae) incidence in the USA and explore potential intervention strategies against syphilis. We find that cycles in syphilis incidence can be driven solely by changing sexual behaviour in structured populations. Our model also explains the lack of similar cycles in gonorrhea incidence even if the two infections share the same propagation pathways. Our model similarly illustrates how sudden epidemic outbreaks can occur on time scales smaller than the characteristic demographic time scale of the population and that weaker infections can lead to more violent outbreaks. Behaviour also appears to be critical for control strategies as we found a bigger sensitivity to behavioural interventions than antibiotic treatment. Thus, behavioural interventions may play a larger role than previously thought, especially in the face of antibiotic resistance and low intervention efficacies. PMID:25100316

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.

Estimating the impact of reducing violence against female sex workers on HIV epidemics in Kenya and Ukraine: a policy modeling exercise.

PubMed

Decker, Michele R; Wirtz, Andrea L; Pretorius, Carel; Sherman, Susan G; Sweat, Michael D; Baral, Stefan D; Beyrer, Chris; Kerrigan, Deanna L

2013-02-01

Female sex workers (FSWs) worldwide suffer disproportionate burdens of HIV and gender-based violence. Despite evidence linking these threats, little is known about the potential HIV epidemic impact of reducing abuse. The Goals model approximated the impact of reducing violence against FSWs on HIV epidemics in Ukraine and Kenya, measured by reductions in new infections among FSWs and adults. Cumulative infections averted over a 5-year period, in which violence declined was calculated, relative to a status quo with no reduction. Projections held HIV interventions constant at baseline levels; subsequently, scenarios adjusted for planned expansion of antiretroviral therapy (ART) coverage. An approximate 25% reduction in incident HIV infections among FSWs was observed when physical or sexual violence was reduced; cumulative infections averted were 21,200 and 4700 in Kenya and Ukraine, respectively. Similar percent reductions were observed assuming ART coverage expansion, with approximately 18,200 and 4400 infections averted among FSWs in Kenya and Ukraine. New infections were also averted in the general population. Reducing violence against FSWs appears to impart significant reductions in new infections among FSWs and in the general adult population in both generalized and concentrated epidemics. Limitations provide direction to improve the precision of future estimates. © 2013 John Wiley & Sons A/S.

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

Forecasting disease risk for increased epidemic preparedness in public health

NASA Technical Reports Server (NTRS)

Myers, M. F.; Rogers, D. J.; Cox, J.; Flahault, A.; Hay, S. I.

2000-01-01

Emerging infectious diseases pose a growing threat to human populations. Many of the world's epidemic diseases (particularly those transmitted by intermediate hosts) are known to be highly sensitive to long-term changes in climate and short-term fluctuations in the weather. The application of environmental data to the study of disease offers the capability to demonstrate vector-environment relationships and potentially forecast the risk of disease outbreaks or epidemics. Accurate disease forecasting models would markedly improve epidemic prevention and control capabilities. This chapter examines the potential for epidemic forecasting and discusses the issues associated with the development of global networks for surveillance and prediction. Existing global systems for epidemic preparedness focus on disease surveillance using either expert knowledge or statistical modelling of disease activity and thresholds to identify times and areas of risk. Predictive health information systems would use monitored environmental variables, linked to a disease system, to be observed and provide prior information of outbreaks. The components and varieties of forecasting systems are discussed with selected examples, along with issues relating to further development.

Transmission network of the 2014-2015 Ebola epidemic in Sierra Leone.

PubMed

Yang, Wan; Zhang, Wenyi; Kargbo, David; Yang, Ruifu; Chen, Yong; Chen, Zeliang; Kamara, Abdul; Kargbo, Brima; Kandula, Sasikiran; Karspeck, Alicia; Liu, Chao; Shaman, Jeffrey

2015-11-06

Understanding the growth and spatial expansion of (re)emerging infectious disease outbreaks, such as Ebola and avian influenza, is critical for the effective planning of control measures; however, such efforts are often compromised by data insufficiencies and observational errors. Here, we develop a spatial-temporal inference methodology using a modified network model in conjunction with the ensemble adjustment Kalman filter, a Bayesian inference method equipped to handle observational errors. The combined method is capable of revealing the spatial-temporal progression of infectious disease, while requiring only limited, readily compiled data. We use this method to reconstruct the transmission network of the 2014-2015 Ebola epidemic in Sierra Leone and identify source and sink regions. Our inference suggests that, in Sierra Leone, transmission within the network introduced Ebola to neighbouring districts and initiated self-sustaining local epidemics; two of the more populous and connected districts, Kenema and Port Loko, facilitated two independent transmission pathways. Epidemic intensity differed by district, was highly correlated with population size (r = 0.76, p = 0.0015) and a critical window of opportunity for containing local Ebola epidemics at the source (ca one month) existed. This novel methodology can be used to help identify and contain the spatial expansion of future (re)emerging infectious disease outbreaks. © 2015 The Author(s).

Plague Doctors in the HIV/AIDS Epidemic: Mental Health Professionals and the "San Francisco Model," 1981-1990.

PubMed

Blair, Thomas R

2016-01-01

Psychiatrists, psychologists, and other mental health professionals were among the first and most crucial responders to HIV/AIDS. Given an epidemic in which behavior and identity played fundamental roles, mental health professionals were uniquely positioned to conduct social research to explain the existence and spread of disease; to develop clinical understanding of psychological aspects of HIV/AIDS as they emerged; and to collaborate with affected communities to promote education and behavioral change. This study examines the roles of mental health professionals as "plague doctors" in San Francisco's response to HIV/AIDS, in the early years of the epidemic. Among the many collaborations and projects that distinguished the "San Francisco model" of response to this plague, bathhouse-based epidemiology, consult-liaison psychiatry, and community partnerships for counseling and education are examined in detail as illustrations of the epidemic-changing engagement of the mental health community.

Forests in transition: Post-epidemic vegetation conditions [Chapter 4

Treesearch

Rob Hubbard; Michael Battaglia; Chuck Rhoades; Jim Thinnes; Tom Martin; Jeff Underhill; Mark Westfahl

2014-01-01

More than 23 million acres of lodgepole pine forests across the western U.S. have experienced overstory mortality following the recent mountain pine beetle (MPB) epidemic (USDA Forest Service 2013). Unknowns regarding the immediate and long-term consequences of the epidemic challenge the ability of managers to make informed decisions aimed at sustaining forest health...

Genomic and phenotypic variation in epidemic-spanning Salmonella enterica serovar Enteritidis isolates

PubMed Central

2009-01-01

Background Salmonella enterica serovar Enteritidis (S. Enteritidis) has caused major epidemics of gastrointestinal infection in many different countries. In this study we investigate genome divergence and pathogenic potential in S. Enteritidis isolated before, during and after an epidemic in Uruguay. Results 266 S. Enteritidis isolates were genotyped using RAPD-PCR and a selection were subjected to PFGE analysis. From these, 29 isolates spanning different periods, genetic profiles and sources of isolation were assayed for their ability to infect human epithelial cells and subjected to comparative genomic hybridization using a Salmonella pan-array and the sequenced strain S. Enteritidis PT4 P125109 as reference. Six other isolates from distant countries were included as external comparators. Two hundred and thirty three chromosomal genes as well as the virulence plasmid were found as variable among S. Enteritidis isolates. Ten out of the 16 chromosomal regions that varied between different isolates correspond to phage-like regions. The 2 oldest pre-epidemic isolates lack phage SE20 and harbour other phage encoded genes that are absent in the sequenced strain. Besides variation in prophage, we found variation in genes involved in metabolism and bacterial fitness. Five epidemic strains lack the complete Salmonella virulence plasmid. Significantly, strains with indistinguishable genetic patterns still showed major differences in their ability to infect epithelial cells, indicating that the approach used was insufficient to detect the genetic basis of this differential behaviour. Conclusion The recent epidemic of S. Enteritidis infection in Uruguay has been driven by the introduction of closely related strains of phage type 4 lineage. Our results confirm previous reports demonstrating a high degree of genetic homogeneity among S. Enteritidis isolates. However, 10 of the regions of variability described here are for the first time reported as being variable in S

Differential Equation Models for Sharp Threshold Dynamics

DTIC Science & Technology

2012-08-01

dynamics, and the Lanchester model of armed conflict, where the loss of a key capability drastically changes dynamics. We derive and demonstrate a step...dynamics using differential equations. 15. SUBJECT TERMS Differential Equations, Markov Population Process, S-I-R Epidemic, Lanchester Model 16...infection, where a detection event drastically changes dynamics, and the Lanchester model of armed conflict, where the loss of a key capability

Competitive epidemic spreading over arbitrary multilayer networks.

PubMed

Darabi Sahneh, Faryad; Scoglio, Caterina

2014-06-01

This study extends the Susceptible-Infected-Susceptible (SIS) epidemic model for single-virus propagation over an arbitrary graph to an Susceptible-Infected by virus 1-Susceptible-Infected by virus 2-Susceptible (SI_{1}SI_{2}S) epidemic model of two exclusive, competitive viruses over a two-layer network with generic structure, where network layers represent the distinct transmission routes of the viruses. We find analytical expressions determining extinction, coexistence, and absolute dominance of the viruses after we introduce the concepts of survival threshold and absolute-dominance threshold. The main outcome of our analysis is the discovery and proof of a region for long-term coexistence of competitive viruses in nontrivial multilayer networks. We show coexistence is impossible if network layers are identical yet possible if network layers are distinct. Not only do we rigorously prove a region of coexistence, but we can quantitate it via interrelation of central nodes across the network layers. Little to no overlapping of the layers' central nodes is the key determinant of coexistence. For example, we show both analytically and numerically that positive correlation of network layers makes it difficult for a virus to survive, while in a network with negatively correlated layers, survival is easier, but total removal of the other virus is more difficult.

Epidemic typhus.

PubMed

Bechah, Yassina; Capo, Christian; Mege, Jean-Louis; Raoult, Didier

2008-07-01

Epidemic typhus is transmitted to human beings by the body louse Pediculus humanus corporis. The disease is still considered a major threat by public-health authorities, despite the efficacy of antibiotics, because poor sanitary conditions are conducive to louse proliferation. Until recently, Rickettsia prowazekii, the causal agent, was thought to be confined to human beings and their body lice. Since 1975, R prowazekii infection in human beings has been related to contact with the flying squirrel Glaucomys volans in the USA. Moreover, Brill-Zinsser disease, a relapsed form of epidemic typhus that appears as sporadic cases many years after the initial infection, is unrelated to louse infestation. Stress or a waning immune system are likely to reactivate this earlier persistent infection, which could be the source of new epidemics when conditions facilitate louse infestation. Finally, R prowazekii is a potential category B bioterrorism agent, because it is stable in dried louse faeces and can be transmitted through aerosols. An increased understanding of the pathogenesis of epidemic typhus may be useful for protection against this bacterial threat.

Spatio-temporal analysis of an HLB epidemic in Florida and implications for spread.

USDA-ARS?s Scientific Manuscript database

Data for Huanglongbing (HLB) epidemics was collected during 5 assessment dates over a 2-year period from 11, 4-ha commercial citrus blocks in Florida. Data were analyzed for regional spatial characteristics via Ripley’s K analyses. Data were fitted to the logistic and Gompertz temporal models, the...

Epidemic outbreaks in complex heterogeneous networks

NASA Astrophysics Data System (ADS)

Moreno, Y.; Pastor-Satorras, R.; Vespignani, A.

2002-04-01

We present a detailed analytical and numerical study for the spreading of infections with acquired immunity in complex population networks. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations in the limit of a very large number of nodes, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures.

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

Population-level differences in disease transmission: A Bayesian analysis of multiple smallpox epidemics

PubMed Central

Elderd, Bret D.; Dwyer, Greg; Dukic, Vanja

2013-01-01

Estimates of a disease’s basic reproductive rate R0 play a central role in understanding outbreaks and planning intervention strategies. In many calculations of R0, a simplifying assumption is that different host populations have effectively identical transmission rates. This assumption can lead to an underestimate of the overall uncertainty associated with R0, which, due to the non-linearity of epidemic processes, may result in a mis-estimate of epidemic intensity and miscalculated expenditures associated with public-health interventions. In this paper, we utilize a Bayesian method for quantifying the overall uncertainty arising from differences in population-specific basic reproductive rates. Using this method, we fit spatial and non-spatial susceptible-exposed-infected-recovered (SEIR) models to a series of 13 smallpox outbreaks. Five outbreaks occurred in populations that had been previously exposed to smallpox, while the remaining eight occurred in Native-American populations that were naïve to the disease at the time. The Native-American outbreaks were close in a spatial and temporal sense. Using Bayesian Information Criterion (BIC), we show that the best model includes population-specific R0 values. These differences in R0 values may, in part, be due to differences in genetic background, social structure, or food and water availability. As a result of these inter-population differences, the overall uncertainty associated with the “population average” value of smallpox R0 is larger, a finding that can have important consequences for controlling epidemics. In general, Bayesian hierarchical models are able to properly account for the uncertainty associated with multiple epidemics, provide a clearer understanding of variability in epidemic dynamics, and yield a better assessment of the range of potential risks and consequences that decision makers face. PMID:24021521

A network-based meta-population approach to model Rift Valley fever epidemics.

PubMed

Xue, Ling; Scott, H Morgan; Cohnstaedt, Lee W; Scoglio, Caterina

2012-08-07

Rift Valley fever virus (RVFV) has been expanding its geographical distribution with important implications for both human and animal health. The emergence of Rift Valley fever (RVF) in the Middle East, and its continuing presence in many areas of Africa, has negatively impacted both medical and veterinary infrastructures and human morbidity, mortality, and economic endpoints. Furthermore, worldwide attention should be directed towards the broader infection dynamics of RVFV, because suitable host, vector and environmental conditions for additional epidemics likely exist on other continents; including Asia, Europe and the Americas. We propose a new compartmentalized model of RVF and the related ordinary differential equations to assess disease spread in both time and space; with the latter driven as a function of contact networks. Humans and livestock hosts and two species of vector mosquitoes are included in the model. The model is based on weighted contact networks, where nodes of the networks represent geographical regions and the weights represent the level of contact between regional pairings for each set of species. The inclusion of human, animal, and vector movements among regions is new to RVF modeling. The movement of the infected individuals is not only treated as a possibility, but also an actuality that can be incorporated into the model. We have tested, calibrated, and evaluated the model using data from the recent 2010 RVF outbreak in South Africa as a case study; mapping the epidemic spread within and among three South African provinces. An extensive set of simulation results shows the potential of the proposed approach for accurately modeling the RVF spreading process in additional regions of the world. The benefits of the proposed model are twofold: not only can the model differentiate the maximum number of infected individuals among different provinces, but also it can reproduce the different starting times of the outbreak in multiple locations

Environmental Predictors of Seasonal Influenza Epidemics across Temperate and Tropical Climates

PubMed Central

Tamerius, James D.; Shaman, Jeffrey; Alonso, Wladmir J.; Bloom-Feshbach, Kimberly; Uejio, Christopher K.; Comrie, Andrew; Viboud, Cécile

2013-01-01

Human influenza infections exhibit a strong seasonal cycle in temperate regions. Recent laboratory and epidemiological evidence suggests that low specific humidity conditions facilitate the airborne survival and transmission of the influenza virus in temperate regions, resulting in annual winter epidemics. However, this relationship is unlikely to account for the epidemiology of influenza in tropical and subtropical regions where epidemics often occur during the rainy season or transmit year-round without a well-defined season. We assessed the role of specific humidity and other local climatic variables on influenza virus seasonality by modeling epidemiological and climatic information from 78 study sites sampled globally. We substantiated that there are two types of environmental conditions associated with seasonal influenza epidemics: “cold-dry” and “humid-rainy”. For sites where monthly average specific humidity or temperature decreases below thresholds of approximately 11–12 g/kg and 18–21°C during the year, influenza activity peaks during the cold-dry season (i.e., winter) when specific humidity and temperature are at minimal levels. For sites where specific humidity and temperature do not decrease below these thresholds, seasonal influenza activity is more likely to peak in months when average precipitation totals are maximal and greater than 150 mm per month. These findings provide a simple climate-based model rooted in empirical data that accounts for the diversity of seasonal influenza patterns observed across temperate, subtropical and tropical climates. PMID:23505366

Diversity of multilayer networks and its impact on collaborating epidemics

NASA Astrophysics Data System (ADS)

Min, Yong; Hu, Jiaren; Wang, Weihong; Ge, Ying; Chang, Jie; Jin, Xiaogang

2014-12-01

Interacting epidemics on diverse multilayer networks are increasingly important in modeling and analyzing the diffusion processes of real complex systems. A viral agent spreading on one layer of a multilayer network can interact with its counterparts by promoting (cooperative interaction), suppressing (competitive interaction), or inducing (collaborating interaction) its diffusion on other layers. Collaborating interaction displays different patterns: (i) random collaboration, where intralayer or interlayer induction has the same probability; (ii) concentrating collaboration, where consecutive intralayer induction is guaranteed with a probability of 1; and (iii) cascading collaboration, where consecutive intralayer induction is banned with a probability of 0. In this paper, we develop a top-bottom framework that uses only two distributions, the overlaid degree distribution and edge-type distribution, to model collaborating epidemics on multilayer networks. We then state the response of three collaborating patterns to structural diversity (evenness and difference of network layers). For viral agents with small transmissibility, we find that random collaboration is more effective in networks with higher diversity (high evenness and difference), while the concentrating pattern is more suitable in uneven networks. Interestingly, the cascading pattern requires a network with moderate difference and high evenness, and the moderately uneven coupling of multiple network layers can effectively increase robustness to resist cascading failure. With large transmissibility, however, we find that all collaborating patterns are more effective in high-diversity networks. Our work provides a systemic analysis of collaborating epidemics on multilayer networks. The results enhance our understanding of biotic and informative diffusion through multiple vectors.