A Model for a Chikungunya Outbreak in a Rural Cambodian Setting: Implications for Disease Control in Uninfected Areas

Following almost 30 years of relative silence, chikungunya fever reemerged in Kenya in 2004. It subsequently spread to the islands of the Indian Ocean, reaching Southeast Asia in 2006. The virus was first detected in Cambodia in 2011 and a large outbreak occurred in the village of Trapeang Roka Kampong Speu Province in March 2012, in which 44% of the villagers had a recent infection biologically confirmed. The epidemic curve was constructed from the number of biologically-confirmed CHIKV cases per day determined from the date of fever onset, which was self-reported during a data collection campaign conducted in the village after the outbreak. All individuals participating in the campaign had infections confirmed by laboratory analysis, allowing for the identification of asymptomatic cases and those with an unreported date of fever onset. We develop a stochastic model explicitly including such cases, all of whom do not appear on the epidemic curve. We estimate the basic reproduction number of the outbreak to be 6.46 (95% C.I. [6.24, 6.78]). We show that this estimate is particularly sensitive to changes in the biting rate and mosquito longevity. Our model also indicates that the infection was more widespread within the population on the reported epidemic start date. We show that the exclusion of asymptomatic cases and cases with undocumented onset dates can lead to an underestimation of the reproduction number which, in turn, could negatively impact control strategies implemented by public health authorities. We highlight the need for properly documenting newly emerging pathogens in immunologically naive populations and the importance of identifying the route of disease introduction.     

Risk maps for the spread of highly pathogenic avian influenza in poultry

Devastating epidemics of highly contagious animal diseases such as avian influenza, classical swine fever, and foot-and-mouth disease underline the need for improved understanding of the factors promoting the spread of these pathogens. Here the authors present a spatial analysis of the between-farm transmission of a highly pathogenic H7N7 avian influenza virus that caused a large epidemic in The Netherlands in 2003. The authors developed a method to estimate key parameters determining the spread of highly transmissible animal diseases between farms based on outbreak data. The method allows for the identification of high-risk areas for propagating spread in an epidemiologically underpinned manner. A central concept is the transmission kernel, which determines the probability of pathogen transmission from infected to uninfected farms as a function of interfarm distance. The authors show how an estimate of the transmission kernel naturally provides estimates of the critical farm density and local reproduction numbers, which allows one to evaluate the effectiveness of control strategies. For avian influenza, the analyses show that there are two poultry-dense areas in The Netherlands where epidemic spread is possible, and in which local control measures are unlikely to be able to halt an unfolding epidemic. In these regions an epidemic can only be brought to an end by the depletion of susceptible farms by infection or massive culling. The analyses provide an estimate of the spatial range over which highly pathogenic avian influenza viruses spread between farms, and emphasize that control measures aimed at controlling such outbreaks need to take into account the local density of farms.     

Protective Vaccine Efficacy when Vaccine Response is Random

Vaccine induced protection against infection is often random because of primary vaccine failures and variation in the immune systems of hosts. We introduce a concept of protective vaccine efficacy in terms of mean relative susceptibility of vaccinated individuals and derive both a lower and an upper bound for it. These bounds apply for all distributions of the vaccine response and can be estimated from data on the size of a major epidemic. Standard errors are given for estimates of the bounds. Bounds are also given for the vaccination coverage required to prevent epidemics and these are also estimable from data on the size of a major epidemic. The results are applied to data on an outbreak of mumps.     

Using Combined Diagnostic Test Results to Hindcast Trends of Infection from Cross-Sectional Data

Infectious disease surveillance is key to limiting the consequences from infectious pathogens and maintaining animal and public health. Following the detection of a disease outbreak, a response in proportion to the severity of the outbreak is required. It is thus critical to obtain accurate information concerning the origin of the outbreak and its forward trajectory. However, there is often a lack of situational awareness that may lead to over- or under-reaction. There is a widening range of tests available for detecting pathogens, with typically different temporal characteristics, e.g. in terms of when peak test response occurs relative to time of exposure. We have developed a statistical framework that combines response level data from multiple diagnostic tests and is able to ‘hindcast’ (infer the historical trend of) an infectious disease epidemic. Assuming diagnostic test data from a cross-sectional sample of individuals infected with a pathogen during an outbreak, we use a Bayesian Markov Chain Monte Carlo (MCMC) approach to estimate time of exposure, and the overall epidemic trend in the population prior to the time of sampling. We evaluate the performance of this statistical framework on simulated data from epidemic trend curves and show that we can recover the parameter values of those trends. We also apply the framework to epidemic trend curves taken from two historical outbreaks: a bluetongue outbreak in cattle, and a whooping cough outbreak in humans. Together, these results show that hindcasting can estimate the time since infection for individuals and provide accurate estimates of epidemic trends, and can be used to distinguish whether an outbreak is increasing or past its peak. We conclude that if temporal characteristics of diagnostics are known, it is possible to recover epidemic trends of both human and animal pathogens from cross-sectional data collected at a single point in time.     

Skip the Trip: Air Travelers' Behavioral Responses to Pandemic Influenza

Theory suggests that human behavior has implications for disease spread. We examine the hypothesis that individuals engage in voluntary defensive behavior during an epidemic. We estimate the number of passengers missing previously purchased flights as a function of concern for swine flu or A/H1N1 influenza using 1.7 million detailed flight records, Google Trends, and the World Health Organization''s FluNet data. We estimate that concern over “swine flu,” as measured by Google Trends, accounted for 0.34% of missed flights during the epidemic. The Google Trends data correlates strongly with media attention, but poorly (at times negatively) with reported cases in FluNet. Passengers show no response to reported cases. Passengers skipping their purchased trips forwent at least $50 M in travel related benefits. Responding to actual cases would have cut this estimate in half. Thus, people appear to respond to an epidemic by voluntarily engaging in self-protection behavior, but this behavior may not be responsive to objective measures of risk. Clearer risk communication could substantially reduce epidemic costs. People undertaking costly risk reduction behavior, for example, forgoing nonrefundable flights, suggests they may also make less costly behavior adjustments to avoid infection. Accounting for defensive behaviors may be important for forecasting epidemics, but linking behavior with epidemics likely requires consideration of risk communication.     

Health newscasts for increasing influenza vaccination coverage: an inductive reasoning game approach

Both pandemic and seasonal influenza are receiving more attention from mass media than ever before. Topics such as epidemic severity and vaccination are changing the way in which we perceive the utility of disease prevention. Voluntary influenza vaccination has been recently modeled using inductive reasoning games. It has thus been found that severe epidemics may occur because individuals do not vaccinate and, instead, attempt to benefit from the immunity of their peers. Such epidemics could be prevented by voluntary vaccination if incentives were offered. However, a key assumption has been that individuals make vaccination decisions based on whether there was an epidemic each influenza season; no other epidemiological information is available to them. In this work, we relax this assumption and investigate the consequences of making more informed vaccination decisions while no incentives are offered. We obtain three major results. First, individuals will not cooperate enough to constantly prevent influenza epidemics through voluntary vaccination no matter how much they learned about influenza epidemiology. Second, broadcasting epidemiological information richer than whether an epidemic occurred may stabilize the vaccination coverage and suppress severe influenza epidemics. Third, the stable vaccination coverage follows the trend of the perceived benefit of vaccination. However, increasing the amount of epidemiological information released to the public may either increase or decrease the perceived benefit of vaccination. We discuss three scenarios where individuals know, in addition to whether there was an epidemic, (i) the incidence, (ii) the vaccination coverage and (iii) both the incidence and the vaccination coverage, every influenza season. We show that broadcasting both the incidence and the vaccination coverage could yield either better or worse vaccination coverage than broadcasting each piece of information on its own.     

Active responses to outbreaks of infectious wildlife diseases: objectives,strategies and constraints determine feasibility and success

Emerging wildlife diseases are taking a heavy toll on animal and plant species worldwide. Mitigation, particularly in the initial epidemic phase, is hindered by uncertainty about the epidemiology and management of emerging diseases, but also by vague or poorly defined objectives. Here, we use a quantitative analysis to assess how the decision context of mitigation objectives, available strategies and practical constraints influences the decision of whether and how to respond to epidemics in wildlife. To illustrate our approach, we parametrized the model for European fire salamanders affected by Batrachochytrium salamandrivorans, and explored different combinations of conservation, containment and budgetary objectives. We found that in approximately half of those scenarios, host removal strategies perform equal to or worse than no management at all during a local outbreak, particularly where removal cannot exclusively target infected individuals. Moreover, the window for intervention shrinks rapidly if an outbreak is detected late or if a response is delayed. Clearly defining the decision context is, therefore, vital to plan meaningful responses to novel outbreaks. Explicitly stating objectives, strategies and constraints, if possible before an outbreak occurs, avoids wasting precious resources and creating false expectations about what can and cannot be achieved during the epidemic phase.     

How do toxicants affect epidemiological dynamics?

Populations are formed of their constituent interacting individuals, each with their own respective within‐host biological processes. Infection not only spreads within the host organism but also spreads between individuals. Here we propose and study a multilevel model which links the within‐host statuses of immunity and parasite density to population epidemiology under sublethal and lethal toxicant exposure. We analyse this nested model in order to better understand how toxicants impact the spread of disease within populations. We demonstrate that outbreak of infection within a population is completely determined by the level of toxicant exposure, and that it is maximised by intermediate toxicant dosage. We classify the population epidemiology into five phases of increasing toxicant exposure and calculate the conditions under which disease will spread, showing that there exists a threshold toxicant level under which epidemics will not occur. In general, higher toxicant load results in either extinction of the population or outbreak of infection. The within‐host statuses of the individual host also determine the outcome of the epidemic at the population level. We discuss applications of our model in the context of environmental epidemiology, predicting that increased exposure to toxicants could result in greater risk of epidemics within ecological systems. We predict that reducing sublethal toxicant exposure below our predicted safe threshold could contribute to controlling population level disease and infection.     

Stochastic two-group models with transmission dependent on host infectivity or susceptibility

ABSTRACT

Stochastic epidemic models with two groups are formulated and applied to emerging and re-emerging infectious diseases. In recent emerging diseases, disease spread has been attributed to superspreaders, highly infectious individuals that infect a large number of susceptible individuals. In some re-emerging infectious diseases, disease spread is attributed to waning immunity in susceptible hosts. We apply a continuous-time Markov chain (CTMC) model to study disease emergence or re-emergence from different groups, where the transmission rates depend on either the infectious host or the susceptible host. Multitype branching processes approximate the dynamics of the CTMC model near the disease-free equilibrium and are used to estimate the probability of a minor or a major epidemic. It is shown that the probability of a major epidemic is greater if initiated by an individual from the superspreader group or by an individual from the highly susceptible group. The models are applied to Severe Acute Respiratory Syndrome and measles.     

Social Network Sensors for Early Detection of Contagious Outbreaks

Current methods for the detection of contagious outbreaks give contemporaneous information about the course of an epidemic at best. It is known that individuals near the center of a social network are likely to be infected sooner during the course of an outbreak, on average, than those at the periphery. Unfortunately, mapping a whole network to identify central individuals who might be monitored for infection is typically very difficult. We propose an alternative strategy that does not require ascertainment of global network structure, namely, simply monitoring the friends of randomly selected individuals. Such individuals are known to be more central. To evaluate whether such a friend group could indeed provide early detection, we studied a flu outbreak at Harvard College in late 2009. We followed 744 students who were either members of a group of randomly chosen individuals or a group of their friends. Based on clinical diagnoses, the progression of the epidemic in the friend group occurred 13.9 days (95% C.I. 9.9–16.6) in advance of the randomly chosen group (i.e., the population as a whole). The friend group also showed a significant lead time (p<0.05) on day 16 of the epidemic, a full 46 days before the peak in daily incidence in the population as a whole. This sensor method could provide significant additional time to react to epidemics in small or large populations under surveillance. The amount of lead time will depend on features of the outbreak and the network at hand. The method could in principle be generalized to other biological, psychological, informational, or behavioral contagions that spread in networks.     

Waning immunity and sub-clinical infection in an epidemic model: implications for pertussis in The Netherlands

In The Netherlands, an epidemic outbreak of pertussis took place in 1996-1997. Understanding of the causes of the epidemic is hampered by the fact that many cases of infection with Bordetella pertussis go by unnoticed, and by the fact that immunity against infection does not last lifelong. Motivated by these observations, we develop and analyze an age-structured epidemic model that takes these factors into account. A distinction is made between infection in immunologically naive individuals, and infection in individuals whose immune system has been primed before by infection or vaccination. While the former often lead to severe symptoms and thus are more often diagnosed and notified, the latter are largely sub-clinical. The main questions are: (1) to what extent do sub-clinical infections contribute to the circulation of B. pertussis; and (2) what might be the causes for the recent epidemic? To answer these questions, we first present a new method to estimate the force of infection from notification data. The method is applied to the 1988-1995 case notification data from The Netherlands. Estimates of the force of infection vary greatly, depending on the rate at which immunity is lost, and on the fraction of sub-clinical infections. For the 1988-1995 period, our analysis indicates that if immunity is lost at a small rate and if a majority of infections is sub-clinical, the contribution of infection in adults to the transmission process cannot be neglected. Our results furthermore indicate that a decrease in the duration of protection after vaccination due to a change in the pathogen is the most likely factor to account for the 1996-1997 epidemic.     

Evaluating Subcriticality during the Ebola Epidemic in West Africa

The 2014–2015 Ebola outbreak is the largest and most widespread to date. In order to estimate ongoing transmission in the affected countries, we estimated the weekly average number of secondary cases caused by one individual infected with Ebola throughout the infectious period for each affected West African country using a stochastic hidden Markov model fitted to case data from the World Health Organization. If the average number of infections caused by one Ebola infection is less than 1.0, the epidemic is subcritical and cannot sustain itself. The epidemics in Liberia and Sierra Leone have approached subcriticality at some point during the epidemic; the epidemic in Guinea is ongoing with no evidence that it is subcritical. Response efforts to control the epidemic should continue in order to eliminate Ebola cases in West Africa.     

Common source epidemics I: A stochastic model

A discrete time stochastic model is formulated for the spread of a disease which is transmitted to an uninfected but susceptible individual through an environmental source and not through contact (either direct or indirect) with infected individuals. The model incorporates both exposure and infection components. The exposure component includes consideration of the introduction of an infectious agent into the environment and the subsequent diffusion of the agent. It also includes time and location patterns for visits by individuals in the target population to the affected environment. The infection component incorporates physiological responses of exposed individuals to the infectious agent. The goal of the model is to provide a method for developing a predicted epidemic curve. Comments are given on an application of the model to the study of an outbreak of toxoplasmosis in Atlanta, Georgia, in 1977. This work was partially supported by BRSG Grant S07 RR0731 awarded by the Biomedical Research Support Grant Program, Division of Research Resources, National Institutes of Health.     

A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks

Epidemic dynamics pose a great challenge to stochastic modelling because chance events are major determinants of the size and the timing of the outbreak. Reintroduction of the disease through contact with infected individuals from other areas is an important latent stochastic variable. In this study we model these stochastic processes to explain extinction and recurrence of epidemics observed in measles. We develop estimating functions for such a model and apply the methodology to temporal case counts of measles in 60 cities in England and Wales. In order to estimate the unobserved spatial contact process we suggest a method based on stochastic simulation and marginal densities. The estimation results show that it is possible to consider a unified model for the UK cities where the parameters depend on the city size. Stochastic realizations from the dynamic model realistically capture the transitions from an endemic cyclic pattern in large populations to irregular epidemic outbreaks in small human host populations.     

Epidemic outbreaks on structured populations

Our chances to halt epidemic outbreaks rely on how accurately we represent the population structure underlying the disease spread. When analysing global epidemics this force us to consider metapopulation models taking into account intra- and inter-community interactions. Here I introduce and analyze a metapopulation model which accounts for several features observed in real outbreaks. First, I demonstrate that depending on the intra-community expected outbreak size and the fraction of social bridges the epidemic outbreaks die out or there is a finite probability to observe a global epidemics. Second, I show that the global scenario is characterized by resurgent epidemics, their number increasing with increasing the intra-community average distance between individuals. Finally, I present empirical data for the AIDS epidemics supporting the model predictions.     

Distinguishing epidemic waves from disease spillover in a wildlife population

Serengeti lions frequently experience viral outbreaks. In 1994, one-third of Serengeti lions died from canine distemper virus (CDV). Based on the limited epidemiological data available from this period, it has been unclear whether the 1994 outbreak was propagated by lion-to-lion transmission alone or involved multiple introductions from other sympatric carnivore species. More broadly, we do not know whether contacts between lions allow any pathogen with a relatively short infectious period to percolate through the population (i.e. reach epidemic proportions). We built one of the most realistic contact network models for a wildlife population to date, based on detailed behavioural and movement data from a long-term lion study population. The model allowed us to identify previously unrecognized biases in the sparse data from the 1994 outbreak and develop methods for judiciously inferring disease dynamics from typical wildlife samples. Our analysis of the model in light of the 1994 outbreak data strongly suggest that, although lions are sufficiently well connected to sustain epidemics of CDV-like diseases, the 1994 epidemic was fuelled by multiple spillovers from other carnivore species, such as jackals and hyenas.     

The spatial spread and final size of models for the deterministic host-vector epidemic

A disease is considered which is transferred between two populations, termed hosts and vectors. The disease is transmitted solely from infected vector to uninfected host and from infected host to uninfected vector. Two models are formulated in which infectious individuals are introduced at time t = 0 into the populations of susceptibles, thus triggering an epidemic through those populations. Conditions are established for a major epidemic to occur, and the final size of the epidemic is obtained for these models when no spatial aspect is considered. When a spatial aspect is included in the models, again the condition for a major epidemic is obtained. The pandemic theorem is proved rigorously, giving a lower bound for the proportion of each population, at each point, who eventually suffer the epidemic. The behavior a long way from the initial focus of infection is also rigorously obtained.     

Estimating absolute and relative case fatality ratios from infectious disease surveillance data

Knowing which populations are most at risk for severe outcomes from an emerging infectious disease is crucial in deciding the optimal allocation of resources during an outbreak response. The case fatality ratio (CFR) is the fraction of cases that die after contracting a disease. The relative CFR is the factor by which the case fatality in one group is greater or less than that in a second group. Incomplete reporting of the number of infected individuals, both recovered and dead, can lead to biased estimates of the CFR. We define conditions under which the CFR and the relative CFR are identifiable. Furthermore, we propose an estimator for the relative CFR that controls for time-varying reporting rates. We generalize our methods to account for elapsed time between infection and death. To demonstrate the new methodology, we use data from the 1918 influenza pandemic to estimate relative CFRs between counties in Maryland. A simulation study evaluates the performance of the methods in outbreak scenarios. An R software package makes the methods and data presented here freely available. Our work highlights the limitations and challenges associated with estimating absolute and relative CFRs in practice. However, in certain situations, the methods presented here can help identify vulnerable subpopulations early in an outbreak of an emerging pathogen such as pandemic influenza.     

Behavioral responses to the 2015 MERS epidemic in Korea

Understanding behavioral responses to epidemics is important in evaluating the broad health consequences of emerging infectious diseases. Building on the economic epidemiology literature, this study investigates individual behavioral responses to the 2015 Middle East Respiratory Syndrome Coronavirus (MERS-CoV) epidemic in Korea using a panel of individuals in a nationally representative survey. Results show that exposure to the epidemic led to lasting impacts on smoking and drinking behaviors, indicating that emerging infectious disease outbreaks are motivations for behavioral changes and opportunities for public policy interventions. In particular, individuals in the hardest-hit regions or socially connected persons were more likely to change their risky behaviors, suggesting that intensity of exposure and social interactions are potential mechanisms.     

On the Role of Asymptomatic Infection in Transmission Dynamics of Infectious Diseases

We propose a compartmental disease transmission model with an asymptomatic (or subclinical) infective class to study the role of asymptomatic infection in the transmission dynamics of infectious diseases with asymptomatic infectives, e.g., influenza. Analytical results are obtained using the respective ratios of susceptible, exposed (incubating), and asymptomatic classes to the clinical symptomatic infective class. Conditions are given for bistability of equilibria to occur, where trajectories with distinct initial values could result in either a major outbreak where the disease spreads to the whole population or a lesser outbreak where some members of the population remain uninfected. This dynamic behavior did not arise in a SARS model without asymptomatic infective class studied by Hsu and Hsieh (SIAM J. Appl. Math. 66(2), 627–647, 2006). Hence, this illustrates that depending on the initial states, control of a disease outbreak with asymptomatic infections may involve more than simply reducing the reproduction number. Moreover, the presence of asymptomatic infections could result in either a positive or negative impact on the outbreak, depending on different sets of conditions on the parameters, as illustrated with numerical simulations. Biological interpretations of the analytical and numerical results are also given.