Simulated epidemics in an empirical spatiotemporal network of 50,185 sexual contacts

Sexual contact patterns, both in their temporal and network structure, can influence the spread of sexually transmitted infections (STI). Most previous literature has focused on effects of network topology; few studies have addressed the role of temporal structure. We simulate disease spread using SI and SIR models on an empirical temporal network of sexual contacts in high-end prostitution. We compare these results with several other approaches, including randomization of the data, classic mean-field approaches, and static network simulations. We observe that epidemic dynamics in this contact structure have well-defined, rather high epidemic thresholds. Temporal effects create a broad distribution of outbreak sizes, even if the per-contact transmission probability is taken to its hypothetical maximum of 100%. In general, we conclude that the temporal correlations of our network accelerate outbreaks, especially in the early phase of the epidemics, while the network topology (apart from the contact-rate distribution) slows them down. We find that the temporal correlations of sexual contacts can significantly change simulated outbreaks in a large empirical sexual network. Thus, temporal structures are needed alongside network topology to fully understand the spread of STIs. On a side note, our simulations further suggest that the specific type of commercial sex we investigate is not a reservoir of major importance for HIV.     

Coalescent inference for infectious disease: meta-analysis of hepatitis C

Genetic analysis of pathogen genomes is a powerful approach to investigating the population dynamics and epidemic history of infectious diseases. However, the theoretical underpinnings of the most widely used, coalescent methods have been questioned, casting doubt on their interpretation. The aim of this study is to develop robust population genetic inference for compartmental models in epidemiology. Using a general approach based on the theory of metapopulations, we derive coalescent models under susceptible–infectious (SI), susceptible–infectious–susceptible (SIS) and susceptible–infectious–recovered (SIR) dynamics. We show that exponential and logistic growth models are equivalent to SI and SIS models, respectively, when co-infection is negligible. Implementing SI, SIS and SIR models in BEAST, we conduct a meta-analysis of hepatitis C epidemics, and show that we can directly estimate the basic reproductive number (R₀) and prevalence under SIR dynamics. We find that differences in genetic diversity between epidemics can be explained by differences in underlying epidemiology (age of the epidemic and local population density) and viral subtype. Model comparison reveals SIR dynamics in three globally restricted epidemics, but most are better fit by the simpler SI dynamics. In summary, metapopulation models provide a general and practical framework for integrating epidemiology and population genetics for the purposes of joint inference.     

Dynamics of stochastic epidemics on heterogeneous networks

Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a heterogeneous network. Using this, we consider analytically the early asymptotic exponential growth phase of such epidemics, showing how the higher order moments of the network degree distribution enter into the stochastic behaviour of the epidemic. We find that the first three moments of the network degree distribution are needed to specify the variance in disease prevalence fully, meaning that the skewness of the degree distribution affects the variance of the prevalence of infection. We compare these asymptotic results to simulation and find a close agreement for city-sized populations.     

The effect of intrinsic stochasticity on transmitted HIV drug resistance patterns

Estimates of transmitted HIV drug-resistance prevalence vary widely among and within epidemiological surveys. Interpretation of trends from available survey data is therefore difficult. Because the emergence of drug-resistance involves small populations of infected drug-resistant individuals, the role of stochasticity (chance events) is likely to be important. The question addressed here is: how much variability in transmitted HIV drug-resistance prevalence patterns arises due to intrinsic stochasticity alone, i.e., if all starting conditions in the different epidemics surveyed were identical? This ‘thought experiment’ gives insight into the minimum expected variabilities within and among epidemics. A simple stochastic mathematical model was implemented. Our results show that stochasticity alone can generate a significant degree of variability and that this depends on the size and variation of the pool of new infections when drug treatment is first introduced. The variability in transmitted drug-resistance prevalence within an epidemic (i.e., the temporal variability) is large when the annual pool of all new infections is small (fewer than 200, typical of the HIV epidemics in Central European and Scandinavian countries) but diminishes rapidly as that pool grows. Epidemiological surveys involving hundreds of new infections annually are therefore needed to allow meaningful interpretation of temporal trends in transmitted drug-resistance prevalence within individual epidemics. The stochastic variability among epidemics shows a similar dependence on the pool of new infections if treatment is introduced after endemic equilibrium is established, but can persist even when there are more than 10,000 new infections annually if drug therapy is introduced earlier. Stochastic models may therefore have an important role to play in interpreting differences in transmitted drug-resistance prevalence trends among epidemiological surveys.     

Effects of predation on host-pathogen dynamics in SIR models

The integration of infectious disease epidemiology with community ecology is an active area of research. Recent studies using SI models without acquired immunity have demonstrated that predation can suppress infectious disease levels. The authors recently showed that incorporating immunity (SIR models) can produce a “hump”-shaped relationship between disease prevalence and predation pressure; thus, low to moderate levels of predation can boost prevalence in hosts with acquired immunity. Here we examine the robustness of this pattern to realistic extensions of a basic SIR model, including density-dependent host regulation, predator saturation, interference, frequency-dependent transmission, predator numerical responses, and explicit resource dynamics. A non-monotonic relationship between disease prevalence and predation pressure holds across all these scenarios. With saturation, there can also be complex responses of mean host abundance to increasing predation, as well as bifurcations leading to unstable cycles (epidemics) and pathogen extinction at larger predator numbers. Firm predictions about the relationship between prevalence and predation thus require one to consider the complex interplay of acquired immunity, host regulation, and foraging behavior of the predator.     

A Covering-Graph Approach to Epidemics on SIS and SIS-Like Networks

In this paper, we introduce a new class of epidemics on networks which we call SI(S/I). SI(S/I) networks differ from SIS networks in allowing an infected individual to become reinfected without first passing to the susceptible state. We use a covering-graph construction to compare SIR, SIS, and SI(S/I) networks. Like the SIR networks that cover them, SI(S/I) networks exhibit infection probabilities that are monotone with respect to both transmission probabilities and the initial set of infectives. The same covering-graph construction allows us to characterize the recurrent states in an SIS or SI(S/I) network with reinfection.     

Spatial Heterogeneity,Host Movement and Mosquito-Borne Disease Transmission

Mosquito-borne diseases are a global health priority disproportionately affecting low-income populations in tropical and sub-tropical countries. These pathogens live in mosquitoes and hosts that interact in spatially heterogeneous environments where hosts move between regions of varying transmission intensity. Although there is increasing interest in the implications of spatial processes for mosquito-borne disease dynamics, most of our understanding derives from models that assume spatially homogeneous transmission. Spatial variation in contact rates can influence transmission and the risk of epidemics, yet the interaction between spatial heterogeneity and movement of hosts remains relatively unexplored. Here we explore, analytically and through numerical simulations, how human mobility connects spatially heterogeneous mosquito populations, thereby influencing disease persistence (determined by the basic reproduction number R ₀), prevalence and their relationship. We show that, when local transmission rates are highly heterogeneous, R ₀ declines asymptotically as human mobility increases, but infection prevalence peaks at low to intermediate rates of movement and decreases asymptotically after this peak. Movement can reduce heterogeneity in exposure to mosquito biting. As a result, if biting intensity is high but uneven, infection prevalence increases with mobility despite reductions in R ₀. This increase in prevalence decreases with further increase in mobility because individuals do not spend enough time in high transmission patches, hence decreasing the number of new infections and overall prevalence. These results provide a better basis for understanding the interplay between spatial transmission heterogeneity and human mobility, and their combined influence on prevalence and R ₀.     

Exploiting temporal network structures of human interaction to effectively immunize populations

Decreasing the number of people who must be vaccinated to immunize a community against an infectious disease could both save resources and decrease outbreak sizes. A key to reaching such a lower threshold of immunization is to find and vaccinate people who, through their behavior, are more likely than average to become infected and to spread the disease further. Fortunately, the very behavior that makes these people important to vaccinate can help us to localize them. Earlier studies have shown that one can use previous contacts to find people that are central in static contact networks. However, real contact patterns are not static. In this paper, we investigate if there is additional information in the temporal contact structure for vaccination protocols to exploit. We answer this affirmative by proposing two immunization methods that exploit temporal correlations and showing that these methods outperform a benchmark static-network protocol in four empirical contact datasets under various epidemic scenarios. Both methods rely only on obtainable, local information, and can be implemented in practice. For the datasets directly related to contact patterns of potential disease spreading (of sexually-transmitted and nosocomial infections respectively), the most efficient protocol is to sample people at random and vaccinate their latest contacts. The network datasets are temporal, which enables us to make more realistic evaluations than earlier studies--we use only information about the past for the purpose of vaccination, and about the future to simulate disease outbreaks. Using analytically tractable models, we identify two temporal structures that explain how the protocols earn their efficiency in the empirical data. This paper is a first step towards real vaccination protocols that exploit temporal-network structure--future work is needed both to characterize the structure of real contact sequences and to devise immunization methods that exploit these.     

Priority effects within coinfected hosts can drive unexpected population‐scale patterns of parasite prevalence

Organisms are frequently coinfected by multiple parasite strains and species, and interactions between parasites within hosts are known to influence parasite prevalence and diversity, as well as epidemic timing. Importantly, interactions between coinfecting parasites can be affected by the order in which they infect hosts (i.e. within‐host priority effects). In this study, we use a single‐host, two‐pathogen, SI model with environmental transmission to explore how within‐host priority effects scale up to alter host population‐scale infection patterns. Specifically, we ask how parasite prevalence changes in the presence of different types of priority effects. We consider two scenarios without priority effects and four scenarios with priority effects where there is either an advantage or a disadvantage to being the first to infect in a coinfected host. Models without priority effects always predict negative relationships between the prevalences of both parasites. In contrast, models with priority effects can yield unimodal prevalence relationships where the prevalence of a focal parasite is minimized or maximized at intermediate prevalences of a coinfecting parasite. The mechanism behind this pattern is that as the prevalence of the coinfecting parasite increases, most infections of the focal parasite change from occurring as solo infections, to first arrival coinfections, to second arrival coinfections. The corresponding changes in parasite fitness as the focal parasite moves from one infection class to another then map to changes in focal parasite prevalence. Further, we found that even when parasites interact negatively within a host, they still can have positive prevalence relationships at the population scale. These results suggest that within‐host priority effects can change host population‐scale infection patterns in systematic (and initially counterintuitive) ways, and that taking them into account may improve disease forecasting in coinfected populations.     

Ecology and dynamics of the blood parasite, Hepatozoon tuatarae (Apicomplexa), in tuatara (Sphenodon punctatus) on Stephens Island, New Zealand

We explored infection patterns and temporal dynamics of the protozoan blood parasite Hepatozoon tuatarae (Apicomplexa) infecting the tuatara (Sphenodon punctatus), a protected reptile living on Stephens Island, New Zealand. In March 2006, we surveyed tuatara in five study sites to examine spatial variation in infection prevalence, and four times, from May 2005 to November 2006, we recaptured marked individuals within three study sites to examine the temporal dynamics of infection. We also examined how blood-parasite infection patterns were influenced by host sex, body size, and host infestation with ticks (Amblyomma sphenodonti) and mites (Neotrombicula spp.), which are potential vectors of the blood parasite. Infection prevalence (16.9-24% infected) and intensity (<0.01-0.1% blood cells infected) were low in all samples. Infection intensity varied among the five sampled sites in March 2006, but prevalence did not. Neither infection prevalence nor intensity varied with time, and infections were detected in consecutive samples from recaptured individuals for up to 18 mo. Neither survey showed an influence of host sex on infection, but both surveys showed infection intensity declined with increasing host body size, as did infection prevalence in the spatial survey. In the temporal survey, we found a positive relationship between the tick numbers on hosts and blood-parasite infection intensity, which were stronger in two of the sampling periods and among larger hosts. These data suggest that exposure and susceptibility to infection decreases with host size and that ticks, but not mites, are probably the vectors in this ancient host-parasite association of a long-lived (>50 yr) host.     

Generation interval contraction and epidemic data analysis

The generation interval is the time between the infection time of an infected person and the infection time of his or her infector. Probability density functions for generation intervals have been an important input for epidemic models and epidemic data analysis. In this paper, we specify a general stochastic SIR epidemic model and prove that the mean generation interval decreases when susceptible persons are at risk of infectious contact from multiple sources. The intuition behind this is that when a susceptible person has multiple potential infectors, there is a "race" to infect him or her in which only the first infectious contact leads to infection. In an epidemic, the mean generation interval contracts as the prevalence of infection increases. We call this global competition among potential infectors. When there is rapid transmission within clusters of contacts, generation interval contraction can be caused by a high local prevalence of infection even when the global prevalence is low. We call this local competition among potential infectors. Using simulations, we illustrate both types of competition. Finally, we show that hazards of infectious contact can be used instead of generation intervals to estimate the time course of the effective reproductive number in an epidemic. This approach leads naturally to partial likelihoods for epidemic data that are very similar to those that arise in survival analysis, opening a promising avenue of methodological research in infectious disease epidemiology.     

Erratic flu vaccination emerges from short-sighted behavior in contact networks

The effectiveness of seasonal influenza vaccination programs depends on individual-level compliance. Perceptions about risks associated with infection and vaccination can strongly influence vaccination decisions and thus the ultimate course of an epidemic. Here we investigate the interplay between contact patterns, influenza-related behavior, and disease dynamics by incorporating game theory into network models. When individuals make decisions based on past epidemics, we find that individuals with many contacts vaccinate, whereas individuals with few contacts do not. However, the threshold number of contacts above which to vaccinate is highly dependent on the overall network structure of the population and has the potential to oscillate more wildly than has been observed empirically. When we increase the number of prior seasons that individuals recall when making vaccination decisions, behavior and thus disease dynamics become less variable. For some networks, we also find that higher flu transmission rates may, counterintuitively, lead to lower (vaccine-mediated) disease prevalence. Our work demonstrates that rich and complex dynamics can result from the interaction between infectious diseases, human contact patterns, and behavior.     

Heterogeneous host susceptibility enhances prevalence of mixed-genotype micro-parasite infections

Dose response in micro-parasite infections is usually shallower than predicted by the independent action model, which assumes that each infectious unit has a probability of infection that is independent of the presence of other infectious units. Moreover, the prevalence of mixed-genotype infections was greater than predicted by this model. No probabilistic infection model has been proposed to account for the higher prevalence of mixed-genotype infections. We use model selection within a set of four alternative models to explain high prevalence of mixed-genotype infections in combination with a shallow dose response. These models contrast dependent versus independent action of micro-parasite infectious units, and homogeneous versus heterogeneous host susceptibility. We specifically consider a situation in which genome differences between genotypes are minimal, and highly unlikely to result in genotype-genotype interactions. Data on dose response and mixed-genotype infection prevalence were collected by challenging fifth instar Spodoptera exigua larvae with two genotypes of Autographa californica multicapsid nucleopolyhedrovirus (AcMNPV), differing only in a 100 bp PCR marker sequence. We show that an independent action model that includes heterogeneity in host susceptibility can explain both the shallow dose response and the high prevalence of mixed-genotype infections. Theoretical results indicate that variation in host susceptibility is inextricably linked to increased prevalence of mixed-genotype infections. We have shown, to our knowledge for the first time, how heterogeneity in host susceptibility affects mixed-genotype infection prevalence. No evidence was found that virions operate dependently. While it has been recognized that heterogeneity in host susceptibility must be included in models of micro-parasite transmission and epidemiology to account for dose response, here we show that heterogeneity in susceptibility is also a fundamental principle explaining patterns of pathogen genetic diversity among hosts in a population. This principle has potentially wide implications for the monitoring, modeling and management of infectious diseases.     

The influence of immune cross-reaction on phase structure in resonant solutions of a multi-strain seasonal SIR model

Resonance in seasonally forced SIR epidemiological models may lead to stable solutions in which the epidemic period is an integer multiple of the forcing period. We examine the influence of immune cross-protection and cross-enhancement on the epidemic phase relationship of resonance solutions in an annually forced two-strain SIR model. Solutions with epidemics of the two strains in-phase commonly occur for wide ranges of cross-reaction intensity. Solutions with epidemics out-of-phase are less common and limited to narrow ranges of cross-reaction intensity. This is broadly as predicted by the two natural periods of the system. The natural period corresponding to out-of-phase solutions is sensitive to changes in the cross-reaction parameter but the natural period corresponding to in-phase solutions is constant. Bifurcation analysis indicates that the stability of in-phase orbits is controlled by pitchfork and period doubling bifurcations while out-of-phase orbits may also be influenced by Andronov-Hopf bifurcations. In order to develop an intuitive understanding of the epidemiological factors governing the occurrence of different solutions we consider how the susceptible, infected and removed components of the system must interact to form a stable solution. This shows that the impact of cross-reaction is moderated by in-phase structures but amplified by out-of-phase structures. Although the average infection rate over long time periods is not affected by phase structure, this analysis indicates that in-phase epidemic patterns are likely to be more consistent and thus allow more effective health care management.     

Estimating incidence from prevalence in generalised HIV epidemics: methods and validation

Background

HIV surveillance of generalised epidemics in Africa primarily relies on prevalence at antenatal clinics, but estimates of incidence in the general population would be more useful. Repeated cross-sectional measures of HIV prevalence are now becoming available for general populations in many countries, and we aim to develop and validate methods that use these data to estimate HIV incidence.

Methods and Findings

Two methods were developed that decompose observed changes in prevalence between two serosurveys into the contributions of new infections and mortality. Method 1 uses cohort mortality rates, and method 2 uses information on survival after infection. The performance of these two methods was assessed using simulated data from a mathematical model and actual data from three community-based cohort studies in Africa. Comparison with simulated data indicated that these methods can accurately estimates incidence rates and changes in incidence in a variety of epidemic conditions. Method 1 is simple to implement but relies on locally appropriate mortality data, whilst method 2 can make use of the same survival distribution in a wide range of scenarios. The estimates from both methods are within the 95% confidence intervals of almost all actual measurements of HIV incidence in adults and young people, and the patterns of incidence over age are correctly captured.

Conclusions

It is possible to estimate incidence from cross-sectional prevalence data with sufficient accuracy to monitor the HIV epidemic. Although these methods will theoretically work in any context, we have able to test them only in southern and eastern Africa, where HIV epidemics are mature and generalised. The choice of method will depend on the local availability of HIV mortality data.     

Host and pathogen ecology drive the seasonal dynamics of a fungal disease,white-nose syndrome

Seasonal patterns in pathogen transmission can influence the impact of disease on populations and the speed of spatial spread. Increases in host contact rates or births drive seasonal epidemics in some systems, but other factors may occasionally override these influences. White-nose syndrome, caused by the emerging fungal pathogen Pseudogymnoascus destructans, is spreading across North America and threatens several bat species with extinction. We examined patterns and drivers of seasonal transmission of P. destructans by measuring infection prevalence and pathogen loads in six bat species at 30 sites across the eastern United States. Bats became transiently infected in autumn, and transmission spiked in early winter when bats began hibernating. Nearly all bats in six species became infected by late winter when infection intensity peaked. In summer, despite high contact rates and a birth pulse, most bats cleared infections and prevalence dropped to zero. These data suggest the dominant driver of seasonal transmission dynamics was a change in host physiology, specifically hibernation. Our study is the first, to the best of our knowledge, to describe the seasonality of transmission in this emerging wildlife disease. The timing of infection and fungal growth resulted in maximal population impacts, but only moderate rates of spatial spread.     

Network-based analysis of stochastic SIR epidemic models with random and proportionate mixing

In this paper, we outline the theory of epidemic percolation networks and their use in the analysis of stochastic susceptible-infectious-removed (SIR) epidemic models on undirected contact networks. We then show how the same theory can be used to analyze stochastic SIR models with random and proportionate mixing. The epidemic percolation networks for these models are purely directed because undirected edges disappear in the limit of a large population. In a series of simulations, we show that epidemic percolation networks accurately predict the mean outbreak size and probability and final size of an epidemic for a variety of epidemic models in homogeneous and heterogeneous populations. Finally, we show that epidemic percolation networks can be used to re-derive classical results from several different areas of infectious disease epidemiology. In an Appendix, we show that an epidemic percolation network can be defined for any time-homogeneous stochastic SIR model in a closed population and prove that the distribution of outbreak sizes given the infection of any given node in the SIR model is identical to the distribution of its out-component sizes in the corresponding probability space of epidemic percolation networks. We conclude that the theory of percolation on semi-directed networks provides a very general framework for the analysis of stochastic SIR models in closed populations.     

Infection, reinfection, and vaccination under suboptimal immune protection: epidemiological perspectives

The SIR (susceptible-infectious-resistant) and SIS (susceptible-infectious-susceptible) frameworks for infectious disease have been extensively studied and successfully applied. They implicitly assume the upper and lower limits of the range of possibilities for host immune response. However, the majority of infections do not fall into either of these extreme categories. We combine two general avenues that straddle this range: temporary immune protection (immunity wanes over time since infection), and partial immune protection (immunity is not fully protective but reduces the risk of reinfection). We present a systematic analysis of the dynamics and equilibrium properties of these models in comparison to SIR and SIS, and analyse the outcome of vaccination programmes. We describe how the waning of immunity shortens inter-epidemic periods, and poses major difficulties to disease eradication. We identify a "reinfection threshold" in transmission when partial immunity is included. Below the reinfection threshold primary infection dominates, levels of infection are low, and vaccination is highly effective (approximately an SIR model). Above the reinfection threshold reinfection dominates, levels of infection are high, and vaccination fails to protect (approximately an SIS situation). This association between high prevalence of infection and vaccine failure emphasizes the problems of controlling recurrent infections in high-burden regions. However, vaccines that induce a better protection than natural infection have the potential to increase the reinfection threshold, and therefore constitute interventions with a surprisingly high capacity to reduce infection where reduction is most needed.     

The effects of social structure and sex-biased transmission on macroparasite infection

Mathematical models of disease dynamics tend to assume that individuals within a population mix at random and so transmission is random, and yet, in reality social structure creates heterogeneous contact patterns. We investigated the effect of heterogeneity in host contact patterns on potential macroparasite transmission by first quantifying the level of assortativity in a socially structured wild rodent population (Apodemus flavicollis) with respect to the directly-transmitted macroparasitic helminth, Heligmosomoides polygyrus. We found the population to be disassortatively mixed (i.e. male mice mixing with female mice more often than same sex mixing) at a constant level over time. The macroparasite H. polygyrus has previously been shown to exhibit male-biased transmission so we used a Susceptible-Infected (SI) mathematical model to simulate the effect of increasing strengths of male-biased transmission on the prevalence of the macroparasite using empirically-derived transmission networks. When transmission was equal between the sexes the model predicted macroparasite prevalence to be 73% and infection was male biased (82% of infection in the male mice). With a male-bias in transmission ten times that of the females, the expected macroparasite prevalence was 50% and was equally prevalent in both sexes, results that both most closely resembled empirical dynamics. As such, disassortative mixing alone did not produce macroparasite dynamics analogous to those from empirical observations; a strong male-bias in transmission was also required. We discuss the relevance of our results in the context of network models for transmission dynamics and control.