Statistical inference to advance network models in epidemiology

Highly scalable maximum likelihood and conjugate Bayesian inference for ERGMs on graph sets with equivalent vertices

The exponential family random graph modeling (ERGM) framework provides a highly flexible approach for the statistical analysis of networks (i.e., graphs). As ERGMs with dyadic dependence involve normalizing factors that are extremely costly to compute, practical strategies for ERGMs inference generally employ a variety of approximations or other workarounds. Markov Chain Monte Carlo maximum likelihood (MCMC MLE) provides a powerful tool to approximate the maximum likelihood estimator (MLE) of ERGM parameters, and is generally feasible for typical models on single networks with as many as a few thousand nodes. MCMC-based algorithms for Bayesian analysis are more expensive, and high-quality answers are challenging to obtain on large graphs. For both strategies, extension to the pooled case—in which we observe multiple networks from a common generative process—adds further computational cost, with both time and memory scaling linearly in the number of graphs. This becomes prohibitive for large networks, or cases in which large numbers of graph observations are available. Here, we exploit some basic properties of the discrete exponential families to develop an approach for ERGM inference in the pooled case that (where applicable) allows an arbitrarily large number of graph observations to be fit at no additional computational cost beyond preprocessing the data itself. Moreover, a variant of our approach can also be used to perform Bayesian inference under conjugate priors, again with no additional computational cost in the estimation phase. The latter can be employed either for single graph observations, or for observations from graph sets. As we show, the conjugate prior is easily specified, and is well-suited to applications such as regularization. Simulation studies show that the pooled method leads to estimates with good frequentist properties, and posterior estimates under the conjugate prior are well-behaved. We demonstrate the usefulness of our approach with applications to pooled analysis of brain functional connectivity networks and to replicated x-ray crystal structures of hen egg-white lysozyme.

Prediction of COVID-19 Infected Population for Indian States through a State Interaction Network-based SEIR Epidemic Model

Objective of this present study is to predict the COVID-19 trajectories in terms of infected population of Indian states. In this work, a state interaction network of sixteen Indian states with highest number of infected caseload is considered, based on networked Susceptible-Exposed-Infected-Recovered (SEIR) epidemic model. An intervention term has been introduced in order to capture the effect of lockdown with different stringencies at different periods of time. The model has been fitted using least absolute shrinkage and selection operator (LASSO). Machine learning methods have been used to train the parameters of the model, cross-validate the data, and predict the parameters. The predictions of infected population for each of the sixteen states have been shown using data considered from January 1, 2021 till writing this manuscript on June 25, 2021. Finally, the effectiveness of the model is manifested by the calculated mean error and confidence interval.

A Semiparametric Bayesian Approach to Epidemics, with Application to the Spread of the Coronavirus MERS in South Korea in 2015

We consider incomplete observations of stochastic processes governing the spread of infectious diseases through finite populations by way of contact. We propose a flexible semiparametric modeling framework with at least three advantages. First, it enables researchers to study the structure of a population contact network and its impact on the spread of infectious diseases. Second, it can accommodate short- and long-tailed degree distributions and detect potential superspreaders, who represent an important public health concern. Third, it addresses the important issue of incomplete data. Starting from first principles, we show when the incomplete-data generating process is ignorable for the purpose of Bayesian inference for the parameters of the population model. We demonstrate the semiparametric modeling framework by simulations and an application to the partially observed MERS epidemic in South Korea in 2015. We conclude with an extended discussion of open questions and directions for future research.

Revealing mechanisms of infectious disease spread through empirical contact networks

The spread of pathogens fundamentally depends on the underlying contacts between individuals. Modeling the dynamics of infectious disease spread through contact networks, however, can be challenging due to limited knowledge of how an infectious disease spreads and its transmission rate. We developed a novel statistical tool, INoDS (Identifying contact Networks of infectious Disease Spread) that estimates the transmission rate of an infectious disease outbreak, establishes epidemiological relevance of a contact network in explaining the observed pattern of infectious disease spread and enables model comparison between different contact network hypotheses. We show that our tool is robust to incomplete data and can be easily applied to datasets where infection timings of individuals are unknown. We tested the reliability of INoDS using simulation experiments of disease spread on a synthetic contact network and find that it is robust to incomplete data and is reliable under different settings of network dynamics and disease contagiousness compared with previous approaches. We demonstrate the applicability of our method in two host-pathogen systems: Crithidia bombi in bumblebee colonies and Salmonella in wild Australian sleepy lizard populations. INoDS thus provides a novel and reliable statistical tool for identifying transmission pathways of infectious disease spread. In addition, application of INoDS extends to understanding the spread of novel or emerging infectious disease, an alternative approach to laboratory transmission experiments, and overcoming common data-collection constraints.

Network models are widely used to understand and predict infectious disease spread in human and animal populations. However, the choice of network model often relies on subjective expert knowledge or disease transmission experiments that are time-consuming and difficult to perform. We developed a novel tool, called INoDS (Identifying contact Networks of infectious Disease Spread), that uses robust statistical approach to establish relevance of a network model in explaining transmission pathways of an infectious disease outbreak. We used computer simulations and real-world dataset to test the accuracy of our tool and robustness to missing data. We found that INoDS is robust to common data-collection constraints, broadly applicable and accurate compared to current approaches. The tool that we have developed can therefore provide immediate epidemiological insights in the event of an epidemic outbreak, and can be used to improve targeted disease control.

Spatiotemporal data mining: a survey on challenges and open problems

Spatiotemporal data mining (STDM) discovers useful patterns from the dynamic interplay between space and time. Several available surveys capture STDM advances and report a wealth of important progress in this field. However, STDM challenges and problems are not thoroughly discussed and presented in articles of their own. We attempt to fill this gap by providing a comprehensive literature survey on state-of-the-art advances in STDM. We describe the challenging issues and their causes and open gaps of multiple STDM directions and aspects. Specifically, we investigate the challenging issues in regards to spatiotemporal relationships, interdisciplinarity, discretisation, and data characteristics. Moreover, we discuss the limitations in the literature and open research problems related to spatiotemporal data representations, modelling and visualisation, and comprehensiveness of approaches. We explain issues related to STDM tasks of classification, clustering, hotspot detection, association and pattern mining, outlier detection, visualisation, visual analytics, and computer vision tasks. We also highlight STDM issues related to multiple applications including crime and public safety, traffic and transportation, earth and environment monitoring, epidemiology, social media, and Internet of Things.

Effects of social structure and management on risk of disease establishment in wild pigs

Contact heterogeneity among hosts determines invasion and spreading dynamics of infectious disease, thus its characterization is essential for identifying effective disease control strategies. Yet, little is known about the factors shaping contact networks in many wildlife species and how wildlife management actions might affect contact networks. Wild pigs in North America are an invasive, socially structured species that pose a health concern for domestic swine given their ability to transmit numerous devastating diseases such as African swine fever (ASF). Using proximity loggers and GPS data from 48 wild pigs in Florida and South Carolina, USA, we employed a probabilistic framework to estimate weighted contact networks. We determined the effects of sex, social group and spatial distribution (monthly home-range overlap and distance) on wild pig contact. We also estimated the impacts of management-induced perturbations on contact and inferred their effects on ASF establishment in wild pigs with simulation. Social group membership was the primary factor influencing contacts. Between-group contacts depended primarily on space use characteristics, with fewer contacts among groups separated by >2 km and no contacts among groups >4 km apart within a month. Modelling ASF dynamics on the contact network demonstrated that indirect contacts resulting from baiting (a typical method of attracting wild pigs or game species to a site to enhance recreational hunting) increased the risk of disease establishment by ~33% relative to direct contact. Low-intensity population reduction (<5.9% of the population) had no detectable impact on contact structure but reduced predicted ASF establishment risk relative to no population reduction. We demonstrate an approach for understanding the relative role of spatial, social and individual-level characteristics in shaping contact networks and predicting their effects on disease establishment risk, thus providing insight for optimizing disease control in spatially and socially structured wildlife species.

A data-driven network model for the emerging COVID-19 epidemics in Wuhan, Toronto and Italy

The ongoing Coronavirus Disease 2019 (COVID-19) pandemic threatens the health of humans and causes great economic losses. Predictive modeling and forecasting the epidemic trends are essential for developing countermeasures to mitigate this pandemic. We develop a network model, where each node represents an individual and the edges represent contacts between individuals where the infection can spread. The individuals are classified based on the number of contacts they have each day (their node degrees) and their infection status. The transmission network model was respectively fitted to the reported data for the COVID-19 epidemic in Wuhan (China), Toronto (Canada), and the Italian Republic using a Markov Chain Monte Carlo (MCMC) optimization algorithm. Our model fits all three regions well with narrow confidence intervals and could be adapted to simulate other megacities or regions. The model projections on the role of containment strategies can help inform public health authorities to plan control measures.

Investigating the drivers of the spatio-temporal patterns of genetic differences between Plasmodium falciparum malaria infections in Kilifi County, Kenya

Knowledge of how malaria infections spread locally is important both for the design of targeted interventions aiming to interrupt malaria transmission and the design of trials to assess the interventions. A previous analysis of 1602 genotyped Plasmodium falciparum parasites in Kilifi, Kenya collected over 12 years found an interaction between time and geographic distance: the mean number of single nucleotide polymorphism (SNP) differences was lower for pairs of infections which were both a shorter time interval and shorter geographic distance apart. We determine whether the empiric pattern could be reproduced by a simple model, and what mean geographic distances between parent and offspring infections and hypotheses about genotype-specific immunity or a limit on the number of infections would be consistent with the data. We developed an individual-based stochastic simulation model of households, people and infections. We parameterized the model for the total number of infections, and population and household density observed in Kilifi. The acquisition of new infections, mutation, recombination, geographic location and clearance were included. We fit the model to the observed numbers of SNP differences between pairs of parasite genotypes. The patterns observed in the empiric data could be reproduced. Although we cannot rule out genotype-specific immunity or a limit on the number of infections per individual, they are not necessary to account for the observed patterns. The mean geographic distance between parent and offspring malaria infections for the base model was 0.5 km (95% CI 0.3-1.5), for a distribution with 68% of distances shorter than the mean. Very short mean distances did not fit well, but mixtures of distributions were also consistent with the data. For a pathogen which undergoes meiosis in a setting with moderate transmission and a low coverage of infections, analytic methods are limited but an individual-based model can be used with genotyping data to estimate parameter values and investigate hypotheses about underlying processes.

Incorporating Contact Network Uncertainty in Individual Level Models of Infectious Disease using Approximate Bayesian Computation

Infectious disease transmission between individuals in a heterogeneous population is often best modelled through a contact network. However, such contact network data are often unobserved. Such missing data can be accounted for in a Bayesian data augmented framework using Markov chain Monte Carlo (MCMC). Unfortunately, fitting models in such a framework can be highly computationally intensive. We investigate the fitting of network-based infectious disease models with completely unknown contact networks using approximate Bayesian computation population Monte Carlo (ABC-PMC) methods. This is done in the context of both simulated data, and data from the UK 2001 foot-and-mouth disease epidemic. We show that ABC-PMC is able to obtain reasonable approximations of the underlying infectious disease model with huge savings in computation time when compared to a full Bayesian MCMC analysis.

Integrating social behaviour, demography and disease dynamics in network models: applications to disease management in declining wildlife populations

The emergence and spread of infections can contribute to the decline and extinction of populations, particularly in conjunction with anthropogenic environmental change. The importance of heterogeneity in processes of transmission, resistance and tolerance is increasingly well understood in theory, but empirical studies that consider both the demographic and behavioural implications of infection are scarce. Non-random mixing of host individuals can impact the demographic thresholds that determine the amplification or attenuation of disease prevalence. Risk assessment and management of disease in threatened wildlife populations must therefore consider not just host density, but also the social structure of host populations. Here we integrate the most recent developments in epidemiological research from a demographic and social network perspective, and synthesize the latest developments in social network modelling for wildlife disease, to explore their applications to disease management in populations in decline and at risk of extinction. We use simulated examples to support our key points and reveal how disease-management strategies can and should exploit both behavioural and demographic information to prevent or control the spread of disease. Our synthesis highlights the importance of considering the combined impacts of demographic and behavioural processes in epidemics to successful disease management in a conservation context. This article is part of the theme issue 'Linking behaviour to dynamics of populations and communities: application of novel approaches in behavioural ecology to conservation'.

Incorporating genomic methods into contact networks to reveal new insights into animal behavior and infectious disease dynamics

Utilization of contact networks has provided opportunities for assessing the dynamic interplay between pathogen transmission and host behavior. Genomic techniques have, in their own right, provided new insight into complex questions in disease ecology, and the increasing accessibility of genomic approaches means more researchers may seek out these tools. The integration of network and genomic approaches provides opportunities to examine the interaction between behavior and pathogen transmission in new ways and with greater resolution. While a number of studies have begun to incorporate both contact network and genomic approaches, a great deal of work has yet to be done to better integrate these techniques. In this review, we give a broad overview of how network and genomic approaches have each been used to address questions regarding the interaction of social behavior and infectious disease, and then discuss current work and future horizons for the merging of these techniques.

Phylogenies from dynamic networks

The relationship between the underlying contact network over which a pathogen spreads and the pathogen phylogenetic trees that are obtained presents an opportunity to use sequence data to learn about contact networks that are difficult to study empirically. However, this relationship is not explicitly known and is usually studied in simulations, often with the simplifying assumption that the contact network is static in time, though human contact networks are dynamic. We simulate pathogen phylogenetic trees on dynamic Erdős-Renyi random networks and on two dynamic networks with skewed degree distribution, of which one is additionally clustered. We use tree shape features to explore how adding dynamics changes the relationships between the overall network structure and phylogenies. Our tree features include the number of small substructures (cherries, pitchforks) in the trees, measures of tree imbalance (Sackin index, Colless index), features derived from network science (diameter, closeness), as well as features using the internal branch lengths from the tip to the root. Using principal component analysis we find that the network dynamics influence the shapes of phylogenies, as does the network type. We also compare dynamic and time-integrated static networks. We find, in particular, that static network models like the widely used Barabasi-Albert model can be poor approximations for dynamic networks. We explore the effects of mis-specifying the network on the performance of classifiers trained identify the transmission rate (using supervised learning methods). We find that both mis-specification of the underlying network and its parameters (mean degree, turnover rate) have a strong adverse effect on the ability to estimate the transmission parameter. We illustrate these results by classifying HIV trees with a classifier that we trained on simulated trees from different networks, infection rates and turnover rates. Our results point to the importance of correctly estimating and modelling contact networks with dynamics when using phylodynamic tools to estimate epidemiological parameters.

Epidemic Network Analysis for Mitigation of Invasive Pathogens in Seed Systems: Potato in Ecuador

Seed systems have an important role in the distribution of high-quality seed and improved varieties. The structure of seed networks also helps to determine the epidemiological risk for seedborne disease. We present a new approach for evaluating the epidemiological role of nodes in seed networks, and apply it to a regional potato farmer consortium (Consorcio de Productores de Papa [CONPAPA]) in Ecuador. We surveyed farmers to estimate the structure of networks of farmer seed tuber and ware potato transactions, and farmer information sources about pest and disease management. Then, we simulated pathogen spread through seed transaction networks to identify priority nodes for disease detection. The likelihood of pathogen establishment was weighted based on the quality or quantity of information sources about disease management. CONPAPA staff and facilities, a market, and certain farms are priorities for disease management interventions such as training, monitoring, and variety dissemination. Advice from agrochemical store staff was common but assessed as significantly less reliable. Farmer access to information (reported number and quality of sources) was similar for both genders. However, women had a smaller amount of the market share for seed tubers and ware potato. Understanding seed system networks provides input for scenario analyses to evaluate potential system improvements. [Formula: see text] Copyright © 2017 The Author(s). This is an open access article distributed under the CC BY 4.0 International license .

Network-based analysis of a small Ebola outbreak

We present a method for estimating epidemic parameters in network-based stochastic epidemic models when the total number of infections is assumed to be small. We illustrate the method by reanalyzing the data from the 2014 Democratic Republic of the Congo (DRC) Ebola outbreak described in Maganga et al. (2014).

Reconstructing contact network parameters from viral phylogenies

Models of the spread of disease in a population often make the simplifying assumption that the population is homogeneously mixed, or is divided into homogeneously mixed compartments. However, human populations have complex structures formed by social contacts, which can have a significant influence on the rate of epidemic spread. Contact network models capture this structure by explicitly representing each contact which could possibly lead to a transmission. We developed a method based on approximate Bayesian computation (ABC), a likelihood-free inference strategy, for estimating structural parameters of the contact network underlying an observed viral phylogeny. The method combines adaptive sequential Monte Carlo for ABC, Gillespie simulation for propagating epidemics though networks, and a kernel-based tree similarity score. We used the method to fit the Barabási-Albert network model to simulated transmission trees, and also applied it to viral phylogenies estimated from ten published HIV sequence datasets. This model incorporates a feature called preferential attachment (PA), whereby individuals with more existing contacts accumulate new contacts at a higher rate. On simulated data, we found that the strength of PA and the number of infected nodes in the network can often be accurately estimated. On the other hand, the mean degree of the network, as well as the total number of nodes, was not estimable with ABC. We observed sub-linear PA power in all datasets, as well as higher PA power in networks of injection drug users. These results underscore the importance of considering contact structures when performing phylodynamic inference. Our method offers the potential to quantitatively investigate the contact network structure underlying viral epidemics.

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

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.

Modeling hepatitis C virus transmission among people who inject drugs: Assumptions, limitations and future challenges

The discovery of highly effective hepatitis C virus (HCV) treatments has led to discussion of elimination and intensified interest in models of HCV transmission. In developed settings, HCV disproportionally affects people who inject drugs (PWID), and models are typically used to provide an evidence base for the effectiveness of interventions such as needle and syringe programs, opioid substitution therapy and more recently treating PWID with new generation therapies to achieve specified reductions in prevalence and / or incidence. This manuscript reviews deterministic compartmental S-I, deterministic compartmental S-I-S and network-based transmission models of HCV among PWID. We detail typical assumptions made when modeling injecting risk behavior, virus transmission, treatment and re-infection and how they correspond with available evidence and empirical data.

The impact of injecting networks on hepatitis C transmission and treatment in people who inject drugs

With the development of new highly efficacious direct-acting antiviral (DAA) treatments for hepatitis C virus (HCV), the concept of treatment as prevention is gaining credence. To date, the majority of mathematical models assume perfect mixing, with injectors having equal contact with all other injectors. This article explores how using a networks-based approach to treat people who inject drugs (PWID) with DAAs affects HCV prevalence. Using observational data, we parameterized an exponential random graph model containing 524 nodes. We simulated transmission of HCV through this network using a discrete time, stochastic transmission model. The effect of five treatment strategies on the prevalence of HCV was investigated; two of these strategies were (1) treat randomly selected nodes and (2) "treat your friends," where an individual is chosen at random for treatment and all their infected neighbors are treated. As treatment coverage increases, HCV prevalence at 10 years reduces for both the high- and low-efficacy treatment. Within each set of parameters, the treat your friends strategy performed better than the random strategy being most marked for higher-efficacy treatment. For example, over 10 years of treating 25 per 1,000 PWID, the prevalence drops from 50% to 40% for the random strategy and to 33% for the treat your friends strategy (6.5% difference; 95% confidence interval: 5.1-8.1).

CONCLUSION

Treat your friends is a feasible means of utilizing network strategies to improve treatment efficiency. In an era of highly efficacious and highly tolerable treatment, such an approach will benefit not just the individual, but also the community more broadly by reducing the prevalence of HCV among PWID.

Local dependence in random graph models: characterization, properties and statistical inference

Dependent phenomena, such as relational, spatial and temporal phenomena, tend to be characterized by local dependence in the sense that units which are close in a well-defined sense are dependent. In contrast with spatial and temporal phenomena, though, relational phenomena tend to lack a natural neighbourhood structure in the sense that it is unknown which units are close and thus dependent. Owing to the challenge of characterizing local dependence and constructing random graph models with local dependence, many conventional exponential family random graph models induce strong dependence and are not amenable to statistical inference. We take first steps to characterize local dependence in random graph models, inspired by the notion of finite neighbourhoods in spatial statistics and M-dependence in time series, and we show that local dependence endows random graph models with desirable properties which make them amenable to statistical inference. We show that random graph models with local dependence satisfy a natural domain consistency condition which every model should satisfy, but conventional exponential family random graph models do not satisfy. In addition, we establish a central limit theorem for random graph models with local dependence, which suggests that random graph models with local dependence are amenable to statistical inference. We discuss how random graph models with local dependence can be constructed by exploiting either observed or unobserved neighbourhood structure. In the absence of observed neighbourhood structure, we take a Bayesian view and express the uncertainty about the neighbourhood structure by specifying a prior on a set of suitable neighbourhood structures. We present simulation results and applications to two real world networks with 'ground truth'.

Network epidemiology and plant trade networks

Models of epidemics in complex networks are improving our predictive understanding of infectious disease outbreaks. Nonetheless, applying network theory to plant pathology is still a challenge. This overview summarizes some key developments in network epidemiology that are likely to facilitate its application in the study and management of plant diseases. Recent surveys have provided much-needed datasets on contact patterns and human mobility in social networks, but plant trade networks are still understudied. Human (and plant) mobility levels across the planet are unprecedented-there is thus much potential in the use of network theory by plant health authorities and researchers. Given the directed and hierarchical nature of plant trade networks, there is a need for plant epidemiologists to further develop models based on undirected and homogeneous networks. More realistic plant health scenarios would also be obtained by developing epidemic models in dynamic, rather than static, networks. For plant diseases spread by the horticultural and ornamental trade, there is the challenge of developing spatio-temporal epidemic simulations integrating network data. The use of network theory in plant epidemiology is a promising avenue and could contribute to anticipating and preventing plant health emergencies such as European ash dieback.

Heterogeneity, mixing, and the spatial scales of mosquito-borne pathogen transmission

The Ross-Macdonald model has dominated theory for mosquito-borne pathogen transmission dynamics and control for over a century. The model, like many other basic population models, makes the mathematically convenient assumption that populations are well mixed; i.e., that each mosquito is equally likely to bite any vertebrate host. This assumption raises questions about the validity and utility of current theory because it is in conflict with preponderant empirical evidence that transmission is heterogeneous. Here, we propose a new dynamic framework that is realistic enough to describe biological causes of heterogeneous transmission of mosquito-borne pathogens of humans, yet tractable enough to provide a basis for developing and improving general theory. The framework is based on the ecological context of mosquito blood meals and the fine-scale movements of individual mosquitoes and human hosts that give rise to heterogeneous transmission. Using this framework, we describe pathogen dispersion in terms of individual-level analogues of two classical quantities: vectorial capacity and the basic reproductive number, . Importantly, this framework explicitly accounts for three key components of overall heterogeneity in transmission: heterogeneous exposure, poor mixing, and finite host numbers. Using these tools, we propose two ways of characterizing the spatial scales of transmission—pathogen dispersion kernels and the evenness of mixing across scales of aggregation—and demonstrate the consequences of a model's choice of spatial scale for epidemic dynamics and for estimation of , both by a priori model formulas and by inference of the force of infection from time-series data.

Pathogens transmitted by mosquitoes, such as malaria and dengue, are notorious for the biological complexity associated with how they are transmitted within local communities. Yet mathematical models for these pathogens, which are critical tools for making recommendations for control policy, are based around concepts originally designed to describe how molecules interact in chemical systems. To provide those interested in mosquito-borne diseases a more appropriate tool for modeling their transmission, we introduce a mathematical framework that is based on the spatial locations where mosquitoes lay eggs and feed on blood and how mosquitoes and hosts move about those locations. Analysis of this framework shows that the transmission contributions of different hosts and locations can be calculated, and that overall potential for transmission in a community depends on three concepts: heterogeneous exposure (some people bitten by mosquitoes more than others), poor mixing (non-random contacts between hosts and mosquitoes), and finite population sizes (each host can contribute at most one new infection towards the population total). Together, these factors determine critical levels of vaccination coverage to eliminate a pathogen and the spatial areas over which transmission should be modeled and studied in the field.

Hepatitis C transmission and treatment in contact networks of people who inject drugs

Hepatitis C virus (HCV) chronically infects over 180 million people worldwide, with over 350,000 estimated deaths attributed yearly to HCV-related liver diseases. It disproportionally affects people who inject drugs (PWID). Currently there is no preventative vaccine and interventions feature long treatment durations with severe side-effects. Upcoming treatments will improve this situation, making possible large-scale treatment interventions. How these strategies should target HCV-infected PWID remains an important unanswered question. Previous models of HCV have lacked empirically grounded contact models of PWID. Here we report results on HCV transmission and treatment using simulated contact networks generated from an empirically grounded network model using recently developed statistical approaches in social network analysis. Our HCV transmission model is a detailed, stochastic, individual-based model including spontaneously clearing nodes. On transmission we investigate the role of number of contacts and injecting frequency on time to primary infection and the role of spontaneously clearing nodes on incidence rates. On treatment we investigate the effect of nine network-based treatment strategies on chronic prevalence and incidence rates of primary infection and re-infection. Both numbers of contacts and injecting frequency play key roles in reducing time to primary infection. The change from "less-" to "more-frequent" injector is roughly similar to having one additional network contact. Nodes that spontaneously clear their HCV infection have a local effect on infection risk and the total number of such nodes (but not their locations) has a network wide effect on the incidence of both primary and re-infection with HCV. Re-infection plays a large role in the effectiveness of treatment interventions. Strategies that choose PWID and treat all their contacts (analogous to ring vaccination) are most effective in reducing the incidence rates of re-infection and combined infection. A strategy targeting infected PWID with the most contacts (analogous to targeted vaccination) is the least effective.

Epidemiologically optimal static networks from temporal network data

One of network epidemiology's central assumptions is that the contact structure over which infectious diseases propagate can be represented as a static network. However, contacts are highly dynamic, changing at many time scales. In this paper, we investigate conceptually simple methods to construct static graphs for network epidemiology from temporal contact data. We evaluate these methods on empirical and synthetic model data. For almost all our cases, the network representation that captures most relevant information is a so-called exponential-threshold network. In these, each contact contributes with a weight decreasing exponentially with time, and there is an edge between a pair of vertices if the weight between them exceeds a threshold. Networks of aggregated contacts over an optimally chosen time window perform almost as good as the exponential-threshold networks. On the other hand, networks of accumulated contacts over the entire sampling time, and networks of concurrent partnerships, perform worse. We discuss these observations in the context of the temporal and topological structure of the data sets.

To understand how diseases spread in a population, it is important to study the network of people in contact. Many methods to model epidemic outbreaks make the assumption that one can treat this network as static. In reality, we know that contact patterns between people change in time, and old contacts are soon irrelevant—it does not matter that we know Marie Antoinette's lovers to understand the HIV epidemic. This paper investigates methods for constructing networks of people that are as relevant as possible for disease spreading. The most promising method we call exponential-threshold network works by letting contacts contribute less, the further from the beginning of an outbreak they take place. We investigate the methods both on artificial models of the contact patterns and empirical data. Except searching for the optimal network representation, we also investigate how the structure of the original data set affects the performance of the representations.

Inferring population-level contact heterogeneity from common epidemic data

Models of infectious disease spread that incorporate contact heterogeneity through contact networks are an important tool for epidemiologists studying disease dynamics and assessing intervention strategies. One of the challenges of contact network epidemiology has been the difficulty of collecting individual and population-level data needed to develop an accurate representation of the underlying host population's contact structure. In this study, we evaluate the utility of common epidemiological measures (R0, epidemic peak size, duration and final size) for inferring the degree of heterogeneity in a population's unobserved contact structure through a Bayesian approach. We test the method using ground truth data and find that some of these epidemiological metrics are effective at classifying contact heterogeneity. The classification is also consistent across pathogen transmission probabilities, and so can be applied even when this characteristic is unknown. In particular, the reproductive number, R0, turns out to be a poor classifier of the degree heterogeneity, while, unexpectedly, final epidemic size is a powerful predictor of network structure across the range of heterogeneity. We also evaluate our framework on empirical epidemiological data from past and recent outbreaks to demonstrate its application in practice and to gather insights about the relevance of particular contact structures for both specific systems and general classes of infectious disease. We thus introduce a simple approach that can shed light on the unobserved connectivity of a host population given epidemic data. Our study has the potential to inform future data-collection efforts and study design by driving our understanding of germane epidemic measures, and highlights a general inferential approach to learning about host contact structure in contemporary or historic populations of humans and animals.

Detectable signals of episodic risk effects on acute HIV transmission: strategies for analyzing transmission systems using genetic data

Episodic high-risk sexual behavior is common and can have a profound effect on HIV transmission. In a model of HIV transmission among men who have sex with men (MSM), changing the frequency, duration and contact rates of high-risk episodes can take endemic prevalence from zero to 50% and more than double transmissions during acute HIV infection (AHI). Undirected test and treat could be inefficient in the presence of strong episodic risk effects. Partner services approaches that use a variety of control options will be likely to have better effects under these conditions, but the question remains: What data will reveal if a population is experiencing episodic risk effects? HIV sequence data from Montreal reveals genetic clusters whose size distribution stabilizes over time and reflects the size distribution of acute infection outbreaks (AIOs). Surveillance provides complementary behavioral data. In order to use both types of data efficiently, it is essential to examine aspects of models that affect both the episodic risk effects and the shape of transmission trees. As a demonstration, we use a deterministic compartmental model of episodic risk to explore the determinants of the fraction of transmissions during acute HIV infection (AHI) at the endemic equilibrium. We use a corresponding individual-based model to observe AIO size distributions and patterns of transmission within AIO. Episodic risk parameters determining whether AHI transmission trees had longer chains, more clustered transmissions from single individuals, or different mixes of these were explored. Encouragingly for parameter estimation, AIO size distributions reflected the frequency of transmissions from acute infection across divergent parameter sets. Our results show that episodic risk dynamics influence both the size and duration of acute infection outbreaks, thus providing a possible link between genetic cluster size distributions and episodic risk dynamics.

Inferring the inter-host transmission of influenza A virus using patterns of intra-host genetic variation

Influenza A viruses (IAVs) cause acute, highly transmissible infections in a wide range of animal species. Understanding how these viruses are transmitted within and between susceptible host populations is critical to the development of effective control strategies. While viral gene sequences have been used to make inferences about IAV transmission dynamics at the epidemiological scale, their utility in accurately determining patterns of inter-host transmission in the short-term--i.e. who infected whom--has not been strongly established. Herein, we use intra-host sequence data from the viral HA1 (hemagglutinin) gene domain from two transmission studies employing different IAV subtypes in their natural hosts--H3N8 in horses and H1N1 in pigs-to determine how well these data recapitulate the known pattern of inter-host transmission. Although no mutations were fixed over the course of either experimental transmission chain, we show that some minor, transient alleles can provide evidence of host-to-host transmission and, importantly, can be distinguished from those that cannot.

Inferring epidemic contact structure from phylogenetic trees

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.

Is network clustering detectable in transmission trees?

Networks are often used to model the contact processes that allow pathogens to spread between hosts but it remains unclear which models best describe these networks. One question is whether clustering in networks, roughly defined as the propensity for triangles to form, affects the dynamics of disease spread. We perform a simulation study to see if there is a signal in epidemic transmission trees of clustering. We simulate susceptible-exposed-infectious-removed (SEIR) epidemics (with no re-infection) over networks with fixed degree sequences but different levels of clustering and compare trees from networks with the same degree sequence and different clustering levels. We find that the variation of such trees simulated on networks with different levels of clustering is barely greater than those simulated on networks with the same level of clustering, suggesting that clustering can not be detected in transmission data when re-infection does not occur.

A network-based analysis of the 1861 Hagelloch measles data

In this article, we demonstrate a statistical method for fitting the parameters of a sophisticated network and epidemic model to disease data. The pattern of contacts between hosts is described by a class of dyadic independence exponential-family random graph models (ERGMs), whereas the transmission process that runs over the network is modeled as a stochastic susceptible-exposed-infectious-removed (SEIR) epidemic. We fit these models to very detailed data from the 1861 measles outbreak in Hagelloch, Germany. The network models include parameters for all recorded host covariates including age, sex, household, and classroom membership and household location whereas the SEIR epidemic model has exponentially distributed transmission times with gamma-distributed latent and infective periods. This approach allows us to make meaningful statements about the structure of the population-separate from the transmission process-as well as to provide estimates of various biological quantities of interest, such as the effective reproductive number, R. Using reversible jump Markov chain Monte Carlo, we produce samples from the joint posterior distribution of all the parameters of this model-the network, transmission tree, network parameters, and SEIR parameters-and perform Bayesian model selection to find the best-fitting network model. We compare our results with those of previous analyses and show that the ERGM network model better fits the data than a Bernoulli network model previously used. We also provide a software package, written in R, that performs this type of analysis.

Phylogenetic and epidemic modeling of rapidly evolving infectious diseases

Epidemic modeling of infectious diseases has a long history in both theoretical and empirical research. However the recent explosion of genetic data has revealed the rapid rate of evolution that many populations of infectious agents undergo and has underscored the need to consider both evolutionary and ecological processes on the same time scale. Mathematical epidemiology has applied dynamical models to study infectious epidemics, but these models have tended not to exploit--or take into account--evolutionary changes and their effect on the ecological processes and population dynamics of the infectious agent. On the other hand, statistical phylogenetics has increasingly been applied to the study of infectious agents. This approach is based on phylogenetics, molecular clocks, genealogy-based population genetics and phylogeography. Bayesian Markov chain Monte Carlo and related computational tools have been the primary source of advances in these statistical phylogenetic approaches. Recently the first tentative steps have been taken to reconcile these two theoretical approaches. We survey the Bayesian phylogenetic approach to epidemic modeling of infection diseases and describe the contrasts it provides to mathematical epidemiology as well as emphasize the significance of the future unification of these two fields.