Effects of heterogeneous and clustered contact patterns on infectious disease dynamics

Network theory may explain the vulnerability of medieval human settlements to the Black Death pandemic

Epidemics can spread across large regions becoming pandemics by flowing along transportation and social networks. Two network attributes, transitivity (when a node is connected to two other nodes that are also directly connected between them) and centrality (the number and intensity of connections with the other nodes in the network), are widely associated with the dynamics of transmission of pathogens. Here we investigate how network centrality and transitivity influence vulnerability to diseases of human populations by examining one of the most devastating pandemic in human history, the fourteenth century plague pandemic called Black Death. We found that, after controlling for the city spatial location and the disease arrival time, cities with higher values of both centrality and transitivity were more severely affected by the plague. A simulation study indicates that this association was due to central cities with high transitivity undergo more exogenous re-infections. Our study provides an easy method to identify hotspots in epidemic networks. Focusing our effort in those vulnerable nodes may save time and resources by improving our ability of controlling deadly epidemics.

Prediction of Pig Trade Movements in Different European Production Systems Using Exponential Random Graph Models

In most European countries, data regarding movements of live animals are routinely collected and can greatly aid predictive epidemic modeling. However, the use of complete movements’ dataset to conduct policy-relevant predictions has been so far limited by the massive amount of data that have to be processed (e.g., in intensive commercial systems) or the restricted availability of timely and updated records on animal movements (e.g., in areas where small-scale or extensive production is predominant). The aim of this study was to use exponential random graph models (ERGMs) to reproduce, understand, and predict pig trade networks in different European production systems. Three trade networks were built by aggregating movements of pig batches among premises (farms and trade operators) over 2011 in Bulgaria, Extremadura (Spain), and Côtes-d’Armor (France), where small-scale, extensive, and intensive pig production are predominant, respectively. Three ERGMs were fitted to each network with various demographic and geographic attributes of the nodes as well as six internal network configurations. Several statistical and graphical diagnostic methods were applied to assess the goodness of fit of the models. For all systems, both exogenous (attribute-based) and endogenous (network-based) processes appeared to govern the structure of pig trade network, and neither alone were capable of capturing all aspects of the network structure. Geographic mixing patterns strongly structured pig trade organization in the small-scale production system, whereas belonging to the same company or keeping pigs in the same housing system appeared to be key drivers of pig trade, in intensive and extensive production systems, respectively. Heterogeneous mixing between types of production also explained a part of network structure, whichever production system considered. Limited information is thus needed to capture most of the global structure of pig trade networks. Such findings will be useful to simplify trade networks analysis and better inform European policy makers on risk-based and more cost-effective prevention and control against swine diseases such as African swine fever, classical swine fever, or porcine reproductive and respiratory syndrome.

Unification of theoretical approaches for epidemic spreading on complex networks

Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.

Compact pairwise models for epidemics with multiple infectious stages on degree heterogeneous and clustered networks

This paper presents a compact pairwise model describing the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian models with exponentially distributed infectious period and epidemics with a constant infectious period. We show how the compact approach leads to a system of equations whose size is independent of the range of node degrees, thus significantly reducing the complexity of the model. Network clustering is incorporated into the model to provide a more accurate representation of realistic contact networks, and the accuracy of proposed closures is analysed for different levels of clustering and number of infection stages. Our results support recent findings that standard closure techniques are likely to perform better when the infectious period is constant.

Disease Surveillance on Complex Social Networks

As infectious disease surveillance systems expand to include digital, crowd-sourced, and social network data, public health agencies are gaining unprecedented access to high-resolution data and have an opportunity to selectively monitor informative individuals. Contact networks, which are the webs of interaction through which diseases spread, determine whether and when individuals become infected, and thus who might serve as early and accurate surveillance sensors. Here, we evaluate three strategies for selecting sensors-sampling the most connected, random, and friends of random individuals-in three complex social networks-a simple scale-free network, an empirical Venezuelan college student network, and an empirical Montreal wireless hotspot usage network. Across five different surveillance goals-early and accurate detection of epidemic emergence and peak, and general situational awareness-we find that the optimal choice of sensors depends on the public health goal, the underlying network and the reproduction number of the disease (R0). For diseases with a low R0, the most connected individuals provide the earliest and most accurate information about both the onset and peak of an outbreak. However, identifying network hubs is often impractical, and they can be misleading if monitored for general situational awareness, if the underlying network has significant community structure, or if R0 is high or unknown. Taking a theoretical approach, we also derive the optimal surveillance system for early outbreak detection but find that real-world identification of such sensors would be nearly impossible. By contrast, the friends-of-random strategy offers a more practical and robust alternative. It can be readily implemented without prior knowledge of the network, and by identifying sensors with higher than average, but not the highest, epidemiological risk, it provides reasonably early and accurate information.

Predicting the epidemic threshold of the susceptible-infected-recovered model

Researchers have developed several theoretical methods for predicting epidemic thresholds, including the mean-field like (MFL) method, the quenched mean-field (QMF) method, and the dynamical message passing (DMP) method. When these methods are applied to predict epidemic threshold they often produce differing results and their relative levels of accuracy are still unknown. We systematically analyze these two issues-relationships among differing results and levels of accuracy-by studying the susceptible-infected-recovered (SIR) model on uncorrelated configuration networks and a group of 56 real-world networks. In uncorrelated configuration networks the MFL and DMP methods yield identical predictions that are larger and more accurate than the prediction generated by the QMF method. As for the 56 real-world networks, the epidemic threshold obtained by the DMP method is more likely to reach the accurate epidemic threshold because it incorporates full network topology information and some dynamical correlations. We find that in most of the networks with positive degree-degree correlations, an eigenvector localized on the high k-core nodes, or a high level of clustering, the epidemic threshold predicted by the MFL method, which uses the degree distribution as the only input information, performs better than the other two methods.

The role of heterogeneity in contact timing and duration in network models of influenza spread in schools

Influenza poses a significant health threat to children, and schools may play a critical role in community outbreaks. Mathematical outbreak models require assumptions about contact rates and patterns among students, but the level of temporal granularity required to produce reliable results is unclear. We collected objective contact data from students aged 5–14 at an elementary school and middle school in the state of Utah, USA, and paired those data with a novel, data-based model of influenza transmission in schools. Our simulations produced within-school transmission averages consistent with published estimates. We compared simulated outbreaks over the full resolution dynamic network with simulations on networks with averaged representations of contact timing and duration. For both schools, averaging the timing of contacts over one or two school days caused average outbreak sizes to increase by 1–8%. Averaging both contact timing and pairwise contact durations caused average outbreak sizes to increase by 10% at the middle school and 72% at the elementary school. Averaging contact durations separately across within-class and between-class contacts reduced the increase for the elementary school to 5%. Thus, the effect of ignoring details about contact timing and duration in school contact networks on outbreak size modelling can vary across different schools.

Modeling optimal treatment strategies in a heterogeneous mixing model

Background

Many mathematical models assume random or homogeneous mixing for various infectious diseases. Homogeneous mixing can be generalized to mathematical models with multi-patches or age structure by incorporating contact matrices to capture the dynamics of the heterogeneously mixing populations. Contact or mixing patterns are difficult to measure in many infectious diseases including influenza. Mixing patterns are considered to be one of the critical factors for infectious disease modeling.

Methods

A two-group influenza model is considered to evaluate the impact of heterogeneous mixing on the influenza transmission dynamics. Heterogeneous mixing between two groups with two different activity levels includes proportionate mixing, preferred mixing and like-with-like mixing. Furthermore, the optimal control problem is formulated in this two-group influenza model to identify the group-specific optimal treatment strategies at a minimal cost. We investigate group-specific optimal treatment strategies under various mixing scenarios.

Results

The characteristics of the two-group influenza dynamics have been investigated in terms of the basic reproduction number and the final epidemic size under various mixing scenarios. As the mixing patterns become proportionate mixing, the basic reproduction number becomes smaller; however, the final epidemic size becomes larger. This is due to the fact that the number of infected people increases only slightly in the higher activity level group, while the number of infected people increases more significantly in the lower activity level group. Our results indicate that more intensive treatment of both groups at the early stage is the most effective treatment regardless of the mixing scenario. However, proportionate mixing requires more treated cases for all combinations of different group activity levels and group population sizes.

Conclusions

Mixing patterns can play a critical role in the effectiveness of optimal treatments. As the mixing becomes more like-with-like mixing, treating the higher activity group in the population is almost as effective as treating the entire populations since it reduces the number of disease cases effectively but only requires similar treatments. The gain becomes more pronounced as the basic reproduction number increases. This can be a critical issue which must be considered for future pandemic influenza interventions, especially when there are limited resources available.

Tracking social contact networks with online respondent-driven detection: who recruits whom?

Background

Transmission of respiratory pathogens in a population depends on the contact network patterns of individuals. To accurately understand and explain epidemic behaviour information on contact networks is required, but only limited empirical data is available. Online respondent-driven detection can provide relevant epidemiological data on numbers of contact persons and dynamics of contacts between pairs of individuals. We aimed to analyse contact networks with respect to sociodemographic and geographical characteristics, vaccine-induced immunity and self-reported symptoms.

Methods

In 2014, volunteers from two large participatory surveillance panels in the Netherlands and Belgium were invited for a survey. Participants were asked to record numbers of contacts at different locations and self-reported influenza-like-illness symptoms, and to invite 4 individuals they had met face to face in the preceding 2 weeks. We calculated correlations between linked individuals to investigate mixing patterns.

Results

In total 1560 individuals completed the survey who reported in total 30591 contact persons; 488 recruiter-recruit pairs were analysed. Recruitment was assortative by age, education, household size, influenza vaccination status and sentiments, indicating that participants tended to recruit contact persons similar to themselves. We also found assortative recruitment by symptoms, reaffirming our objective of sampling contact persons whom a participant may infect or by whom a participant may get infected in case of an outbreak. Recruitment was random by sex and numbers of contact persons. Relationships between pairs were influenced by the spatial distribution of peer recruitment.

Conclusions

Although complex mechanisms influence online peer recruitment, the observed statistical relationships reflected the observed contact network patterns in the general population relevant for the transmission of respiratory pathogens. This provides useful and innovative input for predictive epidemic models relying on network information.

Electronic supplementary material

The online version of this article (doi:10.1186/s12879-015-1250-z) contains supplementary material, which is available to authorized users.

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.

Information content of contact-pattern representations and predictability of epidemic outbreaks

To understand the contact patterns of a population--who is in contact with whom, and when the contacts happen--is crucial for modeling outbreaks of infectious disease. Traditional theoretical epidemiology assumes that any individual can meet any with equal probability. A more modern approach, network epidemiology, assumes people are connected into a static network over which the disease spreads. Newer yet, temporal network epidemiology, includes the time in the contact representations. In this paper, we investigate the effect of these successive inclusions of more information. Using empirical proximity data, we study both outbreak sizes from unknown sources, and from known states of ongoing outbreaks. In the first case, there are large differences going from a fully mixed simulation to a network, and from a network to a temporal network. In the second case, differences are smaller. We interpret these observations in terms of the temporal network structure of the data sets. For example, a fast overturn of nodes and links seem to make the temporal information more important.

Constructing, conducting and interpreting animal social network analysis

1. Animal social networks are descriptions of social structure which, aside from their intrinsic interest for understanding sociality, can have significant bearing across many fields of biology. 2. Network analysis provides a flexible toolbox for testing a broad range of hypotheses, and for describing the social system of species or populations in a quantitative and comparable manner. However, it requires careful consideration of underlying assumptions, in particular differentiating real from observed networks and controlling for inherent biases that are common in social data. 3. We provide a practical guide for using this framework to analyse animal social systems and test hypotheses. First, we discuss key considerations when defining nodes and edges, and when designing methods for collecting data. We discuss different approaches for inferring social networks from these data and displaying them. We then provide an overview of methods for quantifying properties of nodes and networks, as well as for testing hypotheses concerning network structure and network processes. Finally, we provide information about assessing the power and accuracy of an observed network. 4. Alongside this manuscript, we provide appendices containing background information on common programming routines and worked examples of how to perform network analysis using the r programming language. 5. We conclude by discussing some of the major current challenges in social network analysis and interesting future directions. In particular, we highlight the under-exploited potential of experimental manipulations on social networks to address research questions.

Spatial analyses of wildlife contact networks

Datasets from which wildlife contact networks of epidemiological importance can be inferred are becoming increasingly common. A largely unexplored facet of these data is finding evidence of spatial constraints on who has contact with whom, despite theoretical epidemiologists having long realized spatial constraints can play a critical role in infectious disease dynamics. A graph dissimilarity measure is proposed to quantify how close an observed contact network is to being purely spatial whereby its edges are completely determined by the spatial arrangement of its nodes. Statistical techniques are also used to fit a series of mechanistic models for contact rates between individuals to the binary edge data representing presence or absence of observed contact. These are the basis for a second measure that quantifies the extent to which contacts are being mediated by distance. We apply these methods to a set of 128 contact networks of field voles (Microtus agrestis) inferred from mark–recapture data collected over 7 years and from four sites. Large fluctuations in vole abundance allow us to demonstrate that the networks become increasingly similar to spatial proximity graphs as vole density increases. The average number of contacts, , was (i) positively correlated with vole density across the range of observed densities and (ii) for two of the four sites a saturating function of density. The implications for pathogen persistence in wildlife may be that persistence is relatively unaffected by fluctuations in host density because at low density is low but hosts move more freely, and at high density is high but transmission is hampered by local build-up of infected or recovered animals.

Complex dynamics of synergistic coinfections on realistically clustered networks

We investigate the impact of contact structure clustering on the dynamics of multiple diseases interacting through coinfection of a single individual, two problems typically studied independently. We highlight how clustering, which is well known to hinder propagation of diseases, can actually speed up epidemic propagation in the context of synergistic coinfections if the strength of the coupling matches that of the clustering. We also show that such dynamics lead to a first-order transition in endemic states, where small changes in transmissibility of the diseases can lead to explosive outbreaks and regions where these explosive outbreaks can only happen on clustered networks. We develop a mean-field model of coinfection of two diseases following susceptible-infectious-susceptible dynamics, which is allowed to interact on a general class of modular networks. We also introduce a criterion based on tertiary infections that yields precise analytical estimates of when clustering will lead to faster propagation than nonclustered networks. Our results carry importance for epidemiology, mathematical modeling, and the propagation of interacting phenomena in general. We make a call for more detailed epidemiological data of interacting coinfections.

Hybrid epidemics--a case study on computer worm conficker

Conficker is a computer worm that erupted on the Internet in 2008. It is unique in combining three different spreading strategies: local probing, neighbourhood probing, and global probing. We propose a mathematical model that combines three modes of spreading: local, neighbourhood, and global, to capture the worm's spreading behaviour. The parameters of the model are inferred directly from network data obtained during the first day of the Conficker epidemic. The model is then used to explore the tradeoff between spreading modes in determining the worm's effectiveness. Our results show that the Conficker epidemic is an example of a critically hybrid epidemic, in which the different modes of spreading in isolation do not lead to successful epidemics. Such hybrid spreading strategies may be used beneficially to provide the most effective strategies for promulgating information across a large population. When used maliciously, however, they can present a dangerous challenge to current internet security protocols.

Harnessing case isolation and ring vaccination to control Ebola

As a devastating Ebola outbreak in West Africa continues, non-pharmaceutical control measures including contact tracing, quarantine, and case isolation are being implemented. In addition, public health agencies are scaling up efforts to test and deploy candidate vaccines. Given the experimental nature and limited initial supplies of vaccines, a mass vaccination campaign might not be feasible. However, ring vaccination of likely case contacts could provide an effective alternative in distributing the vaccine. To evaluate ring vaccination as a strategy for eliminating Ebola, we developed a pair approximation model of Ebola transmission, parameterized by confirmed incidence data from June 2014 to January 2015 in Liberia and Sierra Leone. Our results suggest that if a combined intervention of case isolation and ring vaccination had been initiated in the early fall of 2014, up to an additional 126 cases in Liberia and 560 cases in Sierra Leone could have been averted beyond case isolation alone. The marginal benefit of ring vaccination is predicted to be greatest in settings where there are more contacts per individual, greater clustering among individuals, when contact tracing has low efficacy or vaccination confers post-exposure protection. In such settings, ring vaccination can avert up to an additional 8% of Ebola cases. Accordingly, ring vaccination is predicted to offer a moderately beneficial supplement to ongoing non-pharmaceutical Ebola control efforts.

Optimizing hybrid spreading in metapopulations

Epidemic spreading phenomena are ubiquitous in nature and society. Examples include the spreading of diseases, information, and computer viruses. Epidemics can spread by local spreading, where infected nodes can only infect a limited set of direct target nodes and global spreading, where an infected node can infect every other node. In reality, many epidemics spread using a hybrid mixture of both types of spreading. In this study we develop a theoretical framework for studying hybrid epidemics, and examine the optimum balance between spreading mechanisms in terms of achieving the maximum outbreak size. We show the existence of critically hybrid epidemics where neither spreading mechanism alone can cause a noticeable spread but a combination of the two spreading mechanisms would produce an enormous outbreak. Our results provide new strategies for maximising beneficial epidemics and estimating the worst outcome of damaging hybrid epidemics.

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics.

Revealing the hidden networks of interaction in mobile animal groups allows prediction of complex behavioral contagion

Coordination among social animals requires rapid and efficient transfer of information among individuals, which may depend crucially on the underlying structure of the communication network. Establishing the decision-making circuits and networks that give rise to individual behavior has been a central goal of neuroscience. However, the analogous problem of determining the structure of the communication network among organisms that gives rise to coordinated collective behavior, such as is exhibited by schooling fish and flocking birds, has remained almost entirely neglected. Here, we study collective evasion maneuvers, manifested through rapid waves, or cascades, of behavioral change (a ubiquitous behavior among taxa) in schooling fish (Notemigonus crysoleucas). We automatically track the positions and body postures, calculate visual fields of all individuals in schools of ∼150 fish, and determine the functional mapping between socially generated sensory input and motor response during collective evasion. We find that individuals use simple, robust measures to assess behavioral changes in neighbors, and that the resulting networks by which behavior propagates throughout groups are complex, being weighted, directed, and heterogeneous. By studying these interaction networks, we reveal the (complex, fractional) nature of social contagion and establish that individuals with relatively few, but strongly connected, neighbors are both most socially influential and most susceptible to social influence. Furthermore, we demonstrate that we can predict complex cascades of behavioral change at their moment of initiation, before they actually occur. Consequently, despite the intrinsic stochasticity of individual behavior, establishing the hidden communication networks in large self-organized groups facilitates a quantitative understanding of behavioral contagion.

The basic reproduction number as a predictor for epidemic outbreaks in temporal networks

The basic reproduction number R₀—the number of individuals directly infected by an infectious person in an otherwise susceptible population—is arguably the most widely used estimator of how severe an epidemic outbreak can be. This severity can be more directly measured as the fraction of people infected once the outbreak is over, Ω. In traditional mathematical epidemiology and common formulations of static network epidemiology, there is a deterministic relationship between R₀ and Ω. However, if one considers disease spreading on a temporal contact network—where one knows when contacts happen, not only between whom—then larger R₀ does not necessarily imply larger Ω. In this paper, we numerically investigate the relationship between R₀ and Ω for a set of empirical temporal networks of human contacts. Among 31 explanatory descriptors of temporal network structure, we identify those that make R₀ an imperfect predictor of Ω. We find that descriptors related to both temporal and topological aspects affect the relationship between R₀ and Ω, but in different ways.

Controlling infectious disease through the targeted manipulation of contact network structure

Individuals in human and animal populations are linked through dynamic contact networks with characteristic structural features that drive the epidemiology of directly transmissible infectious diseases. Using animal movement data from the British cattle industry as an example, this analysis explores whether disease dynamics can be altered by placing targeted restrictions on contact formation to reconfigure network topology. This was accomplished using a simple network generation algorithm that combined configuration wiring with stochastic block modelling techniques to preserve the weighted in- and out-degree of individual nodes (farms) as well as key demographic characteristics of the individual network connections (movement date, livestock market, and animal production type). We then tested a control strategy based on introducing additional constraints into the network generation algorithm to prevent farms with a high in-degree from selling cattle to farms with a high out-degree as these particular network connections are predicted to have a disproportionately strong role in spreading disease. Results from simple dynamic disease simulation models predicted significantly lower endemic disease prevalences on the trade restricted networks compared to the baseline generated networks. As expected, the relative magnitude of the predicted changes in endemic prevalence was greater for diseases with short infectious periods and low transmission probabilities. Overall, our study findings demonstrate that there is significant potential for controlling multiple infectious diseases simultaneously by manipulating networks to have more epidemiologically favourable topological configurations. Further research is needed to determine whether the economic and social benefits of controlling disease can justify the costs of restricting contact formation.

Inferring a district-based hierarchical structure of social contacts from census data

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

Epidemiological and viral genomic sequence analysis of the 2014 ebola outbreak reveals clustered transmission

Using Ebolavirus genomic and epidemiological data, we conducted the first joint analysis in which both data types were used to fit dynamic transmission models for an ongoing outbreak. Our results indicate that transmission is clustered, highlighting a potential bias in medical demand forecasts, and provide the first empirical estimate of underreporting.

Comparison of contact patterns relevant for transmission of respiratory pathogens in Thailand and The Netherlands using respondent-driven sampling

Understanding infection dynamics of respiratory diseases requires the identification and quantification of behavioural, social and environmental factors that permit the transmission of these infections between humans. Little empirical information is available about contact patterns within real-world social networks, let alone on differences in these contact networks between populations that differ considerably on a socio-cultural level. Here we compared contact network data that were collected in The Netherlands and Thailand using a similar online respondent-driven method. By asking participants to recruit contact persons we studied network links relevant for the transmission of respiratory infections. We studied correlations between recruiter and recruited contacts to investigate mixing patterns in the observed social network components. In both countries, mixing patterns were assortative by demographic variables and random by total numbers of contacts. However, in Thailand participants reported overall more contacts which resulted in higher effective contact rates. Our findings provide new insights on numbers of contacts and mixing patterns in two different populations. These data could be used to improve parameterisation of mathematical models used to design control strategies. Although the spread of infections through populations depends on more factors, found similarities suggest that spread may be similar in The Netherlands and Thailand.

Detecting differential transmissibilities that affect the size of self-limited outbreaks

Our ability to respond appropriately to infectious diseases is enhanced by identifying differences in the potential for transmitting infection between individuals. Here, we identify epidemiological traits of self-limited infections (i.e. infections with an effective reproduction number satisfying [0 < R eff < 1) that correlate with transmissibility. Our analysis is based on a branching process model that permits statistical comparison of both the strength and heterogeneity of transmission for two distinct types of cases. Our approach provides insight into a variety of scenarios, including the transmission of Middle East Respiratory Syndrome Coronavirus (MERS-CoV) in the Arabian peninsula, measles in North America, pre-eradication smallpox in Europe, and human monkeypox in the Democratic Republic of the Congo. When applied to chain size data for MERS-CoV transmission before 2014, our method indicates that despite an apparent trend towards improved control, there is not enough statistical evidence to indicate that R eff has declined with time. Meanwhile, chain size data for measles in the United States and Canada reveal statistically significant geographic variation in R eff, suggesting that the timing and coverage of national vaccination programs, as well as contact tracing procedures, may shape the size distribution of observed infection clusters. Infection source data for smallpox suggests that primary cases transmitted more than secondary cases, and provides a quantitative assessment of the effectiveness of control interventions. Human monkeypox, on the other hand, does not show evidence of differential transmission between animals in contact with humans, primary cases, or secondary cases, which assuages the concern that social mixing can amplify transmission by secondary cases. Lastly, we evaluate surveillance requirements for detecting a change in the human-to-human transmission of monkeypox since the cessation of cross-protective smallpox vaccination. Our studies lay the foundation for future investigations regarding how infection source, vaccination status or other putative transmissibility traits may affect self-limited transmission.

Epidemic spreading on complex networks with general degree and weight distributions

The spread of disease on complex networks has attracted wide attention in the physics community. Recent works have demonstrated that heterogeneous degree and weight distributions have a significant influence on the epidemic dynamics. In this study, a novel edge-weight-based compartmental approach is developed to estimate the epidemic threshold and epidemic size (final infected density) on networks with general degree and weight distributions, and a remarkable agreement with numerics is obtained. Even in complex networks with the strong heterogeneous degree and weight distributions, this approach is used. We then propose an edge-weight-based removal strategy with different biases and find that such a strategy can effectively control the spread of epidemic when the highly weighted edges are preferentially removed, especially when the weight distribution of a network is extremely heterogenous. The theoretical results from the suggested method can accurately predict the above removal effectiveness.

Transmission dynamics of oral polio vaccine viruses and vaccine-derived polioviruses on networks

One drawback of oral polio vaccine (OPV) is the potential reversion to more transmissible, virulent circulating vaccine-derived polioviruses (cVDPVs), which may cause outbreaks of paralytic poliomyelitis. Previous modeling studies of the transmission of cVDPVs assume an unrealistic homogeneous mixing of the population and/or ignore that OPV viruses and cVDPVs compete for susceptibles, which we show is a key to understanding the dynamics of the transmission of cVDPVs. We examined the transmission of OPV viruses and cVDPVs on heterogeneous, dynamic contact networks using differential equation-based and individual-based models. Despite the lower transmissibility, OPV viruses may outcompete more transmissible cVDPVs in the short run by spreading extensively before cVDPVs emerge. If viruses become endemic, however, cVDPVs eventually dominate and force OPV viruses to extinction. This study improves our understanding of the emergence of cVDPVs and helps develop more detailed models to plan a policy to control paralytic polio associated with the continued use of OPV in many countries.

Online respondent-driven sampling for studying contact patterns relevant for the spread of close-contact pathogens: a pilot study in Thailand

Background

Information on social interactions is needed to understand the spread of airborne infections through a population. Previous studies mostly collected egocentric information of independent respondents with self-reported information about contacts. Respondent-driven sampling (RDS) is a sampling technique allowing respondents to recruit contacts from their social network. We explored the feasibility of webRDS for studying contact patterns relevant for the spread of respiratory pathogens.

Materials and Methods

We developed a webRDS system for facilitating and tracking recruitment by Facebook and email. One-day diary surveys were conducted by applying webRDS among a convenience sample of Thai students. Students were asked to record numbers of contacts at different settings and self-reported influenza-like-illness symptoms, and to recruit four contacts whom they had met in the previous week. Contacts were asked to do the same to create a network tree of socially connected individuals. Correlations between linked individuals were analysed to investigate assortativity within networks.

Results

We reached up to 6 waves of contacts of initial respondents, using only non-material incentives. Forty-four (23.0%) of the initially approached students recruited one or more contacts. In total 257 persons participated, of which 168 (65.4%) were recruited by others. Facebook was the most popular recruitment option (45.1%). Strong assortative mixing was seen by age, gender and education, indicating a tendency of respondents to connect to contacts with similar characteristics. Random mixing was seen by reported number of daily contacts.

Conclusions

Despite methodological challenges (e.g. clustering among respondents and their contacts), applying RDS provides new insights in mixing patterns relevant for close-contact infections in real-world networks. Such information increases our knowledge of the transmission of respiratory infections within populations and can be used to improve existing modelling approaches. It is worthwhile to further develop and explore webRDS for the detection of clusters of respiratory symptoms in social networks.

Epidemic spread in networks: Existing methods and current challenges

We consider the spread of infectious disease through contact networks of Configuration Model type. We assume that the disease spreads through contacts and infected individuals recover into an immune state. We discuss a number of existing mathematical models used to investigate this system, and show relations between the underlying assumptions of the models. In the process we offer simplifications of some of the existing models. The distinctions between the underlying assumptions are subtle, and in many if not most cases this subtlety is irrelevant. Indeed, under appropriate conditions the models are equivalent. We compare the benefits and disadvantages of the different models, and discuss their application to other populations (e.g., clustered networks). Finally we discuss ongoing challenges for network-based epidemic modeling.

Cocirculation of infectious diseases on networks

We consider multiple diseases spreading in a static configuration model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a disease-specific rate. Infection by one disease confers immediate and permanent immunity to infection by any disease. Under these assumptions, we find a simple, low-dimensional ordinary differential equations model which captures the global dynamics of the infection. The dynamics depend strongly on initial conditions. Although we motivate this Rapid Communication with infectious disease, the model may be adapted to the spread of other infectious agents such as competing political beliefs, or adoption of new technologies if these are influenced by contacts. As an example, we demonstrate how to model an infectious disease which can be prevented by a behavior change.

The importance of contact network topology for the success of vaccination strategies

The effects of a number of vaccination strategies on the spread of an SIR type disease are numerically investigated for several common network topologies including random, scale-free, small world, and meta-random networks. These strategies, namely, prioritized, random, follow links and contact tracing, are compared across networks using extensive simulations with disease parameters relevant for viruses such as pandemic influenza H1N1/09. Two scenarios for a network SIR model are considered. First, a model with a given transmission rate is studied. Second, a model with a given initial growth rate is considered, because the initial growth rate is commonly used to impute the transmission rate from incidence curves and to predict the course of an epidemic. Since a vaccine may not be readily available for a new virus, the case of a delay in the start of vaccination is also considered in addition to the case of no delay. It is found that network topology can have a larger impact on the spread of the disease than the choice of vaccination strategy. Simulations also show that the network structure has a large effect on both the course of an epidemic and the determination of the transmission rate from the initial growth rate. The effect of delay in the vaccination start time varies tremendously with network topology. Results show that, without the knowledge of network topology, predictions on the peak and the final size of an epidemic cannot be made solely based on the initial exponential growth rate or transmission rate. This demonstrates the importance of understanding the topology of realistic contact networks when evaluating vaccination strategies.

Vaccination intervention on epidemic dynamics in networks

Vaccination is an important measure available for preventing or reducing the spread of infectious diseases. In this paper, an epidemic model including susceptible, infected, and imperfectly vaccinated compartments is studied on Watts-Strogatz small-world, Barabási-Albert scale-free, and random scale-free networks. The epidemic threshold and prevalence are analyzed. For small-world networks, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. For scale-free networks, the threshold is found to be strongly dependent both on the effective vaccination rate and on the connectivity distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.

Modelling the spread of diseases in clustered networks

It is now well appreciated that population structure can have a major impact on disease dynamics, outbreak sizes and epidemic thresholds. Indeed, on some networks, epidemics occur only for sufficiently high transmissibility, whereas in others (e.g. scale-free networks), no such threshold effect exists. While the effects of variability in connectivity are relatively well known, the effects of clustering in the population on disease dynamics are still debated. We develop a simple and intuitive model for calculating the reproductive number R(0) on clustered networks with arbitrary degree distribution. The model clearly shows that in general, clustering impedes epidemic spread; however, its effects are usually small and/or coupled with other topological properties of the network. The model is generalized to take into account degree-dependent transmissibility (e.g., relevant for disease vectors). The model is also used to easily rederive a known result concerning the formation of the giant component.

Model hierarchies in edge-based compartmental modeling for infectious disease spread

We consider the family of edge-based compartmental models for epidemic spread developed in Miller et al. (J R Soc Interface 9(70):890-906, 2012). These models allow for a range of complex behaviors, and in particular allow us to explicitly incorporate duration of a contact into our mathematical models. Our focus here is to identify conditions under which simpler models may be substituted for more detailed models, and in so doing we define a hierarchy of epidemic models. In particular we provide conditions under which it is appropriate to use the standard mass action SIR model, and we show what happens when these conditions fail. Using our hierarchy, we provide a procedure leading to the choice of the appropriate model for a given population. Our result about the convergence of models to the mass action model gives clear, rigorous conditions under which the mass action model is accurate.

Edge-based compartmental modelling for infectious disease spread

The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action susceptible-infected-recovered model of Kermack & McKendrick. Its usefulness derives largely from its conceptual and mathematical simplicity; however, it incorrectly assumes that all individuals have the same contact rate and partnerships are fleeting. In this study, we introduce edge-based compartmental modelling, a technique eliminating these assumptions. We derive simple ordinary differential equation models capturing social heterogeneity (heterogeneous contact rates) while explicitly considering the impact of partnership duration. We introduce a graphical interpretation allowing for easy derivation and communication of the model and focus on applying the technique under different assumptions about how contact rates are distributed and how long partnerships last.

Modeling the impact of supra-structural network nodes: The case of anonymous syringe sharing and HIV among people who inject drugs

Networks are well understood as crucial to the diffusion of HIV among injection drug users (IDUs), but quasi-anonymous risk nodes - such as shooting galleries - resist measurement and incorporation into empirical analyses of disease diffusion. Drawing on network data from 767 IDUs in Bushwick, Brooklyn, we illustrate the use of calibrated agent-based models (CABMs) to account for network structure, injection practices, and quasi-anonymous transmission in shooting galleries. Results confirm the importance of network structure and actor heterogeneity to the magnitude and speed of HIV transmission. Models further demonstrate that quasi-anonymous injections in shooting galleries increase the speed of HIV diffusion across the whole network and have the greatest impact on HIV seroconversion levels for IDUs at the network periphery. Shooting galleries are shown to be transmission hubs that operate independently of traceable structural ties, linking otherwise unconnected network components. CABMs potentially increase understandings of HIV diffusion dynamics by infusing computer simulations with empirical data.

Impacts of clustering on interacting epidemics

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