Epidemics Scenarios in the “Romantic Network”

The networks of sexual contacts together with temporal interactions play key roles in the spread of sexually transmitted infections. Unfortunately, data for this kind of network is scarce. One of the few exceptions, the “Romantic network”, is a complete structure of a real sexual network in a high school. Based on many network measurements the authors of the work have concluded that it does not correspond to any other model network. Regarding the temporal structure, several studies indicate that relationship timing can have an effect on the diffusion throughout networks, as relationship order determines transmission routes. The aim is to check if the particular structure, static and dynamic, of the Romantic network is determinant for the propagation of an STI. We performed simulations in two scenarios: the static network where all contacts are available and the dynamic case where contacts evolve over time. In the static case, we compared the epidemic results in the Romantic network with some paradigmatic topologies. In the dynamic scenario, we considered the dynamics of formation of pairs in the Romantic network and we studied the propagation of the diseases. Our results suggest that although this real network cannot be labeled as a Watts-Strogatz network, it is, in regard to the propagation of an STI, very similar to a high disorder network. Additionally, we found that: the effect that any individual contacting an externally infected subject is to make the network closer to a fully connected one, the higher the contact degree of patient zero the faster the spread of the outbreaks, and the epidemic impact is proportional to the numbers of contacts per unit time. Finally, our simulations confirm that relationship timing severely reduced the final outbreak size, and also, show a clear correlation between the average degree and the outbreak size over time.     

Effects of heterogeneous and clustered contact patterns on infectious disease dynamics

The spread of infectious diseases fundamentally depends on the pattern of contacts between individuals. Although studies of contact networks have shown that heterogeneity in the number of contacts and the duration of contacts can have far-reaching epidemiological consequences, models often assume that contacts are chosen at random and thereby ignore the sociological, temporal and/or spatial clustering of contacts. Here we investigate the simultaneous effects of heterogeneous and clustered contact patterns on epidemic dynamics. To model population structure, we generalize the configuration model which has a tunable degree distribution (number of contacts per node) and level of clustering (number of three cliques). To model epidemic dynamics for this class of random graph, we derive a tractable, low-dimensional system of ordinary differential equations that accounts for the effects of network structure on the course of the epidemic. We find that the interaction between clustering and the degree distribution is complex. Clustering always slows an epidemic, but simultaneously increasing clustering and the variance of the degree distribution can increase final epidemic size. We also show that bond percolation-based approximations can be highly biased if one incorrectly assumes that infectious periods are homogeneous, and the magnitude of this bias increases with the amount of clustering in the network. We apply this approach to model the high clustering of contacts within households, using contact parameters estimated from survey data of social interactions, and we identify conditions under which network models that do not account for household structure will be biased.     

Exploiting temporal network structures of human interaction to effectively immunize populations

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

Epidemic Spread on Weighted Networks

The contact structure between hosts shapes disease spread. Most network-based models used in epidemiology tend to ignore heterogeneity in the weighting of contacts between two individuals. However, this assumption is known to be at odds with the data for many networks (e.g. sexual contact networks) and to have a critical influence on epidemics'' behavior. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framework to estimate key epidemiological variables, such as the rate of early epidemic expansion () and the basic reproductive ratio (), from joint probability distributions of number of partners (contacts) and number of interaction events through which contacts are weighted. These distributions are much easier to infer than the exact shape of the network, which makes the approach widely applicable. The framework also allows for a derivation of the full time course of epidemic prevalence and contact behaviour, which we validate with numerical simulations on networks. Overall, incorporating more realistic contact networks into epidemiological models can improve our understanding of the emergence and spread of infectious diseases.     

Scaling properties of childhood infectious diseases epidemics before and after mass vaccination in Canada

The goal of this paper is to analyse the scaling properties of childhood infectious disease time-series data. We present a scaling analysis of the distribution of epidemic sizes of measles, rubella, pertussis, and mumps outbreaks in Canada. This application provides a new approach in assessing infectious disease dynamics in a large vaccinated population. An inverse power-law (IPL) distribution function has been fit to the time series of epidemic sizes, and the results assessed against an exponential benchmark model. We have found that the rubella epidemic size distribution and that of measles in highly vaccinated periods follow an IPL. The IPL suggests the presence of a scale-invariant network for these diseases as a result of the heterogeneity of the individual contact rates. By contrast, it was found that pertussis and mumps were characterized by a uniform network of transmission of the exponential type, which suggests homogeneity in the contact rate or, more likely, boiled down heterogeneity by large intermixing in the population. We conclude that the topology of the network of infectious contacts depends on the disease type and its infection rate. It also appears that the socio-demographic structure of the population may play a part (e.g. pattern of contacts according to age) in the structuring of the topology of the network. The findings suggest that there is relevant information hidden in the variation of the common contagious disease time-series data, and that this information can have a bearing on the strategy of vaccination programs.     

Susceptible-infected-recovered epidemics in dynamic contact networks

Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the duration of an outbreak. In reality, contact patterns may be quite fluid, with individuals frequently making and breaking social or sexual relationships. Here, we develop a mathematical approach to predicting disease transmission on dynamic networks in which each individual has a characteristic behaviour (typical contact number), but the identities of their contacts change in time. We show that dynamic contact patterns shape epidemiological dynamics in ways that cannot be adequately captured in static network models or mass-action models. Our new model interpolates smoothly between static network models and mass-action models using a mixing parameter, thereby providing a bridge between disparate classes of epidemiological models. Using epidemiological and sexual contact data from an Atlanta high school, we demonstrate the application of this method for forecasting and controlling sexually transmitted disease outbreaks.     

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.     

Network frailty and the geometry of herd immunity

The spread of infectious disease through communities depends fundamentally on the underlying patterns of contacts between individuals. Generally, the more contacts one individual has, the more vulnerable they are to infection during an epidemic. Thus, outbreaks disproportionately impact the most highly connected demographics. Epidemics can then lead, through immunization or removal of individuals, to sparser networks that are more resistant to future transmission of a given disease. Using several classes of contact networks-Poisson, scale-free and small-world-we characterize the structural evolution of a network due to an epidemic in terms of frailty (the degree to which highly connected individuals are more vulnerable to infection) and interference (the extent to which the epidemic cuts off connectivity among the susceptible population that remains following an epidemic). The evolution of the susceptible network over the course of an epidemic differs among the classes of networks; frailty, relative to interference, accounts for an increasing component of network evolution on networks with greater variance in contacts. The result is that immunization due to prior epidemics can provide greater community protection than random vaccination on networks with heterogeneous contact patterns, while the reverse is true for highly structured populations.     

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.     

Predicting epidemics on directed contact networks

Contact network epidemiology is an approach to modeling the spread of infectious diseases that explicitly considers patterns of person-to-person contacts within a community. Contacts can be asymmetric, with a person more likely to infect one of their contacts than to become infected by that contact. This is true for some sexually transmitted diseases that are more easily caught by women than men during heterosexual encounters; and for severe infectious diseases that cause an average person to seek medical attention and thereby potentially infect health care workers (HCWs) who would not, in turn, have an opportunity to infect that average person. Here we use methods from percolation theory to develop a mathematical framework for predicting disease transmission through semi-directed contact networks in which some contacts are undirected-the probability of transmission is symmetric between individuals-and others are directed-transmission is possible only in one direction. We find that the probability of an epidemic and the expected fraction of a population infected during an epidemic can be different in semi-directed networks, in contrast to the routine assumption that these two quantities are equal. We furthermore demonstrate that these methods more accurately predict the vulnerability of HCWs and the efficacy of various hospital-based containment strategies during outbreaks of severe respiratory diseases.     

Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics

The epidemic spread of infectious diseases is ubiquitous and often has a considerable impact on public health and economic wealth. The large variability in the spatio-temporal patterns of epidemics prohibits simple interventions and requires a detailed analysis of each epidemic with respect to its infectious agent and the corresponding routes of transmission. To facilitate this analysis, we introduce a mathematical framework which links epidemic patterns to the topology and dynamics of the underlying transmission network. The evolution, both in disease prevalence and transmission network topology, is derived from a closed set of partial differential equations for infections without allowing for recovery. The predictions are in excellent agreement with complementarily conducted agent-based simulations. The capacity of this new method is demonstrated in several case studies on HIV epidemics in synthetic populations: it allows us to monitor the evolution of contact behavior among healthy and infected individuals and the contributions of different disease stages to the spreading of the epidemic. This gives both direction to and a test bed for targeted intervention strategies for epidemic control. In conclusion, this mathematical framework provides a capable toolbox for the analysis of epidemics from first principles. This allows for fast, in silico modeling--and manipulation--of epidemics and is especially powerful if complemented with adequate empirical data for parameterization.     

Modelling disease spread through random and regular contacts in clustered populations

An epidemic spreading through a network of regular, repeated, contacts behaves differently from one that is spread by random interactions: regular contacts serve to reduce the speed and eventual size of an epidemic. This paper uses a mathematical model to explore the difference between regular and random contacts, considering particularly the effect of clustering within the contact network. In a clustered population random contacts have a much greater impact, allowing infection to reach parts of the network that would otherwise be inaccessible. When all contacts are regular, clustering greatly reduces the spread of infection; this effect is negated by a small number of random contacts.     

Assessment of Overlap of Phylogenetic Transmission Clusters and Communities in Simple Sexual Contact Networks: Applications to HIV-1

Background

Transmission patterns of sexually-transmitted infections (STIs) could relate to the structure of the underlying sexual contact network, whose features are therefore of interest to clinicians. Conventionally, we represent sexual contacts in a population with a graph, that can reveal the existence of communities. Phylogenetic methods help infer the history of an epidemic and incidentally, may help detecting communities. In particular, phylogenetic analyses of HIV-1 epidemics among men who have sex with men (MSM) have revealed the existence of large transmission clusters, possibly resulting from within-community transmissions. Past studies have explored the association between contact networks and phylogenies, including transmission clusters, producing conflicting conclusions about whether network features significantly affect observed transmission history. As far as we know however, none of them thoroughly investigated the role of communities, defined with respect to the network graph, in the observation of clusters.

Methods

The present study investigates, through simulations, community detection from phylogenies. We simulate a large number of epidemics over both unweighted and weighted, undirected random interconnected-islands networks, with islands corresponding to communities. We use weighting to modulate distance between islands. We translate each epidemic into a phylogeny, that lets us partition our samples of infected subjects into transmission clusters, based on several common definitions from the literature. We measure similarity between subjects’ island membership indices and transmission cluster membership indices with the adjusted Rand index.

Results and Conclusion

Analyses reveal modest mean correspondence between communities in graphs and phylogenetic transmission clusters. We conclude that common methods often have limited success in detecting contact network communities from phylogenies. The rarely-fulfilled requirement that network communities correspond to clades in the phylogeny is their main drawback. Understanding the link between transmission clusters and communities in sexual contact networks could help inform policymaking to curb HIV incidence in MSMs.     

Epidemic progression on networks based on disease generation time

We investigate the time evolution of disease spread on a network and present an analytical framework using the concept of disease generation time. Assuming a susceptible–infected–recovered epidemic process, this network-based framework enables us to calculate in detail the number of links (edges) within the network that are capable of producing new infectious nodes (individuals), the number of links that are not transmitting the infection further (non-transmitting links), as well as the number of contacts that individuals have with their neighbours (also known as degree distribution) within each epidemiological class, for each generation period. Using several examples, we demonstrate very good agreement between our analytical calculations and the results of computer simulations.     

Floquet theory for seasonal environmental forcing of spatially explicit waterborne epidemics

The transmission of waterborne pathogens is a complex process that is heavily linked to the spatial characteristics of the underlying environmental matrix as well as to the temporal variability of the relevant hydroclimatological drivers. In this work, we propose a time-varying, spatially explicit network model for the dynamics of waterborne diseases. Applying Floquet theory, which allows to extend results of local stability analysis to periodic dynamical systems, we find conditions for pathogen invasion and establishment in systems characterized by fluctuating environmental forcing, thus extending to time-varying contexts the generalized reproduction numbers recently obtained for spatially explicit epidemiology of waterborne disease. We show that temporal variability may have multifaceted effects on the invasion threshold, as it can either favor pathogen invasion or make it less likely. Moreover, environmental fluctuations characterized by distinctive geographical signatures can produce diversified, highly nontrivial effects on pathogen invasion. Our study is complemented by numerical simulations, which show that pathogen establishment is neither necessary nor sufficient for large epidemic outbreaks to occur in time-varying environments. Finally, we show that our framework can be used to reliably characterize the early geography of epidemic outbreaks triggered by fluctuating environmental conditions.     

Structural validation of an individual-based model for plague epidemics simulation

Plague remains endemic in many countries in the world and Madagascar is currently the country where the highest number of human plague cases is reported every year. The investigation of causal factors, which command the disease dynamics in rodent populations, is a crucial step to forecast, control and anticipate the infection extension to humans. This paper presents simulation results obtained from an epidemic model, SIMPEST, designed to simulate bubonic plague in a rodent population at a high level of spatial and temporal resolution. We developed a structurally realistic individual-based model, mobilizing knowledge about fleas and rats behaviour, inter-individual plague transmission, and disease evolution in individual organisms, so that the model reflects the way the real system operates and to generate spatial and temporal patterns of disease spread. To assess the structural validity of our simulations, we perform sensitivity analyses on the initial population size and spatial distribution, and compare our results with theoretical statements, garnered from both previous modelling experiences and repeated field observations. We show our results are consistent with referents about population size conditions for a disease to invade and persist and the effect of the contact network on disease dynamics.     

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.     

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.     

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.