Network theory and SARS: predicting outbreak diversity

Tracking and visualization of space-time activities for a micro-scale flu transmission study

Background

Infectious diseases pose increasing threats to public health with increasing population density and more and more sophisticated social networks. While efforts continue in studying the large scale dissemination of contagious diseases, individual-based activity and behaviour study benefits not only disease transmission modelling but also the control, containment, and prevention decision making at the local scale. The potential for using tracking technologies to capture detailed space-time trajectories and model individual behaviour is increasing rapidly, as technological advances enable the manufacture of small, lightweight, highly sensitive, and affordable receivers and the routine use of location-aware devices has become widespread (e.g., smart cellular phones). The use of low-cost tracking devices in medical research has also been proved effective by more and more studies. This study describes the use of tracking devices to collect data of space-time trajectories and the spatiotemporal processing of such data to facilitate micro-scale flu transmission study. We also reports preliminary findings on activity patterns related to chances of influenza infection in a pilot study.

Methods

Specifically, this study employed A-GPS tracking devices to collect data on a university campus. Spatiotemporal processing was conducted for data cleaning and segmentation. Processed data was validated with traditional activity diaries. The A-GPS data set was then used for visual explorations including density surface visualization and connection analysis to examine space-time activity patterns in relation to chances of influenza infection.

Results

When compared to diary data, the segmented tracking data demonstrated to be an effective alternative and showed greater accuracies in time as well as the details of routes taken by participants. A comparison of space-time activity patterns between participants who caught seasonal influenza and those who did not revealed interesting patterns.

Conclusions

This study proved that tracking technology an effective technique for obtaining data for micro-scale influenza transmission research. The findings revealed micro-scale transmission hotspots on a university campus and provided insights for local control and prevention strategies.

Infectious disease transmission as a forensic problem: who infected whom?

Observations on infectious diseases often consist of a sample of cases, distinguished by symptoms, and other characteristics, such as onset dates, spatial locations, genetic sequence of the pathogen and/or physiological and clinical data. Cases are often clustered, in space and time, suggesting that they are connected. By defining kernel functions for pairwise analysis of cases, a matrix of transmission probabilities can be estimated. We set up a Bayesian framework to integrate various sources of information to estimate the transmission network. The method is illustrated by analysing data from a multi-year study (2002-2007) of nosocomial outbreaks of norovirus in a large university hospital in the Netherlands. The study included 264 cases, the norovirus genotype was known in approximately 60 per cent of the patients. Combining all the available data allowed likely identification of individual transmission links between most of the cases (72%). This illustrates that the proposed method can be used to accurately reconstruct transmission networks, enhancing our understanding of outbreak dynamics and possibly leading to new insights into how to prevent outbreaks.

Variation with land use of immune function and prevalence of avian pox in Galapagos finches

Introduced disease has been implicated in recent wildlife extinctions and population declines worldwide. Both anthropogenic-induced change and natural environmental features can affect pathogen spread. Furthermore, environmental disturbance can result in changes in stress physiology, nutrition, and social structure, which in turn can suppress immune system function. However, it remains unknown whether landscape variation results in heterogeneity in host resistance to pathogens. Avian pox virus, a pathogen implicated in avian declines and extinctions in Hawaii, was introduced to the Galapagos in the 1890 s, and prevalence (total number of current infections) has increased recently in finches. We tested whether prevalence and recovery trends in 7 species of Galapagos finches varied by elevation or human land use. To do so, we used infection data obtained from 545 wild-caught birds. In addition, we determined whether annual changes in 4 aspects of innate immune function (complement protein activity, natural antibody activity, concentration of PIT54 protein, and heterophil:lymphocyte ratio) varied by elevation or land use. Prevalence and recovery rates did not vary by elevation from 2008 to 2009. Avian pox prevalence and proportion of recovered individuals in undeveloped and urban areas did not change from 2008 to 2009. In agricultural areas, avian pox prevalence increased 8-fold (from 2% to 17% of 234 individuals sampled) and proportion of recovered individuals increased (11% to 19%) from 2008 to 2009. These results suggest high disease-related mortality. Variation in immune function across human land-use types correlated with variation in both increased prevalence and susceptibility, which indicates changes in innate immune function may underlie changes in disease susceptibility. Our results suggest anthropogenic disturbance, in particular agricultural practices, may underlie immunological changes in host species that themselves contribute to pathogen emergence.

Percolation centrality: quantifying graph-theoretic impact of nodes during percolation in networks

A number of centrality measures are available to determine the relative importance of a node in a complex network, and betweenness is prominent among them. However, the existing centrality measures are not adequate in network percolation scenarios (such as during infection transmission in a social network of individuals, spreading of computer viruses on computer networks, or transmission of disease over a network of towns) because they do not account for the changing percolation states of individual nodes. We propose a new measure, percolation centrality, that quantifies relative impact of nodes based on their topological connectivity, as well as their percolation states. The measure can be extended to include random walk based definitions, and its computational complexity is shown to be of the same order as that of betweenness centrality. We demonstrate the usage of percolation centrality by applying it to a canonical network as well as simulated and real world scale-free and random networks.

Parasite invasion following host reintroduction: a case study of Yellowstone's wolves

Wildlife reintroductions select or treat individuals for good health with the expectation that these individuals will fare better than infected animals. However, these individuals, new to their environment, may also be particularly susceptible to circulating infections and this may result in high morbidity and mortality, potentially jeopardizing the goals of recovery. Here, using the reintroduction of the grey wolf (Canis lupus) into Yellowstone National Park as a case study, we address the question of how parasites invade a reintroduced population and consider the impact of these invasions on population performance. We find that several viral parasites rapidly invaded the population inside the park, likely via spillover from resident canid species, and we contrast these with the slower invasion of sarcoptic mange, caused by the mite Sarcoptes scabiei. The spatio-temporal patterns of mange invasion were largely consistent with patterns of host connectivity and density, and we demonstrate that the area of highest resource quality, supporting the greatest density of wolves, is also the region that appears most susceptible to repeated disease invasion and parasite-induced declines. The success of wolf reintroduction appears not to have been jeopardized by infectious disease, but now shows signs of regulation or limitation modulated by parasites.

H3N2v and other influenza epidemic risk based on age-specific estimates of sero-protection and contact network interactions

Cases of a novel swine-origin influenza A(H3N2) variant (H3N2v) have recently been identified in the US, primarily among children. We estimated potential epidemic attack rates (ARs) based on age-specific estimates of sero-susceptibility and social interactions. A contact network model previously established for the Greater Vancouver Area (GVA), Canada was used to estimate average epidemic (infection) ARs for the emerging H3N2v and comparator viruses (H1N1pdm09 and an extinguished H3N2 seasonal strain) based on typical influenza characteristics, basic reproduction number (R(0)), and effective contacts taking into account age-specific sero-protection rates (SPRs). SPRs were assessed in sera collected from the GVA in 2009 or earlier (pre-H1N1pdm09) and fall 2010 (post-H1N1pdm09, seasonal A/Brisbane/10/2007(H3N2), and H3N2v) by hemagglutination inhibition (HI) assay. SPR was assigned per convention based on proportion with HI antibody titre ≥40 (SPR40). Recognizing that the HI titre ≥40 was established as the 50%sero-protective threshold we also explored for ½SPR40, SPR80 and a blended gradient defined as: ¼SPR20, ½SPR40, ¾SPR80, SPR160. Base case analysis assumed R(0) = 1.40, but we also explored R(0) as high as 1.80. With R(0) = 1.40 and SPR40, simulated ARs were well aligned with field observations for H1N1pdm09 incidence (AR: 32%), sporadic detections without a third epidemic wave post-H1N1pdm09 (negligible AR<0.1%) as well as A/Brisbane/10/2007(H3N2) seasonal strain extinction and antigenic drift replacement (negligible AR<0.1%). Simulated AR for the novel swine-origin H3N2v was 6%, highest in children 6-11years (16%). However, with modification to SPR thresholds per above, H3N2v AR ≥20% became possible. At SPR40, H3N2v AR ≥10%, ≥15% or ≥30%, occur if R(0)≥1.48, ≥1.56 or ≥1.86, respectively. Based on conventional assumptions, the novel swine-origin H3N2v does not currently pose a substantial pandemic threat. If H3N2v epidemics do occur, overall community ARs are unlikely to exceed typical seasonal influenza experience. However risk assessment may change with time and depends crucially upon the validation of epidemiological features of influenza, notably the serologic correlate of protection and R(0).

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.

Inferring Contagion Patterns in Social Contact Networks with Limited Infection Data

The spread of infectious disease is an inherently stochastic process. As such, real time control and prediction methods present a significant challenge. For diseases which spread through direct human interaction, (e.g., transferred from infected to susceptible individuals) the contagion process can be modeled on a social-contact network where individuals are represented as nodes, and contacts between individuals are represented as links. The model presented in this paper seeks to identify the infection pattern which depicts the current state of an ongoing outbreak. This is accomplished by inferring the most likely paths of infection through a contact network under the assumption of partially available infection data. The problem is formulated as a bi-linear integer program, and heuristic solution methods are developed based on sub-problems which can be solved much more efficiently. The heuristic performance is presented for a range of randomly generated networks and different levels of information. The model results, which include the most likely set of infection spreading contacts, can be used to provide insight into future epidemic outbreak patterns, and aid in the development of intervention strategies.

Modeling the Impact of Behavior Changes on the Spread of Pandemic Influenza

We use mathematical models to assess the impact of behavioral changes in response to an emerging epidemic. Evaluating the quantitative and qualitative impact of public health interventions on the spread of infectious diseases is a crucial public health objective. The recent avian influenza (H5N1) outbreaks and the 2009 H1N1 pandemic have raised significant global concerns about the emergence of a deadly influenza virus causing a pandemic of catastrophic proportions. Mitigation strategies based on behavior changes are some of the only options available in the early stages of an emerging epidemic when vaccines are unlikely to be available and there are only limited stockpiles of antiviral medications. Mathematical models that capture these behavior changes can quantify the relative impact of different mitigation strategies, such as closing schools, in slowing the spread of an infectious disease. Including behavior changes in mathematical models increases complexity and is often left out of the analysis. We present a simple differential equation model which allows for people changing their behavior to decrease their probability of infection. We also describe a large-scale agent-based model that can be used to analyze the impact of isolation scenarios such as school closures and fear-based home isolation during a pandemic. The agent-based model captures realistic individual-level mixing patterns and coordinated reactive changes in human behavior in order to better predict the transmission dynamics of an epidemic. Both models confirm that changes in behavior can be effective in reducing the spread of disease. For example, our model predicts that if school closures are implemented for the duration of the pandemic, the clinical attack rate could be reduced by more than 50%. We also verify that when interventions are stopped too soon, a second wave of infection can occur.

Outcome inelasticity and outcome variability in behaviour-incidence models: an example from an SEIR infection on a dynamic network

Behavior-incidence models have been used to model phenomena such as free-riding vaccinating behavior, where nonvaccinators free ride on herd immunity generated by vaccinators. Here, we develop and analyze a simulation model of voluntary ring vaccination on an evolving social contact network. Individuals make vaccination decisions by examining their expected payoffs, which are influenced by the infection status of their neighbors. We find that stochasticity can make outcomes extremely variable (near critical thresholds) and thus unpredictable: some stochastic realizations result in rapid control through ring vaccination while others result in widespread transmission. We also explore the phenomenon of outcome inelasticity, wherein behavioral responses result in certain outcome measures remaining relatively unchanged. Finally, we explore examples where ineffective or risky vaccines are more widely adopted than safe, effective vaccines. This occurs when such a vaccine is unattractive to a sufficient number of contacts of an index case to cause failure of ring vaccination. As a result, the infection percolates through the entire network, causing the final epidemic size and vaccine coverage to be higher than would otherwise occur. Effects such as extreme outcome variability and outcome inelasticity have implications for vaccination policies that depend on individual choice for their success and predictability.

Modeling of wildlife-associated zoonoses: applications and caveats

Wildlife species are identified as an important source of emerging zoonotic disease. Accordingly, public health programs have attempted to expand in scope to include a greater focus on wildlife and its role in zoonotic disease outbreaks. Zoonotic disease transmission dynamics involving wildlife are complex and nonlinear, presenting a number of challenges. First, empirical characterization of wildlife host species and pathogen systems are often lacking, and insight into one system may have little application to another involving the same host species and pathogen. Pathogen transmission characterization is difficult due to the changing nature of population size and density associated with wildlife hosts. Infectious disease itself may influence wildlife population demographics through compensatory responses that may evolve, such as decreased age to reproduction. Furthermore, wildlife reservoir dynamics can be complex, involving various host species and populations that may vary in their contribution to pathogen transmission and persistence over space and time. Mathematical models can provide an important tool to engage these complex systems, and there is an urgent need for increased computational focus on the coupled dynamics that underlie pathogen spillover at the human-wildlife interface. Often, however, scientists conducting empirical studies on emerging zoonotic disease do not have the necessary skill base to choose, develop, and apply models to evaluate these complex systems. How do modeling frameworks differ and what considerations are important when applying modeling tools to the study of zoonotic disease? Using zoonotic disease examples, we provide an overview of several common approaches and general considerations important in the modeling of wildlife-associated zoonoses.

Assessing the roles of brokerage: an evaluation of a hospital-based Public Health epidemiologist program in North Carolina

CONTEXT

The North Carolina Division of Public Health established an innovative program in 2003 that placed public health epidemiologists (PHEs) in hospitals around the state to improve communication between hospitals and local public health departments (LHDs) and bolster public health surveillance and response.

OBJECTIVE

To use social network analysis to assess how the hospital-based PHE program in North Carolina facilitates the exchange of public health surveillance information.

DESIGN

Using a Gould-Fernandez brokerage analysis, this study examines communication among organizational actors and their dependence on third parties to broker information and knowledge.

PARTICIPANTS

Survey and interview data were collected to identify the interorganizational network among 220 organizational actors and their public health surveillance-related activities, including 11 PHEs, 100 county-level offices of North Carolina's 85 LHDs, and 109 hospitals.

MAIN OUTCOME MEASURES

Social network analysis is used to calculate the frequency with which an actor serves as an intermediary in each of the 5 brokerage roles as well as total brokerage equal to the sum of the number of times an actor occupies each role.

RESULTS

Results identify a frequent tendency for PHEs to serve as an intermediary between LHDs and hospitals. Interactions between these entities are frequently facilitated by PHEs, with a high measure of degree centrality by LHDs and a low frequency of brokerage among hospitals.

CONCLUSIONS

Results validate PHEs' mission to enhance communication between LHDs and hospitals around communicable disease surveillance, reporting, and management.

Inferring the structure of social contacts from demographic data in the analysis of infectious diseases spread

Social contact patterns among individuals encode the transmission route of infectious diseases and are a key ingredient in the realistic characterization and modeling of epidemics. Unfortunately, the gathering of high quality experimental data on contact patterns in human populations is a very difficult task even at the coarse level of mixing patterns among age groups. Here we propose an alternative route to the estimation of mixing patterns that relies on the construction of virtual populations parametrized with highly detailed census and demographic data. We present the modeling of the population of 26 European countries and the generation of the corresponding synthetic contact matrices among the population age groups. The method is validated by a detailed comparison with the matrices obtained in six European countries by the most extensive survey study on mixing patterns. The methodology presented here allows a large scale comparison of mixing patterns in Europe, highlighting general common features as well as country-specific differences. We find clear relations between epidemiologically relevant quantities (reproduction number and attack rate) and socio-demographic characteristics of the populations, such as the average age of the population and the duration of primary school cycle. This study provides a numerical approach for the generation of human mixing patterns that can be used to improve the accuracy of mathematical models in the absence of specific experimental data.

The dynamics of infectious diseases caused by pathogens transmissible from human to human strongly depends on contact patterns between individuals. High quality observational data on contact patterns, usually presented in the form of age-specific contact matrices, are difficult to gather and are currently available only for few countries worldwide. Here we propose a computational approach, based on the simulation of a virtual society of agents, allowing the estimation of contact patterns by age for 26 European countries. We validate the estimated contact matrices against those obtained by the most extensive field study on contact patterns, with data collected in eight European countries. We show that our contact matrices share some common features, e.g. individuals tend to mix preferentially with individuals their own age, and country-specific differences, which can be partly explained by differences in population structures due to different demographic trajectories followed after WWII. Our analysis highlights well defined correlations between epidemiological parameters and socio-demographic features of the populations. This study provides the first estimates of contact matrices for many European countries where specific experimental data are still not available.

Controlling epidemic spread by social distancing: do it well or not at all

BACKGROUND

Existing epidemiological models have largely tended to neglect the impact of individual behaviour on the dynamics of diseases. However, awareness of the presence of illness can cause people to change their behaviour by, for example, staying at home and avoiding social contacts. Such changes can be used to control epidemics but they exact an economic cost. Our aim is to study the costs and benefits of using individual-based social distancing undertaken by healthy individuals as a form of control.

METHODS

Our model is a standard SIR model superimposed on a spatial network, without and with addition of small-world interactions. Disease spread is controlled by allowing susceptible individuals to temporarily reduce their social contacts in response to the presence of infection within their local neighbourhood. We ascribe an economic cost to the loss of social contacts, and weigh this against the economic benefit gained by reducing the impact of the epidemic. We study the sensitivity of the results to two key parameters, the individuals' attitude to risk and the size of the awareness neighbourhood.

RESULTS

Depending on the characteristics of the epidemic and on the relative economic importance of making contacts versus avoiding infection, the optimal control is one of two extremes: either to adopt a highly cautious control, thereby suppressing the epidemic quickly by drastically reducing contacts as soon as disease is detected; or else to forego control and allow the epidemic to run its course. The worst outcome arises when control is attempted, but not cautiously enough to cause the epidemic to be suppressed. The next main result comes from comparing the size of the neighbourhood of which individuals are aware to that of the neighbourhood within which transmission can occur. The control works best when these sizes match and is particularly ineffective when the awareness neighbourhood is smaller than the infection neighbourhood. The results are robust with respect to inclusion of long-range, small-world links which destroy the spatial structure, regardless of whether individuals can or cannot control them. However, addition of many non-local links eventually makes control ineffective.

CONCLUSIONS

These results have implications for the design of control strategies using social distancing: a control that is too weak or based upon inaccurate knowledge, may give a worse outcome than doing nothing.

How complexity science can inform scale-up and spread in health care: understanding the role of self-organization in variation across local contexts

Health care systems struggle to scale-up and spread effective practices across diverse settings. Failures in scale-up and spread (SUS) are often attributed to a lack of consideration for variation in local contexts among different health care delivery settings. We argue that SUS occurs within complex systems and that self-organization plays an important role in the success, or failure, of SUS. Self-organization is a process whereby local interactions give rise to patterns of organizing. These patterns may be stable or unstable, and they evolve over time. Self-organization is a major contributor to local variations across health care delivery settings. Thus, better understanding of self-organization in the context of SUS is needed. We re-examine two cases of successful SUS: 1) the application of a mobile phone short message service intervention to improve adherence to medications during HIV treatment scale up in resource-limited settings, and 2) MRSA prevention in hospital inpatient settings in the United States. Based on insights from these cases, we discuss the role of interdependencies and sensemaking in leveraging self-organization in SUS initiatives. We argue that self-organization, while not completely controllable, can be influenced, and that improving interdependencies and sensemaking among SUS stakeholders is a strategy for facilitating self-organization processes that increase the probability of spreading effective practices across diverse settings.

Heterogeneous length of stay of hosts' movements and spatial epidemic spread

Infectious diseases outbreaks are often characterized by a spatial component induced by hosts’ distribution, mobility, and interactions. Spatial models that incorporate hosts’ movements are being used to describe these processes, to investigate the conditions for propagation, and to predict the spatial spread. Several assumptions are being considered to model hosts’ movements, ranging from permanent movements to daily commuting, where the time spent at destination is either infinite or assumes a homogeneous fixed value, respectively. Prompted by empirical evidence, here we introduce a general metapopulation approach to model the disease dynamics in a spatially structured population where the mobility process is characterized by a heterogeneous length of stay. We show that large fluctuations of the length of stay, as observed in reality, can have a significant impact on the threshold conditions for the global epidemic invasion, thus altering model predictions based on simple assumptions, and displaying important public health implications.

Modelling the long-term dynamics of pre-vaccination pertussis

The dynamics of strongly immunizing childhood infections is still not well understood. Although reports of successful modelling of several data records can be found in the previous literature, the key determinants of the observed temporal patterns have not yet been clearly identified. In particular, different models of immunity waning and degree of protection applied to disease- and vaccine-induced immunity have been debated in the previous literature on pertussis. Here, we study the effect of disease-acquired immunity on the long-term patterns of pertussis prevalence. We compare five minimal models, all of which are stochastic, seasonally forced, well-mixed models of infection, based on susceptible-infective-recovered dynamics in a closed population. These models reflect different assumptions about the immune response of naive hosts, namely total permanent immunity, immunity waning, immunity waning together with immunity boosting, reinfection of recovered and repeat infection after partial immunity waning. The power spectra of the output prevalence time series characterize the long-term dynamics of the models. For epidemiological parameters consistent with published data, the power spectra show quantitative and even qualitative differences, which can be used to test their assumptions by comparison with ensembles of several-decades-long pre-vaccination data records. We illustrate this strategy on two publicly available historical datasets.

The impact of past epidemics on future disease dynamics

Many pathogens spread primarily via direct contact between infected and susceptible hosts. Thus, the patterns of contacts or contact network of a population fundamentally shape the course of epidemics. While there is a robust and growing theory for the dynamics of single epidemics in networks, we know little about the impacts of network structure on long-term epidemic or endemic transmission. For seasonal diseases like influenza, pathogens repeatedly return to populations with complex and changing patterns of susceptibility and immunity acquired through prior infection. Here, we develop two mathematical approaches for modeling consecutive seasonal outbreaks of a partially-immunizing infection in a population with contact heterogeneity. Using methods from percolation theory we consider both leaky immunity, where all previously infected individuals gain partial immunity, and polarized immunity, where a fraction of previously infected individuals are fully immune. By restructuring the epidemiologically active portion of their host population, such diseases limit the potential of future outbreaks. We speculate that these dynamics can result in evolutionary pressure to increase infectiousness.

Hierarchical ordering of reticular networks

The structure of hierarchical networks in biological and physical systems has long been characterized using the Horton-Strahler ordering scheme. The scheme assigns an integer order to each edge in the network based on the topology of branching such that the order increases from distal parts of the network (e.g., mountain streams or capillaries) to the “root” of the network (e.g., the river outlet or the aorta). However, Horton-Strahler ordering cannot be applied to networks with loops because they they create a contradiction in the edge ordering in terms of which edge precedes another in the hierarchy. Here, we present a generalization of the Horton-Strahler order to weighted planar reticular networks, where weights are assumed to correlate with the importance of network edges, e.g., weights estimated from edge widths may correlate to flow capacity. Our method assigns hierarchical levels not only to edges of the network, but also to its loops, and classifies the edges into reticular edges, which are responsible for loop formation, and tree edges. In addition, we perform a detailed and rigorous theoretical analysis of the sensitivity of the hierarchical levels to weight perturbations. In doing so, we show that the ordering of the reticular edges is more robust to noise in weight estimation than is the ordering of the tree edges. We discuss applications of this generalized Horton-Strahler ordering to the study of leaf venation and other biological networks.

Molecular evolution and emergence of avian gammacoronaviruses

Coronaviruses, which are single stranded, positive sense RNA viruses, are responsible for a wide variety of existing and emerging diseases in humans and other animals. The gammacoronaviruses primarily infect avian hosts. Within this genus of coronaviruses, the avian coronavirus infectious bronchitis virus (IBV) causes a highly infectious upper-respiratory tract disease in commercial poultry. IBV shows rapid evolution in chickens, frequently producing new antigenic types, which adds to the multiple serotypes of the virus that do not cross protect. Rapid evolution in IBV is facilitated by strong selection, large population sizes and high genetic diversity within hosts, and transmission bottlenecks between hosts. Genetic diversity within a host arises primarily by mutation, which includes substitutions, insertions and deletions. Mutations are caused both by the high error rate, and limited proof reading capability, of the viral RNA-dependent RNA-polymerase, and by recombination. Recombination also generates new haplotype diversity by recombining existing variants. Rapid evolution of avian coronavirus IBV makes this virus extremely difficult to diagnose and control, but also makes it an excellent model system to study viral genetic diversity and the mechanisms behind the emergence of coronaviruses in their natural host.

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.

EpiFire: An open source C++ library and application for contact network epidemiology

BACKGROUND

Contact network models have become increasingly common in epidemiology, but we lack a flexible programming framework for the generation and analysis of epidemiological contact networks and for the simulation of disease transmission through such networks.

RESULTS

Here we present EpiFire, an applications programming interface and graphical user interface implemented in C++, which includes a fast and efficient library for generating, analyzing and manipulating networks. Network-based percolation and chain-binomial simulations of susceptible-infected-recovered disease transmission, as well as traditional non-network mass-action simulations, can be performed using EpiFire.

CONCLUSIONS

EpiFire provides an open-source programming interface for the rapid development of network models with a focus in contact network epidemiology. EpiFire also provides a point-and-click interface for generating networks, conducting epidemic simulations, and creating figures. This interface is particularly useful as a pedagogical tool.

The impact of imitation on vaccination behavior in social contact networks

Previous game-theoretic studies of vaccination behavior typically have often assumed that populations are homogeneously mixed and that individuals are fully rational. In reality, there is heterogeneity in the number of contacts per individual, and individuals tend to imitate others who appear to have adopted successful strategies. Here, we use network-based mathematical models to study the effects of both imitation behavior and contact heterogeneity on vaccination coverage and disease dynamics. We integrate contact network epidemiological models with a framework for decision-making, within which individuals make their decisions either based purely on payoff maximization or by imitating the vaccination behavior of a social contact. Simulations suggest that when the cost of vaccination is high imitation behavior may decrease vaccination coverage. However, when the cost of vaccination is small relative to that of infection, imitation behavior increases vaccination coverage, but, surprisingly, also increases the magnitude of epidemics through the clustering of non-vaccinators within the network. Thus, imitation behavior may impede the eradication of infectious diseases. Calculations that ignore behavioral clustering caused by imitation may significantly underestimate the levels of vaccination coverage required to attain herd immunity.

Both infectious diseases and behavioral traits can spread via social contacts. Using network-based mathematical models, our study addresses the interplay between these two processes, as disease spreads through a population and individuals copy their social contacts when making vaccination decisions. Imitation can produce clusters of non-vaccinating, susceptible individuals that facilitate relatively large outbreaks of infectious diseases despite high overall vaccination coverage. This may explain, for example, recent measles outbreaks observed in many countries with universal measles vaccination policies. Given that vaccine decisions are likely to be influenced by social contacts and that such imitation can have detrimental epidemiological effects, it is important that policy makers understand its causes, magnitude and implications for disease eradication.

Spatial scaling relationships for spread of disease caused by a wind-dispersed plant pathogen

Spatial scale is of great importance to understanding the spread of organisms exhibiting long-distance dispersal (LDD). We tested whether epidemics spread in direct proportion to the size of the host population and size of the initial disease focus. This was done through analysis of a previous study of the effects of landscape heterogeneity variables on the spread of accelerating epidemics of wheat (Triticum aestivum) stripe rust, caused by the fungus Puccinia striiformis f. sp. tritici. End-of-season disease gradients were constructed by estimating disease prevalence at regular distances from artificially inoculated foci of different sizes, in field plots of different dimensions. In one set of comparisons, all linear dimensions (plot width and length, focus width and length, and distance between observation points) differed by a factor of four. Disease spread was substantially greater in large plot/large focus treatments than in small plot/small focus treatments. However, when disease gradients were plotted using focus width as the unit distance, they were found to be highly similar, suggesting a proportional relationship between focus or plot size and disease spread. A similar relationship held when comparing same-size plots inoculated with different-sized foci, an indication that focus size is the driver of this proportionality. Our results suggest that power law dispersal of LDD organisms results in scale-invariant relationships, which are useful for better understanding spatial spread of biological invasions, extrapolating results from small-scale experiments to invasions spreading over larger scales, and predicting speed and pattern of spread as an invasion expands.

Evaluating temporal factors in combined interventions of workforce shift and school closure for mitigating the spread of influenza

Background

It is believed that combined interventions may be more effective than individual interventions in mitigating epidemic. However there is a lack of quantitative studies on performance of the combination of individual interventions under different temporal settings.

Methodology/Principal Findings

To better understand the problem, we develop an individual-based simulation model running on top of contact networks based on real-life contact data in Singapore. We model and evaluate the spread of influenza epidemic with intervention strategies of workforce shift and its combination with school closure, and examine the impacts of temporal factors, namely the trigger threshold and the duration of an intervention. By comparing simulation results for intervention scenarios with different temporal factors, we find that combined interventions do not always outperform individual interventions and are more effective only when the duration is longer than 6 weeks or school closure is triggered at the 5% threshold; combined interventions may be more effective if school closure starts first when the duration is less than 4 weeks or workforce shift starts first when the duration is longer than 4 weeks.

Conclusions/Significance

We therefore conclude that identifying the appropriate timing configuration is crucial for achieving optimal or near optimal performance in mitigating the spread of influenza epidemic. The results of this study are useful to policy makers in deliberating and planning individual and combined interventions.

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.

Transmission of infectious diseases en route to habitat hotspots

BACKGROUND

The spread of infectious diseases in wildlife populations is influenced by patterns of between-host contacts. Habitat "hotspots"--places attracting a large numbers of individuals or social groups--can significantly alter contact patterns and, hence, disease propagation. Research on the importance of habitat hotspots in wildlife epidemiology has primarily focused on how inter-individual contacts occurring at the hotspot itself increase disease transmission. However, in territorial animals, epidemiologically important contacts may primarily occur as animals cross through territories of conspecifics en route to habitat hotspots. So far, the phenomenon has received little attention. Here, we investigate the importance of these contacts in the case where infectious individuals keep visiting the hotspots and in the case where these individuals are not able to travel to the hotspot any more.

METHODOLOGY AND PRINCIPAL FINDINGS

We developed a simulation epidemiological model to investigate both cases in a scenario when transmission at the hotspot does not occur. We find that (i) hotspots still exacerbate epidemics, (ii) when infectious individuals do not travel to the hotspot, the most vulnerable individuals are those residing at intermediate distances from the hotspot rather than nearby, and (iii) the epidemiological vulnerability of a population is the highest when the number of hotspots is intermediate.

CONCLUSIONS AND SIGNIFICANCE

By altering animal movements in their vicinity, habitat hotspots can thus strongly increase the spread of infectious diseases, even when disease transmission does not occur at the hotspot itself. Interestingly, when animals only visit the nearest hotspot, creating additional artificial hotspots, rather than reducing their number, may be an efficient disease control measure.

HIV transmissions by stage in dynamic sexual partnerships

Most models assessing relative transmissions during different progressive stages of human immunodeficiency virus (HIV) infection assume that infections are transmitted through instantaneous sexual contacts. In reality, however, HIV will often be transmitted through repeated sex acts during partnerships that form and dissolve at varying rates. We sought to understand how dynamic sexual partnerships would influence transmissions during different progression stages of HIV infection: primary HIV infection (PHI) and chronic stage. Using a system of ordinary differential equations with a pair approximation technique, we constructed a model of HIV transmission in a homogeneous population in which sexual partnerships form and dissolve. We derived analytical expressions for useful epidemiological quantities such as basic reproduction number and also did simulation runs of the model. Partnership dynamics strongly influence transmissions during progressive stages of HIV infection. The fraction of transmissions during PHI has a U-shaped relationship with respect to the rate of partnership change, where the minimum and maximum occur given partnerships of about 100 days and fixed partnerships, respectively. Models that assume instantaneous contacts may overestimate transmissions during PHI for real, dynamic sexual partnerships with varying (non-zero) durations.

Systems science methods in public health: dynamics, networks, and agents

Complex systems abound in public health. Complex systems are made up of heterogeneous elements that interact with one another, have emergent properties that are not explained by understanding the individual elements of the system, persist over time, and adapt to changing circumstances. Public health is starting to use results from systems science studies to shape practice and policy, for example in preparing for global pandemics. However, systems science study designs and analytic methods remain underutilized and are not widely featured in public health curricula or training. In this review we present an argument for the utility of systems science methods in public health, introduce three important systems science methods (system dynamics, network analysis, and agent-based modeling), and provide three case studies in which these methods have been used to answer important public health science questions in the areas of infectious disease, tobacco control, and obesity.

Connecting network properties of rapidly disseminating epizoonotics

BACKGROUND

To effectively control the geographical dissemination of infectious diseases, their properties need to be determined. To test that rapid microbial dispersal requires not only susceptible hosts but also a pre-existing, connecting network, we explored constructs meant to reveal the network properties associated with disease spread, which included the road structure.

METHODS

Using geo-temporal data collected from epizoonotics in which all hosts were susceptible (mammals infected by Foot-and-mouth disease virus, Uruguay, 2001; birds infected by Avian Influenza virus H5N1, Nigeria, 2006), two models were compared: 1) 'connectivity', a model that integrated bio-physical concepts (the agent's transmission cycle, road topology) into indicators designed to measure networks ('nodes' or infected sites with short- and long-range links), and 2) 'contacts', which focused on infected individuals but did not assess connectivity.

RESULTS

THE CONNECTIVITY MODEL SHOWED FIVE NETWORK PROPERTIES: 1) spatial aggregation of cases (disease clusters), 2) links among similar 'nodes' (assortativity), 3) simultaneous activation of similar nodes (synchronicity), 4) disease flows moving from highly to poorly connected nodes (directionality), and 5) a few nodes accounting for most cases (a "20:80" pattern). In both epizoonotics, 1) not all primary cases were connected but at least one primary case was connected, 2) highly connected, small areas (nodes) accounted for most cases, 3) several classes of nodes were distinguished, and 4) the contact model, which assumed all primary cases were identical, captured half the number of cases identified by the connectivity model. When assessed together, the synchronicity and directionality properties explained when and where an infectious disease spreads.

CONCLUSIONS

Geo-temporal constructs of Network Theory's nodes and links were retrospectively validated in rapidly disseminating infectious diseases. They distinguished classes of cases, nodes, and networks, generating information usable to revise theory and optimize control measures. Prospective studies that consider pre-outbreak predictors, such as connecting networks, are recommended.

Epidemic threshold and control in a dynamic network

In this paper we present a model describing susceptible-infected-susceptible-type epidemics spreading on a dynamic contact network with random link activation and deletion where link activation can be locally constrained. We use and adapt an improved effective degree compartmental modeling framework recently proposed by Lindquist et al. [J. Math Biol. 62, 143 (2010)] and Marceau et al. [Phys. Rev. E 82, 036116 (2010)]. The resulting set of ordinary differential equations (ODEs) is solved numerically, and results are compared to those obtained using individual-based stochastic network simulation. We show that the ODEs display excellent agreement with simulation for the evolution of both the disease and the network and are able to accurately capture the epidemic threshold for a wide range of parameters. We also present an analytical R0 calculation for the dynamic network model and show that, depending on the relative time scales of the network evolution and disease transmission, two limiting cases are recovered: (i) the static network case when network evolution is slow and (ii) homogeneous random mixing when the network evolution is rapid. We also use our threshold calculation to highlight the dangers of relying on local stability analysis when predicting epidemic outbreaks on evolving networks.

Leveraging social networks for understanding the evolution of epidemics

BACKGROUND

To understand how infectious agents disseminate throughout a population it is essential to capture the social model in a realistic manner. This paper presents a novel approach to modeling the propagation of the influenza virus throughout a realistic interconnection network based on actual individual interactions which we extract from online social networks. The advantage is that these networks can be extracted from existing sources which faithfully record interactions between people in their natural environment. We additionally allow modeling the characteristics of each individual as well as customizing his daily interaction patterns by making them time-dependent. Our purpose is to understand how the infection spreads depending on the structure of the contact network and the individuals who introduce the infection in the population. This would help public health authorities to respond more efficiently to epidemics.

RESULTS

We implement a scalable, fully distributed simulator and validate the epidemic model by comparing the simulation results against the data in the 2004-2005 New York State Department of Health Report (NYSDOH), with similar temporal distribution results for the number of infected individuals. We analyze the impact of different types of connection models on the virus propagation. Lastly, we analyze and compare the effects of adopting several different vaccination policies, some of them based on individual characteristics -such as age- while others targeting the super-connectors in the social model.

CONCLUSIONS

This paper presents an approach to modeling the propagation of the influenza virus via a realistic social model based on actual individual interactions extracted from online social networks. We implemented a scalable, fully distributed simulator and we analyzed both the dissemination of the infection and the effect of different vaccination policies on the progress of the epidemics. The epidemic values predicted by our simulator match real data from NYSDOH. Our results show that our simulator can be a useful tool in understanding the differences in the evolution of an epidemic within populations with different characteristics and can provide guidance with regard to which, and how many, individuals should be vaccinated to slow down the virus propagation and reduce the number of infections.

Vaccination against 2009 pandemic H1N1 in a population dynamical model of Vancouver, Canada: timing is everything

BACKGROUND

Much remains unknown about the effect of timing and prioritization of vaccination against pandemic (pH1N1) 2009 virus on health outcomes. We adapted a city-level contact network model to study different campaigns on influenza morbidity and mortality.

METHODS

We modeled different distribution strategies initiated between July and November 2009 using a compartmental epidemic model that includes age structure and transmission network dynamics. The model represents the Greater Vancouver Regional District, a major North American city and surrounding suburbs with a population of 2 million, and is parameterized using data from the British Columbia Ministry of Health, published studies, and expert opinion. Outcomes are expressed as the number of infections and deaths averted due to vaccination.

RESULTS

The model output was consistent with provincial surveillance data. Assuming a basic reproduction number = 1.4, an 8-week vaccination campaign initiated 2 weeks before the epidemic onset reduced morbidity and mortality by 79-91% and 80-87%, respectively, compared to no vaccination. Prioritizing children and parents for vaccination may have reduced transmission compared to actual practice, but the mortality benefit of this strategy appears highly sensitive to campaign timing. Modeling the actual late October start date resulted in modest reductions in morbidity and mortality (13-25% and 16-20%, respectively) with little variation by prioritization scheme.

CONCLUSION

Delays in vaccine production due to technological or logistical barriers may reduce potential benefits of vaccination for pandemic influenza, and these temporal effects can outweigh any additional theoretical benefits from population targeting. Careful modeling may provide decision makers with estimates of these effects before the epidemic peak to guide production goals and inform policy. Integration of real-time surveillance data with mathematical models holds the promise of enabling public health planners to optimize the community benefits from proposed interventions before the pandemic peak.

Stochastic oscillations in models of epidemics on a network of cities

We carry out an analytic investigation of stochastic oscillations in a susceptible-infected-recovered model of disease spread on a network of n cities. In the model a fraction f(jk) of individuals from city k commute to city j, where they may infect, or be infected by, others. Starting from a continuous-time Markov description of the model the deterministic equations, which are valid in the limit when the population of each city is infinite, are recovered. The stochastic fluctuations about the fixed point of these equations are derived by use of the van Kampen system-size expansion. The fixed point structure of the deterministic equations is remarkably simple: A unique nontrivial fixed point always exists and has the feature that the fraction of susceptible, infected, and recovered individuals is the same for each city irrespective of its size. We find that the stochastic fluctuations have an analogously simple dynamics: All oscillations have a single frequency, equal to that found in the one-city case. We interpret this phenomenon in terms of the properties of the spectrum of the matrix of the linear approximation of the deterministic equations at the fixed point.

Animal social networks as substrate for cultural behavioural diversity

We used individual-based stochastic models to examine how social structure influences the diversity of socially learned behaviour within a non-human population. For continuous behavioural variables we modelled three forms of dyadic social learning, averaging the behavioural value of the two individuals, random transfer of information from one individual to the other, and directional transfer from the individual with highest behavioural value to the other. Learning had potential error. We also examined the transfer of categorical behaviour between individuals with random directionality and two forms of error, the adoption of a randomly chosen existing behavioural category or the innovation of a new type of behaviour. In populations without social structuring the diversity of culturally transmitted behaviour increased with learning error and population size. When the populations were structured socially either by making individuals members of permanent social units or by giving them overlapping ranges, behavioural diversity increased with network modularity under all scenarios, although the proportional increase varied considerably between continuous and categorical behaviour, with transmission mechanism, and population size. Although functions of the form e(c)¹(m)⁻(c)² + (c)³(Log(N)) predicted the mean increase in diversity with modularity (m) and population size (N), behavioural diversity could be highly unpredictable both between simulations with the same set of parameters, and within runs. Errors in social learning and social structuring generally promote behavioural diversity. Consequently, social learning may be considered to produce culture in populations whose social structure is sufficiently modular.

Invasion threshold in structured populations with recurrent mobility patterns

In this paper we develop a framework to analyze the behavior of contagion and spreading processes in complex subpopulation networks where individuals have memory of their subpopulation of origin. We introduce a metapopulation model in which subpopulations are connected through heterogeneous fluxes of individuals. The mobility process among communities takes into account the memory of residence of individuals and is incorporated with the classical susceptible-infectious-recovered epidemic model within each subpopulation. In order to gain analytical insight into the behavior of the system we use degree-block variables describing the heterogeneity of the subpopulation network and a time-scale separation technique for the dynamics of individuals. By considering the stochastic nature of the epidemic process we obtain the explicit expression of the global epidemic invasion threshold, below which the disease dies out before reaching a macroscopic fraction of the subpopulations. This threshold is not present in continuous deterministic diffusion models and explicitly depends on the disease parameters, the mobility rates, and the properties of the coupling matrices describing the mobility across subpopulations. The results presented here take a step further in offering insight into the fundamental mechanisms controlling the spreading of infectious diseases and other contagion processes across spatially structured communities.

Risk-based surveillance for avian influenza control along poultry market chains in South China: The value of social network analysis

Over the past two decades, the poultry sector in China went through a phase of tremendous growth as well as rapid intensification and concentration. Highly pathogenic avian influenza virus (HPAIV) subtype H5N1 was first detected in 1996 in Guangdong province, South China and started spreading throughout Asia in early 2004. Since then, control of the disease in China has relied heavily on wide-scale preventive vaccination combined with movement control, quarantine and stamping out. This strategy has been successful in drastically reducing the number of outbreaks during the past 5years. However, HPAIV H5N1 is still circulating and is regularly isolated in traditional live bird markets (LBMs) where viral infection can persist, which represent a public health hazard for people visiting them. The use of social network analysis in combination with epidemiological surveillance in South China has identified areas where the success of current strategies for HPAI control in the poultry production sector may benefit from better knowledge of poultry trading patterns and the LBM network configuration as well as their capacity for maintaining HPAIV H5N1 infection. We produced a set of LBM network maps and estimated the associated risk of HPAIV H5N1 within LBMs and along poultry market chains, providing new insights into how live poultry trade and infection are intertwined. More specifically, our study provides evidence that several biosecurity factors such as daily cage cleaning, daily cage disinfection or manure processing contribute to a reduction in HPAIV H5N1 presence in LBMs. Of significant importance is that the results of our study also show the association between social network indicators and the presence of HPAIV H5N1 in specific network configurations such as the one represented by the counties of origin of the birds traded in LBMs. This new information could be used to develop more targeted and effective control interventions.

The role of vaccine coverage within social networks in cholera vaccine efficacy

Background

Traditional vaccine trial methods have an underlying assumption that the effect of a vaccine is the same throughout the trial area. There are, however, many spatial and behavioral factors that alter the rates of contact among infectious and susceptible individuals and result in different efficacies across a population. We reanalyzed data from a field trial in Bangladesh to ascertain whether there is evidence of indirect protection from cholera vaccines when vaccination rates are high in an individual's social network.

Methods

We analyzed the first year of surveillance data from a placebo-controlled trial of B subunit-killed whole-cell and killed whole-cell-only oral cholera vaccines in children and adult women in Bangladesh. We calculated whether there was an inverse trend for the relation between the level of vaccine coverage in an individual's social network and the incidence of cholera in individual vaccine recipients or placebo recipients after controlling for potential confounding variables.

Results

Using bari-level social network ties, we found incidence rates of cholera among placebo recipients were inversely related to levels of vaccine coverage (5.28 cases per 1000 in the lowest quintile vs 3.27 cases per 1000 in the highest quintile; p = 0.037 for trend). Receipt of vaccine by an individual and the level of vaccine coverage of the individual's social network were independently related to a reduced risk of cholera.

Conclusions

Findings indicate that progressively higher levels of vaccine coverage in bari-level social networks can lead to increasing levels of indirect protection of non-vaccinated individuals and could also lead to progressively higher levels of total protection of vaccine recipients.

Equal graph partitioning on estimated infection network as an effective epidemic mitigation measure

Controlling severe outbreaks remains the most important problem in infectious disease area. With time, this problem will only become more severe as population density in urban centers grows. Social interactions play a very important role in determining how infectious diseases spread, and organization of people along social lines gives rise to non-spatial networks in which the infections spread. Infection networks are different for diseases with different transmission modes, but are likely to be identical or highly similar for diseases that spread the same way. Hence, infection networks estimated from common infections can be useful to contain epidemics of a more severe disease with the same transmission mode. Here we present a proof-of-concept study demonstrating the effectiveness of epidemic mitigation based on such estimated infection networks. We first generate artificial social networks of different sizes and average degrees, but with roughly the same clustering characteristic. We then start SIR epidemics on these networks, censor the simulated incidences, and use them to reconstruct the infection network. We then efficiently fragment the estimated network by removing the smallest number of nodes identified by a graph partitioning algorithm. Finally, we demonstrate the effectiveness of this targeted strategy, by comparing it against traditional untargeted strategies, in slowing down and reducing the size of advancing epidemics.

Data-model fusion to better understand emerging pathogens and improve infectious disease forecasting

Ecologists worldwide are challenged to contribute solutions to urgent and pressing environmental problems by forecasting how populations, communities, and ecosystems will respond to global change. Rising to this challenge requires organizing ecological information derived from diverse sources and formally assimilating data with models of ecological processes. The study of infectious disease has depended on strategies for integrating patterns of observed disease incidence with mechanistic process models since John Snow first mapped cholera cases around a London water pump in 1854. Still, zoonotic and vector-borne diseases increasingly affect human populations, and methods used to successfully characterize directly transmitted diseases are often insufficient. We use four case studies to demonstrate that advances in disease forecasting require better understanding of zoonotic host and vector populations, as well of the dynamics that facilitate pathogen amplification and disease spillover into humans. In each case study, this goal is complicated by limited data, spatiotemporal variability in pathogen transmission and impact, and often, insufficient biological understanding. We present a conceptual framework for data-model fusion in infectious disease research that addresses these fundamental challenges using a hierarchical state-space structure to (1) integrate multiple data sources and spatial scales to inform latent parameters, (2) partition uncertainty in process and observation models, and (3) explicitly build upon existing ecological and epidemiological understanding. Given the constraints inherent in the study of infectious disease and the urgent need for progress, fusion of data and expertise via this type of conceptual framework should prove an indispensable tool.

Disease transmission in territorial populations: the small-world network of Serengeti lions

Territoriality in animal populations creates spatial structure that is thought to naturally buffer disease invasion. Often, however, territorial populations also include highly mobile, non-residential individuals that potentially serve as disease superspreaders. Using long-term data from the Serengeti Lion Project, we characterize the contact network structure of a territorial wildlife population and address the epidemiological impact of nomadic individuals. As expected, pride contacts are dominated by interactions with neighbouring prides and interspersed by encounters with nomads as they wander throughout the ecosystem. Yet the pride-pride network also includes occasional long-range contacts between prides, making it surprisingly small world and vulnerable to epidemics, even without nomads. While nomads increase both the local and global connectivity of the network, their epidemiological impact is marginal, particularly for diseases with short infectious periods like canine distemper virus. Thus, territoriality in Serengeti lions may be less protective and non-residents less important for disease transmission than previously considered.

Using network properties to predict disease dynamics on human contact networks

Recent studies have increasingly turned to graph theory to model more realistic contact structures that characterize disease spread. Because of the computational demands of these methods, many researchers have sought to use measures of network structure to modify analytically tractable differential equation models. Several of these studies have focused on the degree distribution of the contact network as the basis for their modifications. We show that although degree distribution is sufficient to predict disease behaviour on very sparse or very dense human contact networks, for intermediate density networks we must include information on clustering and path length to accurately predict disease behaviour. Using these three metrics, we were able to explain more than 98 per cent of the variation in endemic disease levels in our stochastic simulations.