Networks and the epidemiology of infectious disease

Tight lower bound for percolation threshold on an infinite graph

We construct a tight lower bound for the site percolation threshold on an infinite graph, which becomes exact for an infinite tree. The bound is given by the inverse of the maximal eigenvalue of the Hashimoto matrix used to count nonbacktracking walks on the original graph. Our bound always exceeds the inverse spectral radius of the graph's adjacency matrix, and it is also generally tighter than the existing bound in terms of the maximum degree. We give a constructive proof for existence of such an eigenvalue in the case of a connected infinite quasitransitive graph, a graph-theoretic analog of a translationally invariant system.

Epidemic control analysis: designing targeted intervention strategies against epidemics propagated on contact networks

In cases where there are limited resources for the eradication of an epidemic, or where we seek to minimise possible adverse impacts of interventions, it is essential to optimise the efficacy of control measures. We introduce a new approach, Epidemic Control Analysis (ECA), to design effective targeted intervention strategies to mitigate and control the propagation of infections across heterogeneous contact networks. We exemplify this methodology in the context of a newly developed individual-level deterministic Susceptible-Infectious-Susceptible (SIS) epidemiological model (we also briefly consider applications to Susceptible-Infectious-Removed (SIR) dynamics). This provides a flexible way to systematically determine the impact of interventions on endemic infections in the population. Individuals are ranked based on their influence on the level of infectivity. The highest-ranked individuals are prioritised for targeted intervention. Many previous intervention strategies have determined prioritisation based mainly on the position of individuals in the network, described by various local and global network centrality measures, and their chance of being infectious. Comparisons of the predictions of the proposed strategy with those of widely used targeted intervention programmes on various model and real-world networks reveal its efficiency and accuracy. It is demonstrated that targeting central individuals or individuals that have high infection probability is not always the best strategy. The importance of individuals is not determined by network structure alone, but can be highly dependent on the infection dynamics. This interplay between network structure and infection dynamics is effectively captured by ECA.

The pits and falls of graphical presentation

Graphics are powerful tools to communicate research results and to gain information from data. However, researchers should be careful when deciding which data to plot and the type of graphic to use, as well as other details. The consequence of bad decisions in these features varies from making research results unclear to distortions of these results, through the creation of “chartjunk” with useless information. This paper is not another tutorial about “good graphics” and “bad graphics”. Instead, it presents guidelines for graphic presentation of research results and some uncommon, but useful examples to communicate basic and complex data types, especially multivariate model results, which are commonly presented only by tables. By the end, there are no answers here, just ideas meant to inspire others on how to create their own graphics.

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

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

Eight challenges for network epidemic models

Networks offer a fertile framework for studying the spread of infection in human and animal populations. However, owing to the inherent high-dimensionality of networks themselves, modelling transmission through networks is mathematically and computationally challenging. Even the simplest network epidemic models present unanswered questions. Attempts to improve the practical usefulness of network models by including realistic features of contact networks and of host-pathogen biology (e.g. waning immunity) have made some progress, but robust analytical results remain scarce. A more general theory is needed to understand the impact of network structure on the dynamics and control of infection. Here we identify a set of challenges that provide scope for active research in the field of network epidemic models.

The effect of clumped population structure on the variability of spreading dynamics

Processes that spread through local contact, including outbreaks of infectious diseases, are inherently noisy, and are frequently observed to be far noisier than predicted by standard stochastic models that assume homogeneous mixing. One way to reproduce the observed levels of noise is to introduce significant individual-level heterogeneity with respect to infection processes, such that some individuals are expected to generate more secondary cases than others. Here we consider a population where individuals can be naturally aggregated into clumps (subpopulations) with stronger interaction within clumps than between them. This clumped structure induces significant increases in the noisiness of a spreading process, such as the transmission of infection, despite complete homogeneity at the individual level. Given the ubiquity of such clumped aggregations (such as homes, schools and workplaces for humans or farms for livestock) we suggest this as a plausible explanation for noisiness of many epidemic time series.

Network epidemiology and plant trade networks

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

The risk of disease to great apes: simulating disease spread in orang-utan (Pongo pygmaeus wurmbii) and chimpanzee (Pan troglodytes schweinfurthii) association networks

All great ape species are endangered, and infectious diseases are thought to pose a particular threat to their survival. As great ape species vary substantially in social organisation and gregariousness, there are likely to be differences in susceptibility to disease types and spread. Understanding the relation between social variables and disease is therefore crucial for implementing effective conservation measures. Here, we simulate the transmission of a range of diseases in a population of orang-utans in Sabangau Forest (Central Kalimantan) and a community of chimpanzees in Budongo Forest (Uganda), by systematically varying transmission likelihood and probability of subsequent recovery. Both species have fission-fusion social systems, but differ considerably in their level of gregariousness. We used long-term behavioural data to create networks of association patterns on which the spread of different diseases was simulated. We found that chimpanzees were generally far more susceptible to the spread of diseases than orang-utans. When simulating different diseases that varied widely in their probability of transmission and recovery, it was found that the chimpanzee community was widely and strongly affected, while in orang-utans even highly infectious diseases had limited spread. Furthermore, when comparing the observed association network with a mean-field network (equal contact probability between group members), we found no major difference in simulated disease spread, suggesting that patterns of social bonding in orang-utans are not an important determinant of susceptibility to disease. In chimpanzees, the predicted size of the epidemic was smaller on the actual association network than on the mean-field network, indicating that patterns of social bonding have important effects on susceptibility to disease. We conclude that social networks are a potentially powerful tool to model the risk of disease transmission in great apes, and that chimpanzees are particularly threatened by infectious disease outbreaks as a result of their social structure.

Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks

The message passing approach of Karrer and Newman [Phys. Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered dynamics on finite trees. Here we show that, assuming Poisson contact processes, a pair-based moment-closure representation [Sharkey, J. Math. Biol. 57, 311 (2008)] can be derived from their equations. We extend the applicability of both representations and discuss their relative merits. On arbitrary time-independent networks, as was shown for the message passing formalism, the pair-based moment-closure equations also provide a rigorous lower bound on the expected number of susceptibles at all times.

Tracking socioeconomic vulnerability using network analysis: insights from an avian influenza outbreak in an ostrich production network

BACKGROUND

The focus of management in many complex systems is shifting towards facilitation, adaptation, building resilience, and reducing vulnerability. Resilience management requires the development and application of general heuristics and methods for tracking changes in both resilience and vulnerability. We explored the emergence of vulnerability in the South African domestic ostrich industry, an animal production system which typically involves 3-4 movements of each bird during its lifetime. This system has experienced several disease outbreaks, and the aim of this study was to investigate whether these movements have contributed to the vulnerability of this system to large disease outbreaks.

METHODOLOGY/PRINCIPAL FINDINGS

The ostrich production system requires numerous movements of birds between different farm types associated with growth (i.e. Hatchery to juvenile rearing farm to adult rearing farm). We used 5 years of movement records between 2005 and 2011 prior to an outbreak of Highly Pathogenic Avian Influenza (H5N2). These data were analyzed using a network analysis in which the farms were represented as nodes and the movements of birds as links. We tested the hypothesis that increasing economic efficiency in the domestic ostrich industry in South Africa made the system more vulnerable to outbreak of Highly Pathogenic Avian Influenza (H5N2). Our results indicated that as time progressed, the network became increasingly vulnerable to pathogen outbreaks. The farms that became infected during the outbreak displayed network qualities, such as significantly higher connectivity and centrality, which predisposed them to be more vulnerable to disease outbreak.

CONCLUSIONS/SIGNIFICANCE

Taken in the context of previous research, our results provide strong support for the application of network analysis to track vulnerability, while also providing useful practical implications for system monitoring and management.

An integrated web system to support veterinary activities in Italy for the management of information in epidemic emergencies

The management of public health emergencies is improved by quick, exhaustive and standardized flow of data on disease outbreaks, by using specific tools for data collection, registration and analysis. In this context, the National Information System for the Notification of Outbreaks of Animal Diseases (SIMAN) has been developed in Italy to collect and share data on the notifications of outbreaks of animal diseases. SIMAN is connected through web services to the national database of animals and holdings (BDN) and has been integrated with tools for the management of epidemic emergencies. The website has been updated with a section dedicated to the contingency planning in case of epidemic emergency. EpiTrace is one such useful tool also integrated in the BDN and based on the Social Network Analysis (SNA) and on network epidemiological models. This tool gives the possibility of assessing the risk associated to holdings and animals on the basis of their trade, in order to support the veterinary services in tracing back and forward the animals in case of outbreaks of infectious diseases.

Dynamics of infectious diseases

Modern infectious disease epidemiology has a strong history of using mathematics both for prediction and to gain a deeper understanding. However the study of infectious diseases is a highly interdisciplinary subject requiring insights from multiple disciplines, in particular a biological knowledge of the pathogen, a statistical description of the available data and a mathematical framework for prediction. Here we begin with the basic building blocks of infectious disease epidemiology--the SIS and SIR type models--before considering the progress that has been made over the recent decades and the challenges that lie ahead. Throughout we focus on the understanding that can be developed from relatively simple models, although accurate prediction will inevitably require far greater complexity beyond the scope of this review. In particular, we focus on three critical aspects of infectious disease models that we feel fundamentally shape their dynamics: heterogeneously structured populations, stochasticity and spatial structure. Throughout we relate the mathematical models and their results to a variety of real-world problems.

Extinction times of epidemic outbreaks in networks

In the Susceptible-Infectious-Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the population. Infections that are not contagious enough die out before they spread to a large fraction of people. We characterize how the maximal extinction time in SIR simulations on networks depend on the network structure. For example we find that the average distances in isolated components, weighted by the component size, is a good predictor of the maximal time to extinction. Furthermore, the transmission probability giving the longest outbreaks is larger than, but otherwise seemingly independent of, the epidemic threshold.

Spreading dynamics on complex networks: a general stochastic approach

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible and susceptible-infectious-removed dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.

Efficient local behavioral-change strategies to reduce the spread of epidemics in networks

It has recently become established that the spread of infectious diseases between humans is affected not only by the pathogen itself but also by changes in behavior as the population becomes aware of the epidemic, for example, social distancing. It is also well known that community structure (the existence of relatively densely connected groups of vertices) in contact networks influences the spread of disease. We propose a set of local strategies for social distancing, based on community structure, that can be employed in the event of an epidemic to reduce the epidemic size. Unlike most social distancing methods, ours do not require individuals to know the disease state (infected or susceptible, etc.) of others, and we do not make the unrealistic assumption that the structure of the entire contact network is known. Instead, the recommended behavior change is based only on an individual's local view of the network. Each individual avoids contact with a fraction of his/her contacts, using knowledge of his/her local network to decide which contacts should be avoided. If the behavior change occurs only when an individual becomes ill or aware of the disease, these strategies can substantially reduce epidemic size with a relatively small cost, measured by the number of contacts avoided.

Endemic infections are always possible on regular networks

We study the dependence of the largest component in regular networks on the clustering coefficient, showing that its size changes smoothly without undergoing a phase transition. We explain this behavior via an analytical approach based on the network structure, and provide an exact equation describing the numerical results. Our work indicates that intrinsic structural properties always allow the spread of epidemics on regular networks.

Social encounter networks: characterizing Great Britain

A major goal of infectious disease epidemiology is to understand and predict the spread of infections within human populations, with the intention of better informing decisions regarding control and intervention. However, the development of fully mechanistic models of transmission requires a quantitative understanding of social interactions and collective properties of social networks. We performed a cross-sectional study of the social contacts on given days for more than 5000 respondents in England, Scotland and Wales, through postal and online survey methods. The survey was designed to elicit detailed and previously unreported measures of the immediate social network of participants relevant to infection spread. Here, we describe individual-level contact patterns, focusing on the range of heterogeneity observed and discuss the correlations between contact patterns and other socio-demographic factors. We find that the distribution of the number of contacts approximates a power-law distribution, but postulate that total contact time (which has a shorter-tailed distribution) is more epidemiologically relevant. We observe that children, public-sector and healthcare workers have the highest number of total contact hours and are therefore most likely to catch and transmit infectious disease. Our study also quantifies the transitive connections made between an individual's contacts (or clustering); this is a key structural characteristic of social networks with important implications for disease transmission and control efficacy. Respondents' networks exhibit high levels of clustering, which varies across social settings and increases with duration, frequency of contact and distance from home. Finally, we discuss the implications of these findings for the transmission and control of pathogens spread through close contact.

Dynamics of stochastic epidemics on heterogeneous networks

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

Unfolding accessibility provides a macroscopic approach to temporal networks

An accessibility graph of a network contains a link wherever there is a path of arbitrary length between two nodes. We generalize the concept of accessibility to temporal networks. Building an accessibility graph by consecutively adding paths of growing length (unfolding), we obtain information about the distribution of shortest path durations and characteristic time scales in temporal networks. Moreover, we define causal fidelity to measure the goodness of their static representation. The practicability of our proposed methods is demonstrated for three examples: networks of social contacts, livestock trade, and sexual contacts.

Host nutrition alters the variance in parasite transmission potential

The environmental conditions experienced by hosts are known to affect their mean parasite transmission potential. How different conditions may affect the variance of transmission potential has received less attention, but is an important question for disease management, especially if specific ecological contexts are more likely to foster a few extremely infectious hosts. Using the obligate-killing bacterium Pasteuria ramosa and its crustacean host Daphnia magna, we analysed how host nutrition affected the variance of individual parasite loads, and, therefore, transmission potential. Under low food, individual parasite loads showed similar mean and variance, following a Poisson distribution. By contrast, among well-nourished hosts, parasite loads were right-skewed and overdispersed, following a negative binomial distribution. Abundant food may, therefore, yield individuals causing potentially more transmission than the population average. Measuring both the mean and variance of individual parasite loads in controlled experimental infections may offer a useful way of revealing risk factors for potential highly infectious hosts.

How big is an outbreak likely to be? Methods for epidemic final-size calculation

Epidemic models have become a routinely used tool to inform policy on infectious disease. A particular interest at the moment is the use of computationally intensive inference to parametrize these models. In this context, numerical efficiency is critically important. We consider methods for evaluating the probability mass function of the total number of infections over the course of a stochastic epidemic, with a focus on homogeneous finite populations, but also considering heterogeneous and large populations. Relevant methods are reviewed critically, with existing and novel extensions also presented. We provide code in M atlab and a systematic comparison of numerical efficiency.

On the robustness of in- and out-components in a temporal network

BACKGROUND

Many networks exhibit time-dependent topologies, where an edge only exists during a certain period of time. The first measurements of such networks are very recent so that a profound theoretical understanding is still lacking. In this work, we focus on the propagation properties of infectious diseases in time-dependent networks. In particular, we analyze a dataset containing livestock trade movements. The corresponding networks are known to be a major route for the spread of animal diseases. In this context chronology is crucial. A disease can only spread if the temporal sequence of trade contacts forms a chain of causality. Therefore, the identification of relevant nodes under time-varying network topologies is of great interest for the implementation of counteractions.

METHODOLOGY/FINDINGS

We find that a time-aggregated approach might fail to identify epidemiologically relevant nodes. Hence, we explore the adaptability of the concept of centrality of nodes to temporal networks using a data-driven approach on the example of animal trade. We utilize the size of the in- and out-component of nodes as centrality measures. Both measures are refined to gain full awareness of the time-dependent topology and finite infectious periods. We show that the size of the components exhibit strong temporal heterogeneities. In particular, we find that the size of the components is overestimated in time-aggregated networks. For disease control, however, a risk assessment independent of time and specific disease properties is usually favored. We therefore explore the disease parameter range, in which a time-independent identification of central nodes remains possible.

CONCLUSIONS

We find a ranking of nodes according to their component sizes reasonably stable for a wide range of infectious periods. Samples based on this ranking are robust enough against varying disease parameters and hence are promising tools for disease control.

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

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

Social encounter networks: collective properties and disease transmission

A fundamental challenge of modern infectious disease epidemiology is to quantify the networks of social and physical contacts through which transmission can occur. Understanding the collective properties of these interactions is critical for both accurate prediction of the spread of infection and determining optimal control measures. However, even the basic properties of such networks are poorly quantified, forcing predictions to be made based on strong assumptions concerning network structure. Here, we report on the results of a large-scale survey of social encounters mainly conducted in Great Britain. First, we characterize the distribution of contacts, which possesses a lognormal body and a power-law tail with an exponent of −2.45; we provide a plausible mechanistic model that captures this form. Analysis of the high level of local clustering of contacts reveals additional structure within the network, implying that social contacts are degree assortative. Finally, we describe the epidemiological implications of this local network structure: these contradict the usual predictions from networks with heavy-tailed degree distributions and contain public-health messages about control. Our findings help us to determine the types of realistic network structure that should be assumed in future population level studies of infection transmission, leading to better interpretations of epidemiological data and more appropriate policy decisions.

An analytical approach to network motif detection in samples of networks with pairwise different vertex labels

Network motifs, overrepresented small local connection patterns, are assumed to act as functional meaningful building blocks of a network and, therefore, received considerable attention for being useful for understanding design principles and functioning of networks. We present an extension of the original approach to network motif detection in single, directed networks without vertex labeling to the case of a sample of directed networks with pairwise different vertex labels. A characteristic feature of this approach to network motif detection is that subnetwork counts are derived from the whole sample and the statistical tests are adjusted accordingly to assign significance to the counts. The associated computations are efficient since no simulations of random networks are involved. The motifs obtained by this approach also comprise the vertex labeling and its associated information and are characteristic of the sample. Finally, we apply this approach to describe the intricate topology of a sample of vertex-labeled networks which originate from a previous EEG study, where the processing of painful intracutaneous electrical stimuli and directed interactions within the neuromatrix of pain in patients with major depression and healthy controls was investigated. We demonstrate that the presented approach yields characteristic patterns of directed interactions while preserving their important topological information and omitting less relevant interactions.

New moment closures based on a priori distributions with applications to epidemic dynamics

Recently, research that focuses on the rigorous understanding of the relation between simulation and/or exact models on graphs and approximate counterparts has gained lots of momentum. This includes revisiting the performance of classic pairwise models with closures at the level of pairs and/or triples as well as effective-degree-type models and those based on the probability generating function formalism. In this paper, for a fully connected graph and the simple SIS (susceptible-infected-susceptible) epidemic model, a novel closure is introduced. This is done via using the equations for the moments of the distribution describing the number of infecteds at all times combined with the empirical observations that this is well described/approximated by a binomial distribution with time dependent parameters. This assumption allows us to express higher order moments in terms of lower order ones and this leads to a new closure. The significant feature of the new closure is that the difference of the exact system, given by the Kolmogorov equations, from the solution of the newly defined approximate system is of order 1/N(2). This is in contrast with the O(1/N) difference corresponding to the approximate system obtained via the classic triple closure. The fully connected nature of the graph also allows us to interpret pairwise equations in terms of the moments and thus treat closures and the two approximate models within the same framework. Finally, the applicability and limitations of the new methodology is discussed in detail.

Propagation on networks: an exact alternative perspective

By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of dynamical variables of this birth-death Markov process greatly simplifies analytical calculations. We show how a dual analytical description, treating large scale epidemics with a Gaussian approximation and small outbreaks with a branching process, provides an accurate approximation of the distribution even for rather small networks. The approach also offers important computational advantages and generalizes to a vast class of systems.

Research agenda for mass gatherings: a call to action

Public health research is essential for the development of effective policies and planning to address health security and risks associated with mass gatherings (MGs). Crucial research topics related to MGs and their effects on global health security are discussed in this review. The research agenda for MGs consists of a framework of five major public health research directions that address issues related to reducing the risk of public health emergencies during MGs; restricting the occurrence of non-communicable and communicable diseases; minimisation of the effect of public health events associated with MGs; optimisation of the medical services and treatment of diseases during MGs; and development and application of modern public health measures. Implementation of the proposed research topics would be expected to provide benefits over the medium to long term in planning for MGs.

Impact of regulatory perturbations to disease spread through cattle movements in Great Britain

During the past decade the British livestock industry has suffered from several major pathogen outbreaks, and a variety of regulatory and disease control measures have been applied to the movement of livestock with the express aim of mitigating the spread of infection. The Rapid Analysis and Detection of Animal-related Risks (RADAR) project, which has been collecting data on the movement of cattle since 1998, provides a relatively comprehensive record of how these policies have influenced the movement of cattle between animal holdings, markets, and slaughterhouses in Britain. Many previous studies have focused on the properties of the network that can be derived from these movements – treating farms as nodes and movements as directed (and potentially weighted) edges in the network. However, of far greater importance is how these policy changes have influenced the potential spread of infectious diseases. Here we use a stochastic fully individual-based model of cattle in Britain to assess how the epidemic potential has varied from 2000 to 2009 as the pattern of movements has changed in response to legislation and market forces. Our simulations show that the majority of policy changes lead to significant decreases in the epidemic potential (measured in multiple ways), but that this potential then increases through time as cattle farmers modify their behaviour in response. Our results suggest that the cattle industry is likely to experience boom-bust dynamics, with the actions that farmers take during epidemic-free periods to maximise their profitability likely to increase the potential for large-scale epidemics to occur.

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.