Epidemic prediction and control in clustered populations

There has been much recent interest in modelling epidemics on networks, particularly in the presence of substantial clustering. Here, we develop pairwise methods to answer questions that are often addressed using epidemic models, in particular: on the basis of potential observations early in an outbreak, what can be predicted about the epidemic outcomes and the levels of intervention necessary to control the epidemic? We find that while some results are independent of the level of clustering (early growth predicts the level of ‘leaky’ vaccine needed for control and peak time, while the basic reproductive ratio predicts the random vaccination threshold) the relationship between other quantities is very sensitive to clustering

Household structure and infectious disease transmission

One of the central tenets of modern infectious disease epidemiology is that an understanding of heterogeneities, both in host demography and transmission, allows control to be efficiently optimized. Due to the strong interactions present, households are one of the most important heterogeneities to consider, both in terms of predicting epidemic severity and as a target for intervention. We consider these effects in the context of pandemic influenza in Great Britain, and find that there is significant local (ward-level) variation in the basic reproductive ratio, with some regions predicted to suffer 50% faster growth rate of infection than the mean. Childhood vaccination was shown to be highly effective at controlling an epidemic, generally outperforming random vaccination and substantially reducing the variation between regions; only nine out of over 10 000 wards did not obey this rule and these can be identified as demographically atypical regions. Since these benefits of childhood vaccination are a product of correlations between household size and number of dependent children in the household, our results are qualitatively robust for a variety of disease scenarios

Insights from unifying modern approximations to infections on networks

Networks are increasingly central to modern science owing to their ability to conceptualize multiple interacting components of a complex system. As a specific example of this, understanding the implications of contact network structure for the transmission of infectious diseases remains a key issue in epidemiology. Three broad approaches to this problem exist: explicit simulation; derivation of exact results for special networks; and dynamical approximations. This paper focuses on the last of these approaches, and makes two main contributions. Firstly, formal mathematical links are demonstrated between several prima facie unrelated dynamical approximations. And secondly, these links are used to derive two novel dynamical models for network epidemiology, which are compared against explicit stochastic simulation. The success of these new models provides improved understanding about the interaction of network structure and transmission dynamics

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

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

From Markovian to pairwise epidemic models and the performance of moment closure approximations

Many if not all models of disease transmission on networks can be linked to the exact state-based Markovian formulation. However the large number of equations for any system of realistic size limits their applicability to small populations. As a result, most modelling work relies on simulation and pairwise models. In this paper, for a simple SIS dynamics on an arbitrary network, we formalise the link between a well known pairwise model and the exact Markovian formulation. This involves the rigorous derivation of the exact ODE model at the level of pairs in terms of the expected number of pairs and triples. The exact system is then closed using two different closures, one well established and one that has been recently proposed. A new interpretation of both closures is presented, which explains several of their previously observed properties. The closed dynamical systems are solved numerically and the results are compared to output from individual-based stochastic simulations. This is done for a range of networks with the same average degree and clustering coefficient but generated using different algorithms. It is shown that the ability of the pairwise system to accurately model an epidemic is fundamentally dependent on the underlying large-scale network structure. We show that the existing pairwise models are a good fit for certain types of network but have to be used with caution as higher-order network structures may compromise their effectiveness

Spreading of healthy mood in adolescent social networks

Depression is a major public health concern worldwide. There is evidence that social support and befriending influence mental health, and an improved understanding of the social processes that drive depression has the potential to bring significant public health benefits. We investigate transmission of mood on a social network of adolescents, allowing flexibility in our model by making no prior assumption as to whether it is low mood or healthy mood that spreads. Here, we show that while depression does not spread, healthy mood among friends is associated with significantly reduced risk of developing and increased chance of recovering from depression. We found that this spreading of healthy mood can be captured using a non-linear complex contagion model. Having sufficient friends with healthy mood can halve the probability of developing, or double the probability of recovering from, depression over a 6–12-month period on an adolescent social network. Our results suggest that promotion of friendship between adolescents can reduce both incidence and prevalence of depression

Information content of household-stratified epidemics

Household structure is a key driver of many infectious diseases, as well as a natural target for interventions such as vaccination programs. Many theoretical and conceptual advances on household-stratified epidemic models are relatively recent, but have successfully managed to increase the applicability of such models to practical problems. To be of maximum realism and hence benefit, they require parameterisation from epidemiological data, and while household-stratified final size data has been the traditional source, increasingly time-series infection data from households are becoming available. This paper is concerned with the design of studies aimed at collecting time-series epidemic data in order to maximize the amount of information available to calibrate household models. A design decision involves a trade-off between the number of households to enrol and the sampling frequency. Two commonly used epidemiological study designs are considered: cross-sectional, where different households are sampled at every time point, and cohort, where the same households are followed over the course of the study period. The search for an optimal design uses Bayesian computationally intensive methods to explore the joint parameter-design space combined with the Shannon entropy of the posteriors to estimate the amount of information in each design. For the cross-sectional design, the amount of information increases with the sampling intensity, i.e., the designs with the highest number of time points have the most information. On the other hand, the cohort design often exhibits a trade-off between the number of households sampled and the intensity of follow-up. Our results broadly support the choices made in existing epidemiological data collection studies. Prospective problem-specific use of our computational methods can bring significant benefits in guiding future study designs

Networks and the epidemiology of infectious disease

The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues

Reflections on the implementation of the Gifted and Talented policy in England, 1999–2011

This paper, as part of an on-going study looking at the impact of gifted and talented policies on an inner-city school, explores the role of the local authority in implementing the various gifted and talented initiatives since 1999, when local authority gifted and talented co-ordinators were first appointed under the Excellence in Cities (DfEE, 1999) programme