Representing the UK's cattle herd as static and dynamic networks

Network models are increasingly being used to understand the spread of diseases through sparsely connected populations, with particular interest in the impact of animal movements upon the dynamics of infectious diseases. Detailed data collected by the UK government on the movement of cattle may be represented as a network, where animal holdings are nodes, and an edge is drawn between nodes where a movement of animals has occurred. These network representations may vary from a simple static representation, to a more complex, fully dynamic one where daily movements are explicitly captured. Using stochastic disease simulations, a wide range of network representations of the UK cattle herd are compared. We find that the simpler static network representations are often deficient when compared with a fully dynamic representation, and should therefore be used only with caution in epidemiological modelling. In particular, due to temporal structures within the dynamic network, static networks consistently fail to capture the predicted epidemic behaviour associated with dynamic networks even when parameterized to match early growth rates

Targeting vaccination against novel infections : risk, age and spatial structure for pandemic influenza in Great Britain

The emergence of a novel strain of H1N1 influenza virus in Mexico in 2009, and its subsequent worldwide spread, has focused attention to the question of optimal deployment of mass vaccination campaigns. Here, we use three relatively simple models to address three issues of primary concern in the targeting of any vaccine. The advantages of such simple models are that the underlying assumptions and effects of individual parameters are relatively clear, and the impact of uncertainty in the parametrization can be readily assessed in the early stages of an outbreak. In particular, we examine whether targeting risk-groups, age-groups or spatial regions could be optimal in terms of reducing the predicted number of cases or severe effects; and how these targeted strategies vary as the epidemic progresses. We examine the conditions under which it is optimal to initially target vaccination towards those individuals within the population who are most at risk of severe effects of infection. Using age-structured mixing matrices, we show that targeting vaccination towards the more epidemiologically important age groups (5-14 year olds and then 15-24 year olds) leads to the greatest reduction in the epidemic growth and hence reduces the total number of cases. Finally, we consider how spatially targeting the vaccine towards regions of country worst affected could provide an advantage. We discuss how all three of these priorities change as both the speed at which vaccination can be deployed and the start of the vaccination programme is varied

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

Human African trypanosomiasis : current status and eradication efforts

Epidemics of human African trypanosomiasis (HAT) in the 20th century led to millions of deaths. However, since the start of the twenty-first century, there is been a continued decline in the number of reported cases, due to increased investment and prioritisation of control efforts. Systematic screening of at-risk areas and widespread access to increasingly advanced diagnostics and treatments, along with much improved vector control, have all helped to make disease elimination achievable in the near future. Despite the progress, the danger of disease resurgence is well-known for HAT and continued surveillance and treatment availability is essential. Additionally, many uncertainties regarding HAT transmission remain and combine to make potential disease eradication a complete unknown

The ecology and evolution of spatial host-parasite systems

All ecological and epidemiological systems are embedded in space and composed of individuals; these facts often have a profound effect on the dynamics and means many tools and definitions require reformulation. Modelling has always been about taking highly complex dynamical systems, such as the natural environment, and attempting to simplify them to a leve that can be conceptualised, in the process losing all the features that are not understood or not anticipated. The individual based spatial models which form the basis of this work start from the simple rules for individuals and build up to a complex system, allowing new, unexpected phenomenon to arise naturally. The local interactions in spatial models lead to short scale correlations and self-induced spatial heterogeneity as the small fluctuations of environmental noise are amplified into macro-scale patterns. These spatial patterns can lead to ephemeral refuges for hosts from where they can disperse stabilising the dynamics. After discussing the importance and variety of host-parasite interactions several techniques to be used in this work are developed and explained on simple examples. Chapters III and IV introduce a caricature host-pathogen model and how how this deviates from the standard mean field theory approximations. Attention is then turned to host-parasitoid systems and the spatially extended Nicholson-Bailey equations; probems with this coupled map lattice are highlighted and an alternative artificial ecology is formulated. Remaining with the Nicholson-Bailey equations these are forced to be integer based by utilising stochastic events, this greatly stabilises the dynamics hence the method was applied to the persistence of measles epidemics in small populations (=500000). Chapter VII demonstrates how the inclusion of space enhances the effects of parasitism in increasing the evolutionary advantage of sexual hosts over asexual ones. Finally general techniques are developed to implicitly model the effects of spatial correlations and stochastic individual based interactions

Concurrency of partnerships, consistency with data, and control of sexually transmitted infections

Sexually transmitted infections (STIs) are a globally increasing public health problem. Mathematical models, carefully matched to available epidemiological and behavioural data, have an important role to play in predicting the action of control measures. Here, we explore the effect of concurrent sexual partnerships on the control of a generic STI with susceptible-infected-susceptible dynamics. Concurrency refers to being in more than one sexual partnership at the same time, and is difficult to measure accurately. We assess the impact of concurrency through the development of three nested pair-formation models: one where infection can only be transmitted via stable sexual partnerships, one where infection can also be transmitted via casual partnerships between single individuals, and one where those individuals in stable partnerships can also acquire infection from casual partnerships. For each model, we include the action of vaccination before sexual debut to inform about the ability to control. As expected, for a fixed transmission rate, concurrency increases both the endemic prevalence of infection and critical level of vaccination required to eliminate the disease significantly. However, when the transmission rate is scaled to maintain a fixed endemic prevalence across models, concurrency has a far smaller impact upon the critical level of vaccination required. Further, when we also constrain the models to have a fixed number of new partnerships over time (both long-term and casual), then increasing concurrency can slightly decrease the critical level of vaccination. These results highlight that accurate measures and models of concurrency may not always be needed for reliable forecasts when models are closely matched to prevalence data. We find that, while increases in concurrency within a population are likely to generate public-health problems, the inclusion of concurrency may be unnecessary when constructing models to determine the efficacy of the control of STIs by vaccination

Incorporating household structure and demography into models of endemic disease

The spread of infectious diseases is intimately linked with the strength and type of contact between individuals. Multiple observational and modelling studies have highlighted the importance of two forms of social mixing: age structure, where the likelihood of interaction between two individuals is determined by their ages; and household structure, which recognizes the much stronger contacts and hence transmission potential within the family setting. Age structure has been ubiquitous in predictive models of both endemic and epidemic infections, in part due to the ease of assessing someone’s age. By contrast, although household structure is potentially the dominant heterogeneity, it has received less attention, in part due to an absence of the necessary methodology. Here, we develop the modelling framework necessary to predict the behaviour of endemic infections (which necessitates capturing demographic processes) in populations that possess both household and age structure. We compare two childhood infections, with measles-like and mumps-like parameters, and two populations with UK-like and Kenya-like characteristics, which allows us to disentangle the impact of epidemiology and demography. For this high-dimensional model, we predict complex nonlinear dynamics, where the dynamics of within-household outbreaks are tempered by historical waves of infection and the immunity of older individuals

Improving pairwise approximations for network models with susceptible-infected-susceptible dynamics

Network models of disease spread play an important role in elucidating the impact of long-lasting infectious contacts on the dynamics of epidemics. Moment-closure approximation is a common method of generating low-dimensional deterministic models of epidemics on networks, which has found particular success for diseases with susceptible-infected-recovered (SIR) dynamics. However, the effect of network structure is arguably more important for sexually transmitted infections, where epidemiologically relevant contacts are comparatively rare and longstanding, and which are in general modelled via the susceptible-infected-susceptible (SIS)-paradigm. In this paper, we introduce an improvement to the standard pairwise approximation for network models with SIS-dynamics for two different network structures: the isolated open triple (three connected individuals in a line) and the -regular network. This improvement is achieved by tracking the rate of change of errors between triple values and their standard pairwise approximation. For the isolated open triple, this improved pairwise model is exact, while for -regular networks a closure is made at the level of triples to obtain a closed set of equations. This improved pairwise approximation provides an insight into the errors introduced by the standard pairwise approximation, and more closely matches both higher-order moment-closure approximations and explicit stochastic simulations with only a modest increase in dimensionality to the standard pairwise approximation

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