Efficient Bayesian modelling of infectious diseases in wildlife

Infectious diseases of wildlife result in significant welfare and conservation costs to wild animal populations. For example, chytridiomycosis is a fungal pathogen driving the mass extinction of numerous amphibian species worldwide, putting at risk >10% of all vertebrate species; while white-nose syndrome is estimated to have caused >6 million bat deaths in North America by 2012 alone. Diseases in wildlife can also have significant impacts on agriculture. For example, bovine tuberculosis (bTB) is a notifiable disease in livestock, which costs the UK government over £100 million per year in terms of testing and compensation for slaughtered animals, and also has huge impacts on the livelihoods of farmers. The pathogen has a wide host range, which includes protected species such as badgers, and currently, bTB is the subject of highly controversial badger culling trials aimed at attenuating disease transmission to livestock. Wildlife infectious diseases also represent a considerable threat to humans, as emerging zoonoses such as Ebola, Zika, West Nile virus, HIV and plague all attest to. In short, the list of WID outbreaks is long and growing, and we desperately need better tools to study their epidemiology.

Mathematical modelling provides tools that enable us to better understand infectious disease dynamics, and can thus be used to help inform management strategies. However, the use of mathematical models without robustly fitting to observed data can lead to poor model predictions and inference, in turn hindering scientific enquiry and increasing the probability of making poor policy decisions. Fitting dynamic transmission models to observed data is highly challenging, since available data is incomplete, and thus standard statistical approaches that rely on estimation of the likelihood function cannot be employed.

We will extend recent advances in simulation-based Bayesian inference methods, which have shown great utility in overcoming these difficulties. These approaches are flexible and tractable, but can be computationally demanding. This project will extend recent advances in the field to deal with key challenges, both in the scaling up of these methods to larger systems, and also in dealing with the complexities that typify wildlife disease systems, such as: incomplete longitudinal sampling of individuals (i.e. capture-mark-recapture), the application of multiple diagnostic tests, uncertainties in diagnostic test performance, complex spatial and meta-population structures, and demographic changes over time. We will explore the development of constrained simulation techniques, which have been shown to greatly improve the efficiency of these inference algorithms in small populations, and hence are good candidates for improving efficiency in larger, more complex populations. We will also explore the use of these algorithms to allow for the fitting and comparison of different transmission models, again extending recent work in the field.

We will ground our research using the high-profile case study of bovine tuberculosis in badgers, which suffers from all of the system-uncertainty and data-quality issues described above. Additionally, the disease has a direct impact on the livelihoods of UK farmers, major policy decisions that influence voter behaviour, and the conservation and management of UK wildlife. We will use an unprecedented 40+ year longitudinal study of bTB in a natural, wild population of badgers, to provide a unique and powerful insight into the aetiology of the disease. Although we focus on wildlife disease systems in this project, the methodological advances developed will be applicable to a wider range of state-space systems.

Wildlife infectious diseases have major impacts on both wildlife (and domestic animal) populations, as well as human populations, as evidenced by recent outbreaks of diseases such as bovine tuberculosis, chytridiomycosis, Ebola and Zika viruses. Mathematical models provide a tractable means to understand the mechanisms of spread of a pathogen in a population, and potentially to predict the future course of an outbreak. However, the utility of these models is linked to the ability to fit them to observed data, and many epidemiological events (such as infection and recovery) are rarely (if ever) fully observed. Instead, the missing information must usually be inferred as part of a model fitting process, and it is important that the uncertainties due to the missing information are correctly characterised in the parameter estimates and model predictions. The increasing use of complex models without accounting for the uncertainties surrounding missing data/hidden states and/or different choices of model will lead to poor predictions, which will hinder scientific enquiry and increase the probability of making poor policy decisions.

This project will extend recent advances in model fitting and model comparison for state-space models in the presence of missing information to develop a pipeline that can be used for model inference, comparison and prediction. As such, the methodology developed would be applicable to a wide range of different state-space systems and thus could be an important addition to the toolbox of methods available to epidemiologists, and facilitate their adoption more widely outside of the statistical community. With the impacts of infectious diseases becoming more widely realised and technology for data collection rapidly improving, this research has potentially important consequences for developing and fitting statistical models to a wide range of important infectious disease systems. Importantly, the ability to more easily implement these methods could help to add to the suite of real-time modelling tools available for modelling epidemic outbreaks.

In addition, bovine tuberculosis (bTB) is a disease with huge socio-economic impacts in Great Britain. It currently costs the UK government >£100 million per year for surveillance and for compensation to cattle owners when infected animals must be culled, and in the face of intensive control measures incidence of the disease in cattle herds has increased dramatically over the past 20 years. In addition, EU legislation requires that the UK government have in place a TB eradication policy. Control of the disease is complicated by the presence of a wildlife reservoir of infection, the European badger (Meles meles). The involvement of a second species complicates disease-control, not least because the dynamics of M. bovis infection in badgers is largely unobserved, due to a national lack of systematic routine surveillance in badger populations. As a result, important mechanisms of within-species spread and persistence of the disease are still poorly understood, and improving our understanding of these mechanisms could shed an important light on the potential for the eventual eradication of the disease in both badger and cattle populations. This project will use detailed data from Woodchester Park in Gloucestershire, where the world's most detailed longitudinal study of badger populations and bTB is being conducted. We will use these data in order to build and compare between competing models of varying complexity to help understand how the disease spreads and is maintained in badger populations. The methodologies and findings from this study will also have wider implications for the study of other wildlife diseases.