Efficient modelling of infectious diseases in wildlife: A case study of bovine tuberculosis in wild badgers.

Bovine tuberculosis (bTB) has significant socio-economic and welfare impacts on the cattle industry in parts of the world. In the United Kingdom and Ireland, disease control is complicated by the presence of infection in wildlife, principally the European badger. Control strategies tend to be applied to whole populations, but better identification of key sources of transmission, whether individuals or groups, could help inform more efficient approaches. Mechanistic transmission models can be used to better understand key epidemiological drivers of disease spread and identify high-risk individuals and groups if they can be adequately fitted to observed data. However, this is a significant challenge, especially within wildlife populations, because monitoring relies on imperfect diagnostic test information, and even under systematic surveillance efforts (such as capture-mark-recapture sampling) epidemiological events are only partially observed. To this end we develop a stochastic compartmental model of bTB transmission, and fit this to individual-level data from a unique > 40-year longitudinal study of 2,391 badgers using a recently developed individual forward filtering backward sampling algorithm. Modelling challenges are further compounded by spatio-temporal meta-population structures and age-dependent mortality. We develop a novel estimator for the individual effective reproduction number that provides quantitative evidence for the presence of superspreader badgers, despite the population-level effective reproduction number being less than one. We also infer measures of the hidden burden of infection in the host population through time; the relative likelihoods of competing routes of transmission; effective and realised infectious periods; and longitudinal measures of diagnostic test performance. This modelling framework provides an efficient and generalisable way to fit state-space models to individual-level data in wildlife populations, which allows identification of high-risk individuals and exploration of important epidemiological questions about bTB and other wildlife diseases.