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Bayesian inference for stochastic epidemics in closed populations

School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, UK, g.streftaris{at}ma.hw.ac.uk

Gavin J Gibson

School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, UK

We consider continuous-time stochastic compartmental models that can be applied in veterinary epidemiology to model the within-herd dynamics of infectious diseases. We focus on an extension of Markovian epidemic models, allowing the infectious period of an individual to follow a Weibull distribution, resulting in a more flexible model for many diseases. Following a Bayesian approach we show how approximation methods can be applied to design efficient MCMC algorithms with favourable mixing properties for fitting non-Markovian models to partial observations of epidemic processes. The methodology is used to analyse real data concerning a smallpox outbreak in a human population, and a simulation study is conducted to assess the effects of the frequency and accuracy of diagnostic tests on the information yielded on the epidemic process.

Key Words: Bayesian inference • diagnostic tests • Markov chain Monte Carlo • Metropolis-Hastings acceptance rate • non-Markovian model • stochastic epidemic modelling

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