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Stochastic epidemic models describe the dynamics of an epidemic as a diseasespreads through a population. Typically, only a fraction of cases are observedat a set of discrete times. The absence of complete information about the timeevolution of an epidemic gives rise to a complicated latent variable problem inwhich the state space size of the epidemic grows large as the population sizeincreases. This makes analytically integrating over the missing data infeasiblefor populations of even moderate size. We present a data augmentation Markovchain Monte Carlo (MCMC) framework for Bayesian estimation of stochasticepidemic model parameters, in which measurements are augmented withsubject-level disease histories. In our MCMC algorithm, we propose each newsubject-level path, conditional on the data, using a time-inhomogeneouscontinuous-time Markov process with rates determined by the infection historiesof other individuals. The method is general, and may be applied, with minimalmodifications, to a broad class of stochastic epidemic models. We present ouralgorithm in the context of multiple stochastic epidemic models in which thedata are binomially sampled prevalence counts, and apply our method to datafrom an outbreak of influenza in a British boarding school.

Efficient data augmentation for fitting stochastic epidemic models to prevalence data