Fitting stochastic epidemic models to data is a non-standard problem because data on the infection processes defined in such models are rarely observed directly. This in turn means that the likelihood of the observed data is intractable in the sense that it is very computationally expensive to obtain. Although data-augmented Markov chain Monte Carlo (MCMC) methods provide a solution to this problem, employing a tractable augmented likelihood, such methods typically deteriorate in large populations due to poor mixing and increased computation time. Here, we describe a new approach that seeks to approximate the likelihood by exploiting the underlying structure of the epidemic model. Simulation study results show that this approach can be a serious competitor to data-augmented MCMC methods. Our approach can be applied to a wide variety of disease transmission models, and we provide examples with applications to the common cold, Ebola, and foot-and-mouth disease.

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