Inference for an epidemic when susceptibility varies

A stochastic epidemic model featuring fixed-length latent periods, gamma-distributed infectious periods and randomly varying heterogeneity among susceptibles is considered. A Markov chain Monte Carlo algorithm is developed for performing Bayesian inference for the parameters governing the infectious-period length and the hyper-parameters governing the heterogeneity of susceptibility. This method of analysis applies to a wider class of diseases than methods proposed previously. An application to smallpox data confirms results about heterogeneity suggested by an earlier analysis that relied on less realistic assumptions.