Statistical inference and computational efficiency for spatial infectious disease models with plantation data

The paper considers data from an aphid infestation on a sugar cane plantation and illustrates the use of an individual level infectious disease model for making inference on the biological process underlying these data. The data are interval censored, and the practical issues involved with the use of Markov chain Monte Carlo algorithms with models of this sort are explored and developed. As inference for spatial infectious disease models is complex and computationally demanding, emphasis is put on a minimal parsimonious model and speed of code execution. With careful coding we can obtain highly efficient Markov chain Monte Carlo algorithms based on a simple random-walk Metropolis-within-Gibbs routine. An assessment of model fit is provided by comparing the predicted numbers of weekly infections from the data to the trajectories of epidemics simulated from the posterior distributions of model parameters. This assessment shows that the data have periods where the epidemic proceeds more slowly and more quickly than the (temporally homogeneous) model predicts.