Fitting and testing spatio-temporal stochastic models with application in plant epidemiology

We propose and illustrate a likelihood-based method for fitting spatio-temporal stochastic models for the spread of a plant disease to experimental observations. The models considered are individual-based, with members of the population occupying discrete sites on a two-dimensional lattice. The disease is assumed to be characterized by presence/absence, and infection of susceptible individuals by infected individuals is represented as a stochastic process. The method described can be applied to estimate parameters in models of this kind when observations consisting of temporal sequences of disease maps are available. The use of measures of spatial aggregation as measured from simulated and real epidemics is proposed as a means of assessing the relative merits of alternative models for the spread of a disease. To illustrate the technique we fit and compare two models, which differ in the relationship between infective pressure and distance, to observations of an epidemic of citrus tristeza virus (CTV). It is demonstrated that a model in which this relationship is a power-law is superior to one which uses a negative exponential and the importance of model choice for the design of control strategies is discussed briefly.