Analytic models for the patchy spread of plant disease

Plant epidemiologists have long been concerned with the patchy nature of pl ant disease epidemics. This paper presents a new analytical model for patch y plant epidemics (and patchy dynamics in general), using a second-order ap proximation to capture the spatial dynamics in terms of the densities and s patial covariances of healthy and infected hosts. Using these spatial momen t equations helps us to explain the dynamic growth of patchiness during the early phase of the epidemic, and how the patchiness feeds back on the grow th rate of the epidemic. Both underlying heterogeneity in the host spatial arrangement and dynamically generated heterogeneity in the spatial arrangem ent of infected plants initially accelerate but later decelerate the epidem ic. (C) 1999 Society for Mathematical Biology.