Analytic models for the patchy spread of plant disease

Plant epidemiologists have long been concerned with the patchy nature of plant disease epidemics. This paper presents a new analytical model for patchy plant epidemics (and patchy dynamics in general), using a second-order approximation to capture the spatial dynamics in terms of the densities and spatial covariances of healthy and infected hosts. Using these spatial moment 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 growth rate of the epidemic. Both underlying heterogeneity in the host spatial arrangement and dynamically generated heterogeneity in the spatial arrangement of infected plants initially accelerate but later decelerate the epidemic.