On the velocity of epidemic waves in model plant disease epidemics

Previous work on the temporal and spatial spread of plant diseases has focused on models generating epidemics with constant frontal velocity (traveling epidemic waves). But the theory of turbulent diffusion, the laws of which govern the dispersal of windborne spores of most foliar plant pathogens, suggests that spread becomes more efficient as the area with diseased plants expands. This should result in epidemics with increasing frontal velocity (dispersive epidemic waves). As a first step toward an analytic treatment of dispersive waves of plant diseases this study considers two simple models based on reaction-diffusion equations with scale-dependent diffusivity. Predictions from these models are compared qualitatively to data on the spread of potato late blight (Phytophthora infestans) epidemics over different temporal and spatial scales. The paper concludes with a brief discussion on the merit of simple, analytical models for studying, interpreting, and testing of abstract epidemiological concepts, such as traveling and dispersive waves.