Twenty-five years of botanical epidemiology

Epidemiological models in plant pathology usually belong to the family of logistic equations, describing the increase in disease intensity with time. Expansion and refinement are possible by applying dynamic simulation techniques on digital computers. Among these are models of disease increase in time and two-dimensional (horizontal) space, and spore dispersal in and over a crop in two-dimensional (vertical) space. Recently, an analytical model was developed by Van den Bosch and co-workers to describe focus expansion in time and two-dimensional (horizontal) space as a function of three biological parameters that were relatively easy to measure: gross reproduction, time kernel, and contact distribution. The model was tested using data from previous experiments not designed for this purpose and from a new experiment specifically designed for validation. The model treats focus expansion as a process with a constant radial velocity and seems valid on a small scale of a few metres and, after rescaling, on a large scale of hundreds of kilometres.