A discrete probability model for polycyclic infection by soil–borne plant parasites

SUMMARY A discrete, theoretical infection model is developed to describe the temporal progress of an epidemic of a soil‐borne pathogen. The model is based upon the probability of escape of host units, such as roots, seeds or entire plants from two sources of inoculum, a primary source, comprising randomly dispersed propagules in soil, and a secondary source derived from infected hosts. A polycyclic sequence of infection is modelled: thus infections derived from soil inoculum serve as sources of infection, giving rise to secondary infections which, in turn, give rise to tertiary infections and so on to the the cycle. The discrete, successive cyclical progression is generalized by the introduction of a parameter for survival of existing infections. The problem of a dynamically varying population of host units is discussed. A simplification of the model is obtained to give a continuous analogue, in which non‐integer values for time replace cycle number. Statistical methods of fitting the model to experimental data are discussed and illustrated by the fit to disease progress curves for the infection and damping–off of cress seedlings, Lepidium sativum L., by Pythium ultimum Trow.