A model of plant virus disease epidemics in asynchronously-planted cropping systems

A mathematical model was developed of the dynamics of a plant virus disease within a spatially-referenced lattice of fields of a host crop. The model can be applied to crops in continuous, contiguous cultivation such as tropical irrigated rice. Disease progress in each field of the host crop was assumed to be logistic and determined by incidence within the field itself as well as incidence in neighbouring fields, depending on the gradient of disease spread. The frequency distribution of planting dates (represented by the proportion of the total number of fields planted in successive months) was assumed to follow a normal distribution and the variance of planting date was used as a measure of cropping asynchrony. Analysis of the model revealed that disease incidence within the lattice (i.e. mean incidence over all fields) depended upon the infection efficiency, the slope of the dispersal gradient, and the variance in planting date. Disease endemicity depended mainly on planting date variance and disease persisted in the lattice if this variance exceeded a certain threshold. Above the threshold for persistence, the response of mean disease incidence to planting date variance was non-linear and the region of greatest sensitivity was closest to the threshold. Thus, disease systems that show moderate rather than high cropping asynchrony are more likely to be influenced by changes in the variance of planting date. Implications for the area-wide management of rice tungro virus disease are discussed.