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

Abstract

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.

Modelling the spatio‐temporal deployment of resistant varieties to reduce the incidence of rice tungro disease in a dynamic cropping system

“…The analysis presented in this paper uses a model of simple structure but which has the essential features to enable variety deployment questions to be investigated. The model was described in detail in Holt & Chancellor (1997). The cropping system was represented by a square lattice of four hundred fields.…”

“…Of course, if planting synchrony is increased such that the ‘green bridge’ is removed, then carry‐over is prevented and the disease cycle can be broken ( Vanderplank, 1963). As was clear from an analysis of cropping synchrony ( Holt & Chancellor, 1997), if even a small amount of carry‐over occurred, incidence could build up significantly during the main cropping seasons, and the model proved very sensitive to changes in cropping synchrony close to the threshold for disease persistence. Unless the deployment of resistant varieties in the dry season will enable incidence to be reduced to a very low level (approximately 0.01%), therefore, it is unlikely to be effective in strategic disease suppression.…”

“…This was consistent with the steep decline in RTVD infection risk observed with increasing distance to the nearest inoculum source ( Holt et al ., 1996 ). As described in Holt & Chancellor (1997), spread between fields and the rate of disease increase in fields can be combined in a single expression, so for each field (at co‐ordinates x , y ) in the lattice:…”

“…Holt & Chancellor (1997) estimated that for RTVD‐susceptible varieties, values of r and b were in the range 1.2–2.8 month −1 and 2.5–6.0 field‐width −1 , respectively, assuming a field size of about 1 ha. Fields of two variety types were specified in this paper, being resistant or susceptible to RTVD, with the infection rate in fields of a resistant variety, r r , being less than that in fields of a susceptible variety, r s .…”

“…Using a model of the epidemiology of RTVD in a continuous, contiguous rice cropping system ( Holt & Chancellor, 1997) several key questions were asked:…”