Modelling plant virus epidemics in a plantation-nursery system

The material used for propagation and planting of many perennial crop plants is derived from vegetative cuttings which are first multiplied in a nursery. This situation was modelled to analyse the dynamics of a plant virus epidemic in a combined nursery-plantation system and the comparative effects of disease management activities in the plantation and in the nursery. The plant populations were partitioned into healthy and diseased categories and were linked according to basic SI models of disease transmission. Removal of diseased plants and replanting operations in both the plantation and nursery were included in the model and two variants were analysed in which mother plants (from which cuttings were taken) remained in the plantation or were harvested. The former is shown to be the limiting case for a large number of cuttings per plant. A criterion was derived for the invasion of disease into a healthy combined system. This consisted of four additive terms: the basic reproductive numbers of disease in the plantation alone and in the nursery alone, and two terms describing the cycling of diseased material between the plantation and nursery. Disease can still invade the system with basic reproductive numbers in the plantation or in the nursery less than 1 depending on the magnitude of cycling. Under some conditions only diseased plants remain in the plantation and nursery. For such a case a criterion was derived for the invasion of healthy plants into a fully diseased system. This depended on replanting rates in the plantation and nursery, and infection, mortality and removal rates of healthy plants.