A continuous-time and deterministic model was used to characterize plant virus disease epidemics in relation to virus transmission mechanism and population dynamics of the insect vectors. The model can be written as a set of linked differential equations for healthy (virus-free), latently infected, infectious, and removed (postinfectious) plant categories, and virus-free, latent, and infective insects, with parameters based on the transmission classes, vector population dynamics, immigration/emigration rates, and virus-plant interactions. The rate of change in diseased plants is a function of the density of infective insects, the number of plants visited per time, and the probability of transmitting the virus per plant visit. The rate of change in infective insects is a function of the density of infectious plants, the number of plants visited per time by an insect, and the probability of acquiring the virus per plant visit. Numerical solutions of the differential equations were used to determine transitional and steady-state levels of disease incidence (d*); d* was also determined directly from the model parameters. Clear differences were found in disease development among the four transmission classes: nonpersistently transmitted (stylet-borne [NP]); semipersistently transmitted (foregut-borne [SP]); circulative, persistently transmitted (CP); and propagative, persistently transmitted (PP), with the highest disease incidence (d) for the SP and CP classes relative to the others, especially at low insect density when there was no insect migration or when the vector status of emigrating insects was the same as that of immigrating ones. The PP and CP viruses were most affected by changes in vector longevity, rates of acquisition, and inoculation of the virus by vectors, whereas the PP viruses were least affected by changes in insect mobility. When vector migration was explicitly considered, results depended on the fraction of infective insects in the immigration pool and the fraction of dying and emigrating vectors replaced by immigrants. The PP and CP viruses were most sensitive to changes in these factors. Based on model parameters, the basic reproductive number (R0)—number of new infected plants resulting, from an infected plant introduced into a susceptible plant population—was derived for some circumstances and used to determine the steady-state level of disease incidence and an approximate exponential rate of disease increase early in the epidemic. Results can be used to evaluate disease management strategies.
A model of plant virus disease epidemics in asynchronously-planted cropping systems