Modelling virus- and host-limitation in vectored plant disease epidemics

Models of plant virus epidemics have received less attention than those caused by fungal pathogens. Intuitively, the fact that virus diseases are systemic means that the individual diseased plant can be considered as the population unit which simplifies modelling. However, the fact that a vector is required in the vast majority of cases for virus transmission, means that explicit consideration must be taken of the vector, or, the involvement of the vector in the transmission process must be considered implicitly. In the latter case it is also important that within-plant processes, such as virus multiplication and systemic movement, are taken into account. In this paper we propose an approach based on the linking of transmission at the population level with virus multiplication within plants. The resulting models are parameter-sparse and hence simplistic. However, the range of model outcomes is representative of field observations relating to the apparent limitation of epidemic development in populations of healthy susceptible plants. We propose that epidemic development can be constrained by virus limitation in the early stages of an epidemic when the availability of healthy susceptible hosts is not limiting. There is an inverse relationship between levels of transmission in the population and the mean virus titre/infected plant. In the case of competition between viruses, both virus and host limitation are likely to be important in determining whether one virus can displace another or whether both viruses can co-exist in a plant population. Lotka-Volterra type equations are derived to describe density-dependent competition between two viruses multiplying within plants, embedded within a population level epidemiological model. Explicit expressions determining displacement or co-existence of the viruses are obtained. Unlike the classical Lotka-Volterra competition equations, the co-existence requirement for the competition coefficients to be both less than 1 can be relaxed.