Relationship between spatial scale of pathogen dispersal and host landscape that minimizes infection rate in agricultural crops

The initial rate of invasion of crop pathogens depends on the degree of spatial aggregation of susceptible crops and the dispersal characteristics of the pathogen. We introduce an analytical approach to identify the largest degree of aggregation that minimises the initial infection rate of an invading pest or pathogen. The degree of aggregation is described in terms of the size of clusters of crop fields within a landscape and the corresponding separation distance between these clusters. Results are calculated for several common dispersal kernels including the Gaussian, negative exponential, and power-law kernels, and can be extended to other dispersal kernels. Our analytical results align well with computer simulations of an individual-based model for pathogen invasion and spread through a broad range of artificial host landscapes. We also analysed an example of the dispersal of cassava brown streak virus through a realistic cassava landscape. The results of this paper can assist crop growers, advisers and regulators by providing insights into spatial configurations of host landscapes that most effectively slow the spread of invading pathogens.