A reaction–diffusion model for the control of Eldana saccharina Walker in sugarcane using the sterile insect technique

Abstract

A reaction–diffusion model is formulated for the population dynamics of an Eldana saccharina Walker infestation of sugarcane under the influence of partially sterile released insects. The model describes the population growth of and interaction between normal and sterile E. saccharina moths in a temporally variable and spatially heterogeneous environment. It consists of a discretized reaction–diffusion system with variable diffusion coefficients, subject to strictly positive initial data and zero-flux Neumann boundary conditions on a bounded spatial domain. The primary objectives are to establish a model which may be used within an area-wide integrated pest management programme for E. saccharina in order to investigate the efficiency of different sterile moth release strategies without having to conduct formal field experiments, and to present guidelines according to which release ratios, release frequencies and spatial distributions of releases may be estimated which are expected to lead to suppression of the pest. Although many reaction–diffusion models have been formulated in the literature describing the sterile insect technique, few of these models describe the technique for Lepidopteran species with more than one life stage and where F1-sterility is relevant. In addition, none of these models consider the technique when fully sterile females and partially sterile males are released. The model formulated here is also the first reaction–diffusion model formulated describing E. saccharina growth and migration, and the sterile insect technique applied specifically to E. saccharina.