Modelling the effects of the sterile insect technique applied to Eldana saccharina Walker in sugarcane

Abstract

A mathematical 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, but spatially homogeneous environment. The model consists of a deterministic system of difference equations subject to strictly positive initial data. The primary objective of this model is to determine suitable parameters in terms of which the above population growth and interaction may be quantified and according to which E.saccharina infestation levels and the associated sugarcane damage may be measured. Although many models have been formulated in the past 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 being released. The model formulated is also the first to describe the technique applied specifically to E.saccharina, and to consider the economic viability of applying the technique to this species. Pertinent decision support is provided to farm managers in terms of the best timing for releases, release ratios and release frequencies.