Stability and Optimal Control in a Host–Pest Model with Sterile Insect and Pheromone Interventions

Abstract

We develop a nonlinear system of ordinary differential equations to model the suppression of the false codling moth (Thaumatotibia leucotreta) through a combined strategy of sterile insect release and pheromone trapping. The model tracks ten interacting state variables representing host biomass, pest life stages, and control agents. We derive the basic reproduction number R 0 using the next-generation matrix and establish conditions for the existence and local stability of equilibria. Centre manifold analysis reveals a backward bifurcation, implying that eradication requires more than reducing R 0 below unity. Sensitivity analysis identifies the sterile-mating rate and trap capture efficiency as the most influential parameters. An optimal control framework is formulated and solved via Pontryagin’s Minimum Principle, yielding time-dependent release and trap schedules that minimise economic loss. Numerical simulations confirm that the optimal protocol achieves rapid pest collapse and crop recovery at reduced cost compared to constant or periodic controls. The results provide quantitative insights for integrated pest management in perennial crop systems