Optimal control of eggplant pest populations in a Predator–Prey–Parasitoid model with seasonal growth effects

Abstract

This study investigates the population dynamics of the eggplant fruit and shoot borer (EFSB), emphasizing the role of natural enemies — predators and parasitoids — in pest management. A mathematical model, comprising three variables representing each population, is constructed to analyze the interactions. The model exhibits six equilibrium points, with particular focus on the predator-free and coexistence equilibria. Crucially, the model incorporates the seasonal variability of the pest’s growth rate, reflecting the influence of environmental factors such as temperature changes. Optimal control strategies are explored, encompassing both chemical and biological approaches, including the use of parasitoids. For chemical control, Pontryagin’s Minimum Principle is employed to derive optimal strategies under varying seasonal growth conditions. The biological control strategy, centered on parasitoid release, is analyzed using State-Dependent Riccati Equations (SDRE) to determine optimal continuous and impulsive release methods. The findings highlight the importance of considering seasonal variations in pest growth and demonstrate the efficacy of impulsive parasitoid releases for pest management. This research provides valuable insights into sustainable pest management and offers a robust framework for applying mathematical modeling to complex agricultural systems.