Integrated Pest Management Model with Natural Enemy and Pest-Harvesting

This research aims to develop a mathematical model that describes the dynamics of pests, natural enemies, and refugia plants within the framework of Integrated Pest Management (IPM). The model integrates biological control through predation, mutualistic relationships between natural enemies and refugia plants, and mechanical control through pest harvesting. The proposed model is then analyzed dynamically to study its qualitative behavior. It has been shown that the solutions of the proposed model are non-negative and finite, demonstrating the biological feasibility of the model. We also analyze the local stability of the equilibrium point to gain insight into the system's long-term behavior and to identify conditions that allow effective pest control. We show that the model has seven feasible equilibrium points, but only four of them are stable under certain conditions. In particular, the pest-free equilibrium point is conditionally stable, indicating the potential for effective pest control. Finally, we perform several numerical simulations to confirm the results of our analysis, especially the stability of the four stable equilibrium points. This study provides insight into integrating biological and mechanical strategies in pest management, emphasizing the importance of ecological interactions for sustainable agriculture. Keywords: integrated pest management, local stability, natural enemy, numerical simulation, refugia plant.