Dynamics of a prey-predator type ecological model in relevance to pest control

In this article, we propose and analyze a prey-predator-type ecological model in relevance to pest control. We consider that the system consists of two types of pests and their natural enemy as predator. The basic biological feasibility of the system is studied. Then, local stability analysis of all possible equilibria of the model is examined. Also, the global stability of the coexisting equilibrium point is studied using a suitable Lyapunov functional. Moreover, an optimal control problem is formulated and solved to find out the optimal pest control policy. Finally, we have illustrated some of the results through numerical simulations.

Automated summary

This article proposes and analyzes a prey-predator-type ecological model relevant to pest control, studying the biological feasibility, local stability, and global stability of the system. Additionally, an optimal control problem is formulated and solved to determine the optimal pest control policy, with results illustrated through numerical simulations.