Mathematical modeling, analysis, and optimal control of the cochineal insect impact on cacti plants

This paper introduces a mathematical model, denoted as SIRM C, aimed at understanding the dynamics of cochineal infestation in cacti plants. The model incorporates two control strategies: biological control through Hyperaspis trifurcata, a natural predator of cochineal, and chemical control via insecticide spraying. The objective is to reduce the number of infected cacti while also achieving a balance between minimizing infection, maximizing recovery over time, and minimizing the costs associated with the control measures. The proposed framework effectively integrates these strategies to manage cochineal dynamics. Optimal control strategies are derived using Pontryagin’s maximum principle, and numerical simulations conducted in MATLAB validate the theoretical results.

کلیدواژه ها:

Mathematical modeling ، Optimal control theory ، Pontryagin Maximum ، Cochineal ، Cacti plants