Mathematical modeling and optimal control strategies to limit cochineal infestation on Cacti plants

Iranian Journal of Numerical Analysis and Optimization

مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 26 اردیبهشت 1404

نوع مقاله: Review Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2025.90998.1557

نویسندگان

Sofiane khassal^* ؛ Omar Balatif

Laboratory of Fundamental Mathematics and their Applications, Department of Mathematics, Faculty of Sciences, University of Chouaib Doukkali, El jadida, Morocco

چکیده

This paper introduces a mathematical model, denoted as $SIRMC $, aimed at understanding the dynamics of cochineal infestation in cacti plants. The model incorporates two control strategies: biological control through \textit{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.

کلیدواژه‌ها

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