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

Articles in Press

Document Type : Research Article

Authors

• Sofiane Khassal ¹
• El Mehdi Moumine ²
• Omar Balatif ¹

¹ Laboratory of Fundamental Mathematics and Their Applications , Department of Mathematics Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco.

² Laboratory of Analysis, Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of science Ben M'sik, University Hassan II, Casablanca, Morocco.

10.22067/ijnao.2025.91108.1558

Abstract

We propose a mathematical model, $SIM$, that describes the dynamics of cochineal insect spread among cacti and examines the effects of various control strategies. The model is analyzed for the existence and uniqueness of solutions, and we investigate the equilibrium points and stability of the system using both local and global stability analyses. By performing numerical simulations in MATLAB, we validate our theoretical findings. Furthermore, we propose an optimal control strategy to minimize the cochineal population in cacti fields. The optimal control problem is formulated using Pontryagin’s maximum principle, and the corresponding optimality system is solved iteratively. Our study compares three control strategies: cutting and burning infected cacti, insecticide spraying, and a combined approach. The results demonstrate that the combined strategy is the most effective in reducing the cochineal population. This research provides valuable insights into managing cochineal infestations and offers practical recommendations for farmers to control the spread of these pests.

Keywords

• Mathematical modeling
• Stability analysis
• Optimal control
• Cochineal insect
• Cacti plants

Main Subjects

• Modeling and Simulation

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