A fractional order model for Malaria control using optimal strategies and numerical simulations

Articles in Press

Document Type : Research Article

Authors

• Abdelfatah Kouidere ¹
• Amine Elbhih ²
• Issam Minifi ³
• Khalid Adnaoui ³

¹ Department of Mathematics, Sidi Bennour Polydisciplinary Faculty, Chouaib Doukkali University, Morocco.

² Multidisciplinary Research and Innovation Laboratory (LPRI), Moroccan School of Engineering Sciences (EMSI), Casablanca, Morocco.

³ LAMS, Department of Mathematics and Computer Science, Faculty of Sciences, Ben M’Sik, Hassan II University of Casablanca. Morocco.

10.22067/ijnao.2025.94037.1667

Abstract

This paper develops and analyzes a fractional‑order model for malaria transmission that captures memory effects in host–vector dynamics and enables a more flexible treatment of control strategies. The proposed model extends the classical SEIR framework by incorporating fractional-order derivatives, which offer a more accurate representation of the memory and hereditary effects in malaria transmission. The human population is divided into four compartments: people susceptible ($S_{P}$), people exposed ($E_{P}$), people infected ($I_{P}$), prople recovered ($R_{P}$),and The mosquitoes population is divided into two compartments: mosquitoes susceptible ($S_{M}$), mosquitoes infected ($I_{M}$), respectively. The model introduces two time-dependent control variables: public awareness campaigns, treatment. These controls aim to prevent new infections, reduce the number of individuals in infectious compartments, and mitigate long-term complications in recovered individuals. Pontryagin’s maximum principle is employed to derive the necessary conditions for optimal control, and the resulting system is solved using an iterative numerical method. Simulation results, implemented in \textsc{Matlab}, illustrate the influence of fractional-order derivatives on disease dynamics and demonstrate the comparative effectiveness of the control strategies. This work provides a novel fractional-order control framework for malaria and highlights the importance of integrated intervention strategies.

Keywords

• Malaria
• Optimal control
• Malaria disease
• Fractional-order model
• Mathematical

Main Subjects

• Optimal Control

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