FRACTIONAL OPTIMAL CONTROL FOR THE ANALYTICAL TREATMENT OF MALARIA MODEL

Muhammad Nadeem, Mustafa Habib, Aman Waris, Loredana Florentina Iambor, P. A. Azeem Hafiz and Sharifah E. Alhazmi
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Muhammad Nadeem: School of Mathematics and Statistics, Qujing Normal University, 655011 Qujing, P. R. China
Mustafa Habib: ��Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan
Aman Waris: ��Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan
Loredana Florentina Iambor: ��Department of Mathematics and Computer Science, University of Oradea, 1 University Street, 410087 Oradea, Romania
P. A. Azeem Hafiz: �Department of Industrial Engineering, College of Engineering, King Khalid University, Abha, Saudi Arabia
Sharifah E. Alhazmi: �Mathematics Department, Al-Qunfudah University College, Umm Al-Qura University, Mecca, Saudi Arabia

FRACTALS (fractals), 2025, vol. 33, issue 08, 1-13

Abstract: Fractional calculus has been an effective method for modeling and controlling dynamical systems that display memory-dependent and nonlocal behaviors in recent times. This research suggests a novel fractional optimal control method for treating malaria model. We capture the long-range interactions and memory effects inherent in the spread of malaria by adding Caputo fractional derivatives to the mathematical model of transmission dynamics. Disease-free, endemic equilibrium points and basic reproduction number are obtained. The basic reproduction number is evaluated. Stability and instability of equilibrium points are determined by using Routh–Hurwitz criteria. We illustrate the effectiveness of fractional optimum control strategies in reducing the transmission of malaria using numerical simulations and analysis. Comparing fractional derivatives to traditional methods, our findings show that they allow for more accurate modeling of the dynamics of disease and, consequently, better control measures.

Keywords: Fractional Optimal Control; Mathematical Dynamics; Malaria Model; Routh–Hurwitz Criteria (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25401772

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