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A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative

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  • Abdul-Aziz Hussein
  • Benyam Mebrate

Abstract

In this paper, we are concerned with a deterministic Caputo fractional derivative mathematical model of HIV/AIDS with treatment and optimal control. We formulate a mathematical model that contains six compartments (including primary infection and treatment) and show that the model is well‐posed. We calculate the reproduction number and free and endemic equilibrium points. We prove the stability of free and endemic equilibrium points. The local stability is carried out by the linearization method, whereas the global stability is performed by Mittag–Leffler stability. We consider four control mechanisms and show their impact on the prevalence of HIV infection. Numerical solutions are performed using the optimal case of the two‐stage explicit fractional order Runge–Kutta methods.

Suggested Citation

  • Abdul-Aziz Hussein & Benyam Mebrate, 2025. "A Fractional Order Model for HIV/AIDS With Treatment and Optimal Control Using Caputo Derivative," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:9342227
    DOI: 10.1155/ijmm/9342227
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    References listed on IDEAS

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    1. Belaynesh Melkamu & Benyam Mebrate & Nasser-Eddine Tatar, 2022. "A Fractional Model for the Dynamics of Smoking Tobacco Using Caputo–Fabrizio Derivative," Journal of Applied Mathematics, Hindawi, vol. 2022, pages 1-10, December.
    2. Belaynesh Melkamu & Benyam Mebrate, 2022. "A Fractional Model for the Dynamics of Smoking Tobacco Using Caputo–Fabrizio Derivative," Journal of Applied Mathematics, John Wiley & Sons, vol. 2022(1).
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    5. Mohammadi, Hakimeh & Kumar, Sunil & Rezapour, Shahram & Etemad, Sina, 2021. "A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    6. Saif Ullah & Mohamed Altanji & Muhammad Altaf Khan & Ahmed Alshaheri & Wojciech Sumelka, 2023. "The Dynamics Of Hiv/Aids Model With Fractal-Fractional Caputo Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-20.
    7. Klaus Deimling, 1985. "Nonlinear Functional Analysis," Springer Books, Springer, number 978-3-662-00547-7, March.
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    Cited by:

    1. Kar, Silajit & Maiti, Dilip Kumar & Maiti, Atasi Patra, 2026. "Memory tracing in fractional-order modeling of HIV/AIDS: Analyzing periodic transmission, anxiety, economic constraints, and treatment barriers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 242(C), pages 199-229.

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