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A Study on Dynamics of CD4 + T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials

Author

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  • Hashem Najafi

    (Department of Mathematics, College of Sciences, Shiraz University, Shiraz 7187919556, Iran
    These authors contributed equally to this work.)

  • Sina Etemad

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
    These authors contributed equally to this work.)

  • Nichaphat Patanarapeelert

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
    These authors contributed equally to this work.)

  • Joshua Kiddy K. Asamoah

    (Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
    These authors contributed equally to this work.)

  • Shahram Rezapour

    (Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
    These authors contributed equally to this work.)

  • Thanin Sitthiwirattham

    (Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
    These authors contributed equally to this work.)

Abstract

In recent decades, AIDS has been one of the main challenges facing the medical community around the world. Due to the large human deaths of this disease, researchers have tried to study the dynamic behaviors of the infectious factor of this disease in the form of mathematical models in addition to clinical trials. In this paper, we study a new mathematical model in which the dynamics of CD 4 + T-cells under the effect of HIV-1 infection are investigated in the context of a generalized fractal-fractional structure for the first time. The kernel of these new fractal-fractional operators is of the generalized Mittag-Leffler type. From an analytical point of view, we first derive some results on the existence theory and then the uniqueness criterion. After that, the stability of the given fractal-fractional system is reviewed under four different cases. Next, from a numerical point of view, we obtain two numerical algorithms for approximating the solutions of the system via the Adams-Bashforth method and Newton polynomials method. We simulate our results via these two algorithms and compare both of them. The numerical results reveal some stability and a situation of lacking a visible order in the early days of the disease dynamics when one uses the Newton polynomial.

Suggested Citation

  • Hashem Najafi & Sina Etemad & Nichaphat Patanarapeelert & Joshua Kiddy K. Asamoah & Shahram Rezapour & Thanin Sitthiwirattham, 2022. "A Study on Dynamics of CD4 + T-Cells under the Effect of HIV-1 Infection Based on a Mathematical Fractal-Fractional Model via the Adams-Bashforth Scheme and Newton Polynomials," Mathematics, MDPI, vol. 10(9), pages 1-32, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1366-:d:797261
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    References listed on IDEAS

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    8. Khan, Hasib & Alam, Khurshaid & Gulzar, Haseena & Etemad, Sina & Rezapour, Shahram, 2022. "A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 455-473.
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