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Study of HIV Disease and Its Association with Immune Cells under Nonsingular and Nonlocal Fractal-Fractional Operator

Author

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  • Shabir Ahmad
  • Aman Ullah
  • Ali Akgül
  • Manuel De la Sen
  • Ning Cai

Abstract

HIV, like many other infections, is a severe and lethal infection. Fractal-fractional operators are frequently used in modeling numerous physical processes in the current decade. These operators provide better dynamics of a mathematical model because these are the generalization of integer and fractional-order operators. This paper aims to study the dynamics of the HIV model during primary infection by fractal-fractional Atangana–Baleanu (AB) operators. The sufficient conditions for the existence and uniqueness of the solution of the proposed model under the AB operator are derived via fixed point theory. The numerical scheme is presented by using the Adams–Bashforth method. Numerical results are demonstrated for different fractal and fractional orders to see the effect of fractional order and fractal dimension on the dynamics of HIV and CD4+ T-cells during primary infection.

Suggested Citation

  • Shabir Ahmad & Aman Ullah & Ali Akgül & Manuel De la Sen & Ning Cai, 2021. "Study of HIV Disease and Its Association with Immune Cells under Nonsingular and Nonlocal Fractal-Fractional Operator," Complexity, Hindawi, vol. 2021, pages 1-12, August.
    • Handle: RePEc:hin:complx:1904067
    DOI: 10.1155/2021/1904067
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    Cited by:

    1. 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.
    2. Kanwal, Tanzeela & Hussain, Azhar & Avcı, İbrahim & Etemad, Sina & Rezapour, Shahram & Torres, Delfim F.M., 2024. "Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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