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

Hashem Najafi, Sina Etemad, Nichaphat Patanarapeelert, Joshua Kiddy K. Asamoah, Shahram Rezapour and Thanin Sitthiwirattham
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Hashem Najafi: Department of Mathematics, College of Sciences, Shiraz University, Shiraz 7187919556, Iran
Sina Etemad: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
Nichaphat Patanarapeelert: Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
Joshua Kiddy K. Asamoah: Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Shahram Rezapour: Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz 3751-71379, Iran
Thanin Sitthiwirattham: Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand

Mathematics, 2022, vol. 10, issue 9, 1-32

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.

Keywords: existence; fractal-fractional derivative; HIV-1 infection; Newton polynomial; Adams-Bashforth (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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