Fractional numerical simulation of mathematical model of HIV-1 infection with stem cell therapy

Noufe H. Aljahdaly; R. A. Alharbey; Noufe H. Aljahdaly; R. A. Alharbey

doi:10.3934/math.2021394

AIMS Mathematics

2021, Volume 6, Issue 7: 6715-6725. doi: 10.3934/math.2021394

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Research article

Fractional numerical simulation of mathematical model of HIV-1 infection with stem cell therapy

Noufe H. Aljahdaly ^{1
,
,},
R. A. Alharbey ²

1.
Mathematics Department, Faculty of Sciences and Arts-Rabigh Campus, King Abdulaziz University, Jeddah, Saudi Arabia
2.
Mathematics Department, Faculty of Science, Al-Sulymania Women's Campus, Jeddah 21589, King AbdulAziz University, Saudi Arabia

Received: 19 November 2020 Accepted: 02 April 2021 Published: 20 April 2021
MSC : 34K25, 34C27, 34D20, 92D25

This paper introduces fractional-order into a mathematical model of HIV infection of CD4$ ^{+} $ T-cells combining with the rate of multiply uninfected CD4$ ^{+} $ T-cells through mitosis and stem cell therapy. The paper shows the theoretical studies including positivity and stability of the solution. In addition, the numerical solutions are obtained and illustrated. The results show that the stem cell's therapy increases the quality of a HIV patient's life only for short time. This results are consistent with medical case studies.
- HIV infection,
- stem cell therapy,
- fractional numerical solution
Citation: Noufe H. Aljahdaly, R. A. Alharbey. Fractional numerical simulation of mathematical model of HIV-1 infection with stem cell therapy[J]. AIMS Mathematics, 2021, 6(7): 6715-6725. doi: 10.3934/math.2021394

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Abstract

This paper introduces fractional-order into a mathematical model of HIV infection of CD4$ ^{+} $ T-cells combining with the rate of multiply uninfected CD4$ ^{+} $ T-cells through mitosis and stem cell therapy. The paper shows the theoretical studies including positivity and stability of the solution. In addition, the numerical solutions are obtained and illustrated. The results show that the stem cell's therapy increases the quality of a HIV patient's life only for short time. This results are consistent with medical case studies.

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