Dynamic analysis and optimal control of a fractional order HIV/HTLV co-infection model with HIV-specific antibody immune response

Ruiqing Shi; Yihong Zhang; Ruiqing Shi; Yihong Zhang

doi:10.3934/math.2024462

AIMS Mathematics

2024, Volume 9, Issue 4: 9455-9493. doi: 10.3934/math.2024462

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Dynamic analysis and optimal control of a fractional order HIV/HTLV co-infection model with HIV-specific antibody immune response

Ruiqing Shi ^,,
Yihong Zhang

School of Mathematics and Computer Science, Shanxi Normal University, Taiyuan 030031, China

Received: 28 December 2023 Revised: 23 February 2024 Accepted: 27 February 2024 Published: 07 March 2024
MSC : 26A33, 92B05

In this paper, a fractional order HIV/HTLV co-infection model with HIV-specific antibody immune response is established. Two cases are considered: constant control and optimal control. For the constant control system, the existence and uniqueness of the positive solutions are proved, and then the sufficient conditions for the existence and stability of five equilibriums are obtained. For the second case, the Pontryagin's Maximum Principle is used to analyze the optimal control, and the formula of the optimal solution are derived. After that, some numerical simulations are performed to validate the theoretical prediction. Numerical simulations indicate that in the case of HIV/HTLV co-infection, the concentration of $CD4^{+}T$ cells is no longer suitable as an effective reference data for understanding the development process of the disease. On the contrary, the number of HIV virus particles should be used as an important indicator for reference.
- HIV/HTLV co-infection,
- fractional order,
- basic reproduction number,
- stability,
- optimal control
Citation: Ruiqing Shi, Yihong Zhang. Dynamic analysis and optimal control of a fractional order HIV/HTLV co-infection model with HIV-specific antibody immune response[J]. AIMS Mathematics, 2024, 9(4): 9455-9493. doi: 10.3934/math.2024462

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Abstract

In this paper, a fractional order HIV/HTLV co-infection model with HIV-specific antibody immune response is established. Two cases are considered: constant control and optimal control. For the constant control system, the existence and uniqueness of the positive solutions are proved, and then the sufficient conditions for the existence and stability of five equilibriums are obtained. For the second case, the Pontryagin's Maximum Principle is used to analyze the optimal control, and the formula of the optimal solution are derived. After that, some numerical simulations are performed to validate the theoretical prediction. Numerical simulations indicate that in the case of HIV/HTLV co-infection, the concentration of $CD4^{+}T$ cells is no longer suitable as an effective reference data for understanding the development process of the disease. On the contrary, the number of HIV virus particles should be used as an important indicator for reference.

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