Stability analysis for a HIV model with cell-to-cell transmission, two immune responses and induced apoptosis

Ru Meng; Yantao Luo; Tingting Zheng; Ru Meng; Yantao Luo; Tingting Zheng

doi:10.3934/math.2024719

AIMS Mathematics

2024, Volume 9, Issue 6: 14786-14806. doi: 10.3934/math.2024719

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Research article

Stability analysis for a HIV model with cell-to-cell transmission, two immune responses and induced apoptosis

1.
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830017, China
2.
College of Medical Engineering and Technology, Xinjiang Medical University, Urumqi 830017, China
3.
Xinjiang Key Laboratory of Applied Mathematics, Urumqi 830017, China

Received: 07 March 2024 Revised: 05 April 2024 Accepted: 11 April 2024 Published: 24 April 2024
MSC : 34D23, 92D20, 92D30

In this paper, a dynamic HIV model with cell-to-cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non-negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number $ R_{0} $ is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection.
- HIV model,
- cell-to-cell transmission,
- induced apoptosis,
- global asymptotic stability,
- Lyapunov function
Citation: Ru Meng, Yantao Luo, Tingting Zheng. Stability analysis for a HIV model with cell-to-cell transmission, two immune responses and induced apoptosis[J]. AIMS Mathematics, 2024, 9(6): 14786-14806. doi: 10.3934/math.2024719

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Abstract

In this paper, a dynamic HIV model with cell-to-cell transmission, two immune responses, and induced apoptosis is proposed and studied. First, the non-negativity and boundedness of the solutions of the model are given, and then the exact expression of the basic reproduction number $ R_{0} $ is obtained by using the next generation matrix method. Second, criteria are obtained for the local stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses. Furthermore, the threshold conditions are also derived for the global asymptotic stability of the disease-free equilibrium, immune response-free equilibrium, and the infected equilibrium with both humoral and cellular immune responses by constructing the suitable Lyapunov function. Finally, some numerical simulations are conducted to verify the theoretical results; the numerical simulation results show that the increase of apoptosis rate had a positive role in the control of viral infection.

References

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