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A stochastic HIV infection model with T-cell proliferation and CTL immune response

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  • Wang, Yan
  • Jiang, Daqing
  • Hayat, Tasawar
  • Ahmad, Bashir

Abstract

A stochastic HIV infection model with T-cell proliferation and CTL immune response is formulated to investigate the effect of environmental fluctuations on the HIV viral dynamics. We obtain that the model solution is positive and global, and analyze the extinction of the model. We also derive a critical condition R0s, when R0s is greater than one, the existence of ergodic stationary distribution of the model solution is established by constructing suitable Lyapunov functions. Numerical simulations are performed to investigate the effect of white noises on model behavior, we investigate that the small intensities of white noise can maintain the irregular recurrence of HIV virus and CTL immune response, while the larger ones may be help to the elimination of the virus and CTL immune response, and the medium intensities of white noises may cause both the persistence and extinction on model dynamics behavior.

Suggested Citation

  • Wang, Yan & Jiang, Daqing & Hayat, Tasawar & Ahmad, Bashir, 2017. "A stochastic HIV infection model with T-cell proliferation and CTL immune response," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 477-493.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:477-493
    DOI: 10.1016/j.amc.2017.07.062
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    1. David D. Ho & Avidan U. Neumann & Alan S. Perelson & Wen Chen & John M. Leonard & Martin Markowitz, 1995. "Rapid Turnover of Plasma Virions and CD4 Lymphocytes in HIV-1 Infection," Working Papers 95-01-002, Santa Fe Institute.
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    1. Cheng, Yan & Li, Mingtao & Zhang, Fumin, 2019. "A dynamics stochastic model with HIV infection of CD4+ T-cells driven by Lévy noise," Chaos, Solitons & Fractals, Elsevier, vol. 129(C), pages 62-70.
    2. Liu, Qun & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2018. "Stationary distribution and extinction of a stochastic HIV-1 model with Beddington–DeAngelis infection rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 414-426.
    3. Zhang, Tongqian & Xu, Xinna & Wang, Xinzeng, 2023. "Dynamic analysis of a cytokine-enhanced viral infection model with time delays and CTL immune response," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
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    5. Akdim, Khadija & Ez-zetouni, Adil & Danane, Jaouad & Allali, Karam, 2020. "Stochastic viral infection model with lytic and nonlytic immune responses driven by Lévy noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    6. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    7. Qesmi, Redouane & Hammoumi, Aayah, 2020. "A stochastic delay model of HIV pathogenesis with reactivation of latent reservoirs," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    8. Tan, Yiping & Cai, Yongli & Sun, Xiaodan & Wang, Kai & Yao, Ruoxia & Wang, Weiming & Peng, Zhihang, 2022. "A stochastic SICA model for HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
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    10. Wang, Yan & Qi, Kai & Jiang, Daqing, 2021. "An HIV latent infection model with cell-to-cell transmission and stochastic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    11. Lu, Minmin & Wang, Yan & Jiang, Daqing, 2021. "Stationary distribution and probability density function analysis of a stochastic HIV model with cell-to-cell infection," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    12. Chinnadurai, M. & Fatini, Mohamed El & Rathinasamy, A., 2023. "Stochastic perturbation to 2-LTR dynamical model in HIV infected patients," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 473-497.
    13. Arshad, Sadia & Defterli, Ozlem & Baleanu, Dumitru, 2020. "A second order accurate approximation for fractional derivatives with singular and non-singular kernel applied to a HIV model," Applied Mathematics and Computation, Elsevier, vol. 374(C).
    14. Prakash, M. & Rakkiyappan, R. & Manivannan, A. & Cao, Jinde, 2019. "Dynamical analysis of antigen-driven T-cell infection model with multiple delays," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 266-281.
    15. Shi, Zhenfeng & Jiang, Daqing, 2022. "Dynamical behaviors of a stochastic HTLV-I infection model with general infection form and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    16. Qi, Haokun & Meng, Xinzhu, 2021. "Mathematical modeling, analysis and numerical simulation of HIV: The influence of stochastic environmental fluctuations on dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 700-719.
    17. Shi, Ruiqing & Lu, Ting & Wang, Cuihong, 2021. "Dynamic analysis of a fractional-order model for HIV with drug-resistance and CTL immune response," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 509-536.

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