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Mathematical modeling, analysis and numerical simulation of HIV: The influence of stochastic environmental fluctuations on dynamics

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  • Qi, Haokun
  • Meng, Xinzhu

Abstract

In this paper, we explore the effect of the stochastic environmental fluctuations on the dynamics of an HIV system with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity. First, the existence and uniqueness of the global positive solution and the stochastically ultimate boundedness of the stochastic HIV system are discussed. Then, by constructing a series of suitable Lyapunov functions and using some differential inequality techniques, the long-time asymptotic properties of the stochastic delayed system are investigated. These properties reveal that the solution of the stochastic system oscillates around the equilibrium points of the deterministic system when the intensity of environmental perturbations is appropriate. In addition, the sufficient condition for persistence in mean and extinction of the stochastic system are established under the suitable condition. At last, numerous numerical simulations show that the HIV will disappear if the intensity of environmental fluctuations is sufficiently large. This means that appropriate stochastic environmental fluctuations can effectively suppress the outbreak of HIV.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:700-719
    DOI: 10.1016/j.matcom.2021.03.027
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    1. Ji, Chunyan & Liu, Qun & Jiang, Daqing, 2018. "Dynamics of a stochastic cell-to-cell HIV-1 model with distributed delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1053-1065.
    2. Liu, Qun & Jiang, Daqing & Shi, Ningzhong, 2018. "Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 310-325.
    3. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    4. Wang, Jinliang & Guo, Min & Liu, Xianning & Zhao, Zhitao, 2016. "Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 149-161.
    5. 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.
    6. Alan S. Perelson & Avidan U. Neumann & Martin Markowitz & John M. Leonard & David D. Ho, 1996. "HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time," Working Papers 96-02-004, Santa Fe Institute.
    7. Feng, Tao & Qiu, Zhipeng & Meng, Xinzhu & Rong, Libin, 2019. "Analysis of a stochastic HIV-1 infection model with degenerate diffusion," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 437-455.
    8. Lin, Jiazhe & Xu, Rui & Tian, Xiaohong, 2017. "Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 516-530.
    9. Guo, Wenjuan & Zhang, Qimin, 2021. "Explicit numerical approximation for an impulsive stochastic age-structured HIV infection model with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 86-115.
    10. Aaron A. King & Edward L. Ionides & Mercedes Pascual & Menno J. Bouma, 2008. "Inapparent infections and cholera dynamics," Nature, Nature, vol. 454(7206), pages 877-880, August.
    11. Zhang, Yue & Li, Yang & Zhang, Qingling & Li, Aihua, 2018. "Behavior of a stochastic SIR epidemic model with saturated incidence and vaccination rules," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 178-187.
    12. Xiaoting Fan & Yi Song & Wencai Zhao, 2018. "Modeling Cell-to-Cell Spread of HIV-1 with Nonlocal Infections," Complexity, Hindawi, vol. 2018, pages 1-10, August.
    13. Jeffrey Sachs & Pia Malaney, 2002. "The economic and social burden of malaria," Nature, Nature, vol. 415(6872), pages 680-685, February.
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    5. 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).
    6. 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).

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