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Asymptotic behaviors of a cell-to-cell HIV-1 infection model perturbed by white noise

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  • Liu, Qun

Abstract

In this paper, we analyze a mathematical model of cell-to-cell HIV-1 infection to CD4+ T cells perturbed by stochastic perturbations. First of all, we investigate that there exists a unique global positive solution of the system for any positive initial value. Then by using Lyapunov analysis methods, we study the asymptotic property of this solution. Moreover, we discuss whether there is a stationary distribution for this system and if it owns the ergodic property. Numerical simulations are presented to illustrate the theoretical results.

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  • Liu, Qun, 2017. "Asymptotic behaviors of a cell-to-cell HIV-1 infection model perturbed by white noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 407-418.
    • Handle: RePEc:eee:phsmap:v:467:y:2017:i:c:p:407-418
    DOI: 10.1016/j.physa.2016.09.061
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    References listed on IDEAS

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    1. Jessica M Conway & Daniel Coombs, 2011. "A Stochastic Model of Latently Infected Cell Reactivation and Viral Blip Generation in Treated HIV Patients," PLOS Computational Biology, Public Library of Science, vol. 7(4), pages 1-15, April.
    2. 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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    Cited by:

    1. 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.
    2. 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.
    3. Ma, Yuanlin & Yu, Xingwang, 2020. "The effect of environmental noise on threshold dynamics for a stochastic viral infection model with two modes of transmission and immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    4. Wang, Yan & Jiang, Daqing & Alsaedi, Ahmed & Hayat, Tasawar, 2018. "Modelling a stochastic HIV model with logistic target cell growth and nonlinear immune response function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 276-292.
    5. Rathinasamy, A. & Chinnadurai, M. & Athithan, S., 2021. "Analysis of exact solution of stochastic sex-structured HIV/AIDS epidemic model with effect of screening of infectives," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 213-237.

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