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Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay

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  • Wang, Jinliang
  • Guo, Min
  • Liu, Xianning
  • Zhao, Zhitao

Abstract

The goal of this paper is to study the threshold dynamics of an HIV-1 viral infection model with cell-mediated immune responses and direct cell-to-cell transmission mechanism. The model demonstrates global threshold dynamics with respect to the reproductive numbers for viral infection ℜ0 and for CTL immune response ℜ1. The proofs of main results come from suitable uses of analyzing the characteristic equation and constructing Lyapunov functionals. Specifically, if ℜ0 < 1, the infection-free equilibrium E0 is locally and globally asymptotically stable, and the viruses are cleared. If ℜ1 < 1 < ℜ0, the CTL-inactivated equilibrium E1 is locally and globally asymptotically stable, and the infection becomes chronic but without persistent CTLs response. If ℜ1 > 1, the CTL-activated equilibrium E2 is locally and globally asymptotically stable, and the infection is chronic with persistent CTLs response. Numerical simulations are performed to support our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:291:y:2016:i:c:p:149-161
    DOI: 10.1016/j.amc.2016.06.032
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    Cited by:

    1. 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.
    2. Sonjoy Pan & Siddhartha P. Chakrabarty, 2020. "Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1673-1695, December.
    3. 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.
    4. Mann Manyombe, M.L. & Mbang, J. & Chendjou, G., 2021. "Stability and Hopf bifurcation of a CTL-inclusive HIV-1 infection model with both viral and cellular infections, and three delays," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    5. Elaiw, Ahmed M. & Alshehaiween, Safiya F. & Hobiny, Aatef D., 2020. "Impact of B-cell impairment on virus dynamics with time delay and two modes of transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    6. 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).
    7. Elaiw, Ahmed M. & Alshaikh, Matuka A., 2020. "Global stability of discrete pathogen infection model with humoral immunity and cell-to-cell transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    8. Xu, Jinhu & Geng, Yan & Zhou, Yicang, 2017. "Global dynamics for an age-structured HIV virus infection model with cellular infection and antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 62-83.
    9. Pan, Sonjoy & Chakrabarty, Siddhartha P., 2022. "Analysis of a reaction–diffusion HCV model with general cell-to-cell incidence function incorporating B cell activation and cure rate," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 431-450.
    10. 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).

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