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Stability and Hopf bifurcation of a CTL-inclusive HIV-1 infection model with both viral and cellular infections, and three delays

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  • Mann Manyombe, M.L.
  • Mbang, J.
  • Chendjou, G.

Abstract

In this paper, we assess the viral dynamics of a HIV-1 mathematical model that incorporates virus-to-cell and cell-to-cell transmissions, CTL response immune and three delays describing intracellular delays and immune response delay. The model includes a constant production rate of CTLs export from thymus. Our focus is on the effect of three delays on the infection dynamics. The basic reproduction number, R0, which depends on the intracellular delay, is shown to determine stability conditions of the model steady states. Employing a suitable Lyapunov function, we show that the infection-free equilibrium is globally asymptotically stable including the three time delays when the basic reproduction number is a smaller amount than one. Additionally, for the special case where there is no immune delay in the model, the global stability of the unique endemic equilibrium is also established (using suitable Lyapunov functions) whenever R0 is larger than one. Furthermore, we study the local and hopf bifurcation of the endemic equilibrium in general case with all delays being positive. When the three delays are positive, we determine some conditions for stability switches of the endemic equilibrium by using the immune delay as a bifurcation parameter. Numerical simulations indicate that an increase of the immune delay can stabilize and/or destabilize the endemic equilibrium.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:144:y:2021:i:c:s0960077921000485
    DOI: 10.1016/j.chaos.2021.110695
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    References listed on IDEAS

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    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. Li, Xiuling & Wei, Junjie, 2005. "On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 519-526.
    3. Mendy, A. & Tewa, J.J. & Lam, M. & Tchinda Mouofo, P., 2019. "Hopf bifurcation in a grazing system with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 163(C), pages 90-129.
    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.
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    Cited by:

    1. Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. 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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