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Stability of a general adaptive immunity HIV infection model with silent infected cell-to-cell spread

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  • AlShamrani, N.H.

Abstract

This paper proposes and analyzes an adaptive immunity HIV infection model. The model describes the interaction between healthy CD4+T cells, silent (latent) infected cells, active infected cells, free HIV particles, Cytotoxic T lymphocytes (CTLs) and antibodies. The healthy CD4+T cells can be infected when they are contacted by one of the following: (i) free HIV particles, and this is known as virus-to-cell (VTC) transmission (ii) silent infected cells, and we call this mode of infection as silent HIV-infected cell-to-cell (CTC) transmission, and (iii) active infected cells, and we call this mechanism active HIV-infected CTC transmission. The incidence rates of the healthy CD4+T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD4+T cells. We first show that the model is well-posed. Then, we show that the model has five equilibria and their existence are governed by five threshold parameters. Under a set of conditions on the general functions and the threshold parameters, we have proven the global asymptotic stability of all equilibria by using Lyapunov’s method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of CTC transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of the healthy CD4+ T cells and increases the concentrations of the infected cells and free HIV particles.

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  • AlShamrani, N.H., 2021. "Stability of a general adaptive immunity HIV infection model with silent infected cell-to-cell spread," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077920308158
    DOI: 10.1016/j.chaos.2020.110422
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    References listed on IDEAS

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    1. Dubey, Preeti & Dubey, Uma S. & Dubey, Balram, 2018. "Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 120-137.
    2. Mojaver, Aida & Kheiri, Hossein, 2015. "Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 258-270.
    3. Hattaf, Khalid & Dutta, Hemen, 2020. "Modeling the dynamics of viral infections in presence of latently infected cells," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    4. Alex Sigal & Jocelyn T. Kim & Alejandro B. Balazs & Erez Dekel & Avi Mayo & Ron Milo & David Baltimore, 2011. "Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy," Nature, Nature, vol. 477(7362), pages 95-98, September.
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    Cited by:

    1. Noura H. AlShamrani & Reham H. Halawani & Wafa Shammakh & Ahmed M. Elaiw, 2023. "Global Properties of HIV-1 Dynamics Models with CTL Immune Impairment and Latent Cell-to-Cell Spread," Mathematics, MDPI, vol. 11(17), pages 1-29, August.
    2. Miled El Hajji & Rahmah Mohammed Alnjrani, 2023. "Periodic Behaviour of HIV Dynamics with Three Infection Routes," Mathematics, MDPI, vol. 12(1), pages 1-23, December.

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