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A. M. Elaiw, N. H. AlShamrani. STABILITY OF A DELAYED ADAPTIVE IMMUNITY HIV INFECTION MODEL WITH SILENT INFECTED CELLS AND CELLULAR INFECTION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 964-1005. doi: 10.11948/20200124
Citation: A. M. Elaiw, N. H. AlShamrani. STABILITY OF A DELAYED ADAPTIVE IMMUNITY HIV INFECTION MODEL WITH SILENT INFECTED CELLS AND CELLULAR INFECTION[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 964-1005. doi: 10.11948/20200124
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STABILITY OF A DELAYED ADAPTIVE IMMUNITY HIV INFECTION MODEL WITH SILENT INFECTED CELLS AND CELLULAR INFECTION

  • 1.

    Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

  • 2.

    Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut, Egypt

  • 3.

    Department of Mathematics, Faculty of Science, University of Jeddah,P.

    Abstract

  • In this paper we formulate a mathematical model to investigate the within-host HIV dynamics under the effect of both antibody and Cytotoxic T lymphocytes (CTL) immune responses. The model consists of five components: healthy CD$ 4^{+} $T cells, silent infected cells, active infected cells, free HIV particles, CTLs and antibodies. The healthy CD$ 4^{+} $T cells can be infected when they are contacted by (ⅰ) free HIV particles, (ⅱ) active infected cells, and (ⅲ) silent infected cells. The model is an improvement of some existing HIV infection models with both virus-to-cell (VTC) and cell-to-cell (CTC) transmissions by incorporating the incidence between the silent infected cells and healthy CD$ 4^{+} $T cells. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We have shown that the model has five equilibria and their existence is governed by five threshold parameters. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have presented numerical simulations to illustrate the theoretical results. We have studied the effects of CTC transmission and time delays on the dynamical behavior of the system. We have shown that inclusion of time delay can significantly increase the concentration of the uninfected CD4$ ^{+} $ T cells and reduce the concentrations of the infected cells and free HIV particles. While the inclusion of CTC transmission decreases the concentration of the uninfected CD4$ ^{+} $ T cells and increases the concentrations of the infected cells and free HIV particles.
    MSC: 34D20, 34D23, 37N25, 92B05
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