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Global Dynamics of an HIV Infection Model with Two Classes of Target Cells and Distributed Delays

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  • A. M. Elaiw

Abstract

We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4 + T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types of distributed time delays describing time needed for infection of target cell and virus replication. This model can be seen as a generalization of several models given in the literature describing the interaction of the HIV with one class of target cells, CD4 + T cells. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of the model. We have proven that if the basic reproduction number is less than unity then the uninfected steady state is globally asymptotically stable, and if then the infected steady state exists and it is globally asymptotically stable.

Suggested Citation

  • A. M. Elaiw, 2012. "Global Dynamics of an HIV Infection Model with Two Classes of Target Cells and Distributed Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-13, August.
    • Handle: RePEc:hin:jnddns:253703
    DOI: 10.1155/2012/253703
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    Cited by:

    1. Ahmed M. Elaiw & Safiya F. Alshehaiween & Aatef D. Hobiny, 2019. "Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions," Mathematics, MDPI, vol. 7(9), pages 1-27, September.
    2. 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).
    3. A. M. Elaiw & N. H. AlShamrani & E. Dahy & A. A. Abdellatif & Aeshah A. Raezah, 2023. "Effect of Macrophages and Latent Reservoirs on the Dynamics of HTLV-I and HIV-1 Coinfection," Mathematics, MDPI, vol. 11(3), pages 1-26, January.
    4. A. M. Elaiw & E. Kh. Elnahary, 2019. "Analysis of General Humoral Immunity HIV Dynamics Model with HAART and Distributed Delays," Mathematics, MDPI, vol. 7(2), pages 1-35, February.

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