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Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions

Author

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  • Ahmed M. Elaiw

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

  • Safiya F. Alshehaiween

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Taibah University, P.O. Box 344, Medina 42353, Saudi Arabia)

  • Aatef D. Hobiny

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

Abstract

In this paper, we construct an Human immunodeficiency virus (HIV) dynamics model with impairment of B-cell functions and the general incidence rate. We incorporate three types of infected cells, (i) latently-infected cells, which contain the virus, but do not generate HIV particles, (ii) short-lived productively-infected cells, which live for a short time and generate large numbers of HIV particles, and (iii) long-lived productively-infected cells, which live for a long time and generate small numbers of HIV particles. The model considers five distributed time delays to characterize the time between the HIV contact of an uninfected CD4 + T-cell and the creation of mature HIV. The nonnegativity and boundedness of the solutions are proven. The model admits two equilibria, infection-free equilibrium E P 0 and endemic equilibrium E P 1 . We derive the basic reproduction number R 0 , which determines the existence and stability of the two equilibria. The global stability of each equilibrium is proven by utilizing the Lyapunov function and LaSalle’s invariance principle. We prove that if R 0 < 1 , then E P 0 is globally asymptotically stable, and if R 0 > 1 , then E P 1 is globally asymptotically stable. These theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions, time delays, and antiviral treatment on the HIV dynamics are studied. We show that if the functions of B-cells are impaired, then the concentration of HIV is increased in the plasma. Moreover, we observe that the time delay has a similar effect to drug efficacy. This gives some impression for developing a new class of treatments to increase the delay period and then suppress the HIV replication.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:837-:d:265874
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    References listed on IDEAS

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    1. 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.
    2. Wang, Tianlei & Hu, Zhixing & Liao, Fucheng & Ma, Wanbiao, 2013. "Global stability analysis for delayed virus infection model with general incidence rate and humoral immunity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 89(C), pages 13-22.
    3. 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.
    4. Alan S. Perelson & Paulina Essunger & Yunzhen Cao & Mika Vesanen & Arlene Hurley & Kalle Saksela & Martin Markowitz & David D. Ho, 1997. "Decay characteristics of HIV-1-infected compartments during combination therapy," Nature, Nature, vol. 387(6629), pages 188-191, May.
    5. Liu, Huijuan & Zhang, Jia-Fang, 2019. "Dynamics of two time delays differential equation model to HIV latent infection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 384-395.
    6. Miao, Hui & Abdurahman, Xamxinur & Teng, Zhidong & Zhang, Long, 2018. "Dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and humoral immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 280-291.
    7. 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.
    8. Elaiw, A.M. & Almuallem, N.A., 2015. "Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1067-1089.
    9. A. M. Elaiw & A. A. Almatrafi & A. D. Hobiny & K. Hattaf, 2019. "Global Properties of a General Latent Pathogen Dynamics Model with Delayed Pathogenic and Cellular Infections," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-18, July.
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    Cited by:

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    2. Ahmed Elaiw & Afnan Al Agha, 2020. "Global Analysis of a Reaction-Diffusion Within-Host Malaria Infection Model with Adaptive Immune Response," Mathematics, MDPI, vol. 8(4), pages 1-32, April.

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