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Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells

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  • Elaiw, A.M.
  • Almuallem, N.A.

Abstract

The objective of this work is to investigate the qualitative behaviors of three HIV dynamical models with two types of cocirculating target cells and intracellular discrete time delay. In the two types of target cells, the drug efficacy is assumed to be different. The models take into account both short-lived infected cells and long-lived chronically infected cells. The incidence rate of infection is given by bilinear and saturation functional response in the first and second model, respectively, while it is given by a general function in the third model. Lyapunov functionals are constructed and LaSalle’s invariance principle is applied to prove the global asymptotic stability of all equilibria of the models. In the first two models, we have derived the basic reproduction number R0. It has been proven that the disease-free equilibrium is globally asymptotically stable (GAS) when R0 ≤ 1, and the endemic equilibrium is GAS when R0 > 1. For the third model, we have derived R0 and established a set of sufficient conditions for global stability of both disease-free and endemic equilibria of the model. At the end theoretical results have been checked by numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:1067-1089
    DOI: 10.1016/j.amc.2015.06.011
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    References listed on IDEAS

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    1. 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.
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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, A.M. & Al Agha, A.D., 2021. "Global dynamics of SARS-CoV-2/cancer model with immune responses," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    3. Elaiw, Ahmed M. & Alshehaiween, Safiya F. & Hobiny, Aatef D., 2020. "Impact of B-cell impairment on virus dynamics with time delay and two modes of transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. 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).
    5. Elaiw, A.M. & Hobiny, A.D. & Al Agha, A.D., 2020. "Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immune response," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    6. Elaiw, Ahmed M. & Al Agha, Afnan D., 2019. "Stability of a general HIV-1 reaction–diffusion model with multiple delays and immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).

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