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Stability of a general HIV-1 reaction–diffusion model with multiple delays and immune response

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  • Elaiw, Ahmed M.
  • Al Agha, Afnan D.

Abstract

The aim of this paper is to study a general HIV-1 reaction–diffusion model with space-dependent diffusion coefficients and antibody immune response. The model contains four discrete time delays and three categories of infected cells: Latently infected cells, short-lived productively infected cells and long-lived productively infected cells. The effect of highly active antiretroviral therapies (HAART) used to treat HIV-1 is incorporated into the model. The existence, non-negativity and boundedness of solutions are studied in order to verify the well-posedness of the model. All possible equilibria of the model are evaluated and the threshold parameters needed for their existence and stability are investigated. The global asymptotic stability of the corresponding equilibria are proved by building suitable Lyapunov functionals. The numerical simulations are conducted in order to confirm the theoretical results and show the behavior of solutions in space and time.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:536:y:2019:i:c:s0378437119314839
    DOI: 10.1016/j.physa.2019.122593
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Xiaohong Tian & Rui Xu, 2011. "Global Stability of a Virus Infection Model with Time Delay and Absorption," Discrete Dynamics in Nature and Society, Hindawi, vol. 2011, pages 1-20, June.
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    Citations

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    Cited by:

    1. Noura H. AlShamrani & Ahmed Elaiw & Aeshah A. Raezah & Khalid Hattaf, 2023. "Global Dynamics of a Diffusive Within-Host HTLV/HIV Co-Infection Model with Latency," Mathematics, MDPI, vol. 11(6), pages 1-47, March.

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