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Periodic Behaviour of HIV Dynamics with Three Infection Routes

Author

Listed:
  • Miled El Hajji

    (Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

  • Rahmah Mohammed Alnjrani

    (Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P.O. Box 80327, Jeddah 21589, Saudi Arabia)

Abstract

In this study, we consider a system of nonlinear differential equations modeling the human immunodeficiency virus type-1 ( HIV -1) in a variable environment. Infected cells were subdivided into two compartments describing both latently and productively infected cells. Thus, three routes of infection were considered including the HIV -to-cell contact, latently infected cell-to-cell contact, and actively infected cell-to-cell contact. The nonnegativity and boundedness of the trajectories of the dynamics were proved. The basic reproduction number was determined through an integral operator. The global stability of steady states is then analyzed using the Lyapunov theory together with LaSalle’s invariance principle for the case of a fixed environment. Similarly, for the case of a variable environment, we showed that the virus-free periodic solution is globally asymptotically stable once R 0 ≤ 1 , while the virus will persist once R 0 > 1 . Finally, some numerical examples are provided illustrating the theoretical investigations.

Suggested Citation

  • Miled El Hajji & Rahmah Mohammed Alnjrani, 2023. "Periodic Behaviour of HIV Dynamics with Three Infection Routes," Mathematics, MDPI, vol. 12(1), pages 1-23, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:123-:d:1310392
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    References listed on IDEAS

    as
    1. AlShamrani, N.H., 2021. "Stability of a general adaptive immunity HIV infection model with silent infected cell-to-cell spread," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    2. Noura H. AlShamrani & Reham H. Halawani & Wafa Shammakh & Ahmed M. Elaiw, 2023. "Global Properties of HIV-1 Dynamics Models with CTL Immune Impairment and Latent Cell-to-Cell Spread," Mathematics, MDPI, vol. 11(17), pages 1-29, August.
    3. Miled El Hajji & Dalal M. Alshaikh & Nada A. Almuallem, 2023. "Periodic Behaviour of an Epidemic in a Seasonal Environment with Vaccination," Mathematics, MDPI, vol. 11(10), pages 1-20, May.
    4. Mahmoud A. Ibrahim & Attila Dénes, 2023. "Stability and Threshold Dynamics in a Seasonal Mathematical Model for Measles Outbreaks with Double-Dose Vaccination," Mathematics, MDPI, vol. 11(8), pages 1-20, April.
    5. Alan S. Perelson & Avidan U. Neumann & Martin Markowitz & John M. Leonard & David D. Ho, 1996. "HIV-1 Dynamics In Vivo: Virion Clearance Rate, Infected Cell Lifespan, and Viral Generation Time," Working Papers 96-02-004, Santa Fe Institute.
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