IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2023i1p123-d1310392.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/1/123/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/1/123/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Sutimin, & Wijaya, Karunia Putra & Páez Chávez, Joseph & Tian, Tianhai, 2021. "An in-host HIV-1 infection model incorporating quiescent and activated CD4+ T cells as well as CTL response," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    3. Iraj Hosseini & Feilim Mac Gabhann, 2012. "Multi-Scale Modeling of HIV Infection in vitro and APOBEC3G-Based Anti-Retroviral Therapy," PLOS Computational Biology, Public Library of Science, vol. 8(2), pages 1-17, February.
    4. Amer Hassan Albargi & Miled El Hajji, 2023. "Bacterial Competition in the Presence of a Virus in a Chemostat," Mathematics, MDPI, vol. 11(16), pages 1-17, August.
    5. E Fabian Cardozo & Adriana Andrade & John W Mellors & Daniel R Kuritzkes & Alan S Perelson & Ruy M Ribeiro, 2017. "Treatment with integrase inhibitor suggests a new interpretation of HIV RNA decay curves that reveals a subset of cells with slow integration," PLOS Pathogens, Public Library of Science, vol. 13(7), pages 1-18, July.
    6. Nicola Bellomo & Richard Bingham & Mark A.J. Chaplain & Giovanni Dosi & Guido Forni & Damian A. Knopoff & John Lowengrub & Reidun Twarock & Maria Enrica Virgillito, 2020. "A multi-scale model of virus pandemic: Heterogeneous interactive entities in a globally connected world," LEM Papers Series 2020/16, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    7. Sun, Hongquan & Li, Jin, 2020. "A numerical method for a diffusive virus model with general incidence function, cell-to-cell transmission and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    8. 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.
    9. Arthur, Joseph & Attarian, Adam & Hamilton, Franz & Tran, Hien, 2018. "Nonlinear Kalman filtering for censored observations," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 155-166.
    10. Mojaver, Aida & Kheiri, Hossein, 2015. "Mathematical analysis of a class of HIV infection models of CD4+ T-cells with combined antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 258-270.
    11. Chávez, Joseph Páez & Wijaya, Karunia Putra & Pinto, Carla M.A. & Burgos-Simón, Clara, 2022. "A model for type I diabetes in an HIV-infected patient under highly active antiretroviral therapy," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    12. Marc Lavielle & Adeline Samson & Ana Karina Fermin & France Mentré, 2011. "Maximum Likelihood Estimation of Long-Term HIV Dynamic Models and Antiviral Response," Biometrics, The International Biometric Society, vol. 67(1), pages 250-259, March.
    13. Yu Shi & Zizhao Zhang & Weng Kee Wong, 2019. "Particle swarm based algorithms for finding locally and Bayesian D-optimal designs," Journal of Statistical Distributions and Applications, Springer, vol. 6(1), pages 1-17, December.
    14. Wang, Jinliang & Guo, Min & Liu, Xianning & Zhao, Zhitao, 2016. "Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 149-161.
    15. Precharattana, Monamorn & Triampo, Wannapong, 2014. "Modeling dynamics of HIV infected cells using stochastic cellular automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 407(C), pages 303-311.
    16. Heffernan, J.M. & Keeling, M.J., 2008. "An in-host model of acute infection: Measles as a case study," Theoretical Population Biology, Elsevier, vol. 73(1), pages 134-147.
    17. Singh, Harendra, 2021. "Analysis of drug treatment of the fractional HIV infection model of CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    18. A. Adam Ding & Hulin Wu, 2000. "A Comparison Study of Models and Fitting Procedures for Biphasic Viral Dynamics in HIV-1 Infected Patients Treated with Antiviral Therapies," Biometrics, The International Biometric Society, vol. 56(1), pages 293-300, March.
    19. Xu, Jinhu & Geng, Yan & Zhou, Yicang, 2017. "Global dynamics for an age-structured HIV virus infection model with cellular infection and antiretroviral therapy," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 62-83.
    20. Yangxin Huang & Dacheng Liu & Hulin Wu, 2006. "Hierarchical Bayesian Methods for Estimation of Parameters in a Longitudinal HIV Dynamic System," Biometrics, The International Biometric Society, vol. 62(2), pages 413-423, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:123-:d:1310392. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.