IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v225y2024icp370-395.html
   My bibliography  Save this article

Stability and backward bifurcation for an HIV model with macrophages and CD4+T cells with latent reservoirs

Author

Listed:
  • Hmarrass, Hanane
  • Qesmi, Redouane

Abstract

Human immunodeficiency virus (HIV) primarily attacks CD4+ T cells but can also attack macrophage and dendritic cells leading to AIDS disease. Antiretroviral therapies are unavoidable to treat patients with HIV. However, the existing therapies failed in eliminating viral particles in infected patients. The establishment of a latency state in these patients could play a major role in this failure. To better understand the impact of different drug therapies on HIV dynamics, we propose an in-host model describing the dynamics of HIV and its interaction with both CD4+T and macrophage cells. This model incorporates the CD4+T latent reservoir as well. Results on the positivity, boundedness, and stability of solutions are shown. Furthermore, the basic reproduction number R0 is obtained using the next generation-matrix method. It is shown that the model is locally asymptotically stable at disease-free equilibrium (DFE) when the basic reproduction number R0<1. Moreover, the model exhibits either forward or backward bifurcation when R0=1. The global asymptotic stability of equilibria is investigated using suitable Lyapunov functions. To study the impact of our model parameters on the model dynamics, a sensitivity analysis is performed using the partial rank correlation coefficient method and the Latin hypercube sampling. Finally, numerical simulations are carried out to assess several drug therapy strategies to reduce HIV infection and improve health outcomes for HIV infected patients.

Suggested Citation

  • Hmarrass, Hanane & Qesmi, Redouane, 2024. "Stability and backward bifurcation for an HIV model with macrophages and CD4+T cells with latent reservoirs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 370-395.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:370-395
    DOI: 10.1016/j.matcom.2024.05.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037847542400199X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.05.026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Yan & Qi, Kai & Jiang, Daqing, 2021. "An HIV latent infection model with cell-to-cell transmission and stochastic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. 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.
    3. Wang, Xia & Song, Xinyu & Tang, Sanyi & Rong, Libin, 2016. "Analysis of HIV models with multiple target cell populations and general nonlinear rates of viral infection and cell death," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 124(C), pages 87-103.
    4. Qesmi, Redouane & Hammoumi, Aayah, 2020. "A stochastic delay model of HIV pathogenesis with reactivation of latent reservoirs," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    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. Ahmed M. Elaiw & Taofeek O. Alade & Saud M. Alsulami, 2018. "Global Stability of Within-Host Virus Dynamics Models with Multitarget Cells," Mathematics, MDPI, vol. 6(7), pages 1-19, July.
    2. Qi, Kai & Jiang, Daqing & Hayat, Tasawar & Alsaedi, Ahmed, 2021. "Virus dynamic behavior of a stochastic HIV/AIDS infection model including two kinds of target cell infections and CTL immune responses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 548-570.
    3. 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.
    4. Lu, Xiaosun & Huang, Yangxin & Zhu, Yiliang, 2016. "Finite mixture of nonlinear mixed-effects joint models in the presence of missing and mismeasured covariate, with application to AIDS studies," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 119-130.
    5. 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.
    6. Samson, Adeline & Lavielle, Marc & Mentre, France, 2006. "Extension of the SAEM algorithm to left-censored data in nonlinear mixed-effects model: Application to HIV dynamics model," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1562-1574, December.
    7. Nicolas Rapin & Ole Lund & Massimo Bernaschi & Filippo Castiglione, 2010. "Computational Immunology Meets Bioinformatics: The Use of Prediction Tools for Molecular Binding in the Simulation of the Immune System," PLOS ONE, Public Library of Science, vol. 5(4), pages 1-14, April.
    8. Derksen, Laura & Muula, Adamson & van Oosterhout, Joep, 2022. "Love in the time of HIV: How beliefs about externalities impact health behavior," Journal of Development Economics, Elsevier, vol. 159(C).
    9. Liu, Qun & Jiang, Daqing, 2020. "Dynamical behavior of a higher order stochastically perturbed HIV/AIDS model with differential infectivity and amelioration," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    10. Baleanu, Dumitru & Hasanabadi, Manijeh & Mahmoudzadeh Vaziri, Asadollah & Jajarmi, Amin, 2023. "A new intervention strategy for an HIV/AIDS transmission by a general fractional modeling and an optimal control approach," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    11. Jessica M Conway & Daniel Coombs, 2011. "A Stochastic Model of Latently Infected Cell Reactivation and Viral Blip Generation in Treated HIV Patients," PLOS Computational Biology, Public Library of Science, vol. 7(4), pages 1-15, April.
    12. James B Gilmore & Anthony D Kelleher & David A Cooper & John M Murray, 2013. "Explaining the Determinants of First Phase HIV Decay Dynamics through the Effects of Stage-dependent Drug Action," PLOS Computational Biology, Public Library of Science, vol. 9(3), pages 1-12, March.
    13. Chowdhury, Sourav & Ghosh, Jayanta Kumar & Ghosh, Uttam, 2024. "Co-infection dynamics between HIV-HTLV-I disease with the effects of Cytotoxic T-lymphocytes, saturated incidence rate and study of optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 195-218.
    14. Dagne Getachew & Huang Yangxin, 2012. "Bayesian inference for a nonlinear mixed-effects Tobit model with multivariate skew-t distributions: application to AIDS studies," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-24, September.
    15. Han, Cheng & Wang, Yan & Jiang, Daqing, 2023. "Dynamics analysis of a stochastic HIV model with non-cytolytic cure and Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    16. Li, Hui-zhong & Liu, Xiang-dong & Yan, Rui & Liu, Cheng, 2020. "Hopf bifurcation analysis of a tumor virotherapy model with two time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 553(C).
    17. Tao Lu & Yangxin Huang & Min Wang & Feng Qian, 2014. "A refined parameter estimating approach for HIV dynamic model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(8), pages 1645-1657, August.
    18. Attaullah, & Jan, Rashid & Yüzbaşı, Şuayip, 2021. "Dynamical behaviour of HIV Infection with the influence of variable source term through Galerkin method," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    19. Hanze Zhang & Yangxin Huang, 2020. "Quantile regression-based Bayesian joint modeling analysis of longitudinal–survival data, with application to an AIDS cohort study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(2), pages 339-368, April.
    20. Rebecca M. D'Amato & Richard T. D'Aquila & Lawrence M. Wein, 2000. "Management of Antiretroviral Therapy for HIV Infection: Analyzing When to Change Therapy," Management Science, INFORMS, vol. 46(9), pages 1200-1213, September.

    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:eee:matcom:v:225:y:2024:i:c:p:370-395. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.