IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v409y2021ics0096300321004999.html
   My bibliography  Save this article

An in-host HIV-1 infection model incorporating quiescent and activated CD4+ T cells as well as CTL response

Author

Listed:
  • Sutimin,
  • Wijaya, Karunia Putra
  • Páez Chávez, Joseph
  • Tian, Tianhai

Abstract

A mathematical model is proposed to capture the implication of quiescent and activated CD4+ T cells as well as the cytotoxic T lymphocyte (CTL) response on HIV-1 infection in an early stage. It underlies the different mechanisms behind the productive and latent infection, whereby virion-cell contact, cell-cell contact, immune response, slow-kinetic viral reverse transcription in quiescent cells, lytic death, pyroptosis, and virus survival play their significant role within. The existence, uniqueness, and global stability of both the virus-free and endemic equilibrium with respect to the magnitudes of the basic reproduction ratio are studied. Due to technical difficulties in revealing the close form of the endemic equilibrium, determining the whole picture of forward bifurcation around the virus-free states is accomplished with the aid of bifurcation theory. The sufficient condition for the forward bifurcation is satisfied by the choices of the parameter values, and simulations are presented to illustrate the analytical findings. In an effort to study which parameters can be attacked through the applications of RTIs, PIs, and vaccination toward foremost reduction of the basic reproduction ratio, a local sensitivity analysis is presented. Finally, a model version combining productive and latent infection, also treating disparate time scales from CD4+ T cells and CTLs as well as virions is studied. As long as any solution trajectory is initiated around the stable part of the critical manifold, it approaches and stays around the manifold and eventually lands in the manifold when the lifespans of CTLs and virions are comparably small. If the corresponding basic reproduction ratio is sufficiently large, then not only does the endemic equilibrium locate in the unstable part of the critical manifold, but all the solution trajectories (from the stable part) converge to the equilibrium due to global stability, indicating the existence of canards.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300321004999
    DOI: 10.1016/j.amc.2021.126410
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300321004999
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2021.126410?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. 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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Singh, Harendra, 2021. "Analysis of drug treatment of the fractional HIV infection model of CD4+ T-cells," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    8. 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.
    9. Jianwei Chen, 2010. "Modelling long‐term human immunodeficiency virus dynamic models with application to acquired immune deficiency syndrome clinical study," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 59(5), pages 805-820, November.
    10. Musharif Ahmed & Muhammad Aamer Saleem & Muhammad Zubair & Ijaz Mansoor Qureshi & Saad Zafar, 2022. "Stability analysis and memetic computation using differential evolution for in-host HIV model," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(1), pages 76-91, March.
    11. Dubey, Preeti & Dubey, Uma S. & Dubey, Balram, 2018. "Modeling the role of acquired immune response and antiretroviral therapy in the dynamics of HIV infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 144(C), pages 120-137.
    12. Yang, Junyuan & Wang, Xiaoyan, 2019. "Dynamics and asymptotical profiles of an age-structured viral infection model with spatial diffusion," Applied Mathematics and Computation, Elsevier, vol. 360(C), pages 236-254.
    13. Jessica M Conway & Alan S Perelson & Jonathan Z Li, 2019. "Predictions of time to HIV viral rebound following ART suspension that incorporate personal biomarkers," PLOS Computational Biology, Public Library of Science, vol. 15(7), pages 1-26, July.
    14. Chen, Wei & Zhang, Long & Wang, Ning & Teng, Zhidong, 2024. "Bifurcation analysis and chaos for a double-strains HIV coinfection model with intracellular delays, saturated incidence and Logistic growth," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 617-641.
    15. Guo, Wenjuan & Zhang, Qimin, 2021. "Explicit numerical approximation for an impulsive stochastic age-structured HIV infection model with Markovian switching," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 86-115.
    16. González, Ramón E.R. & Coutinho, Sérgio & Zorzenon dos Santos, Rita Maria & de Figueirêdo, Pedro Hugo, 2013. "Dynamics of the HIV infection under antiretroviral therapy: A cellular automata approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4701-4716.
    17. Bernhard Konrad & Naveen Vaidya & Robert Smith?, 2011. "Modelling Mutation to a Cytotoxic T-lymphocyte HIV Vaccine," Mathematical Population Studies, Taylor & Francis Journals, vol. 18(2), pages 122-149.
    18. Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
    19. Ulrich D Kadolsky & Becca Asquith, 2010. "Quantifying the Impact of Human Immunodeficiency Virus-1 Escape From Cytotoxic T-Lymphocytes," PLOS Computational Biology, Public Library of Science, vol. 6(11), pages 1-11, November.
    20. Mélanie Prague & Daniel Commenges & Julia Drylewicz & Rodolphe Thiébaut, 2012. "Treatment Monitoring of HIV-Infected Patients based on Mechanistic Models," Biometrics, The International Biometric Society, vol. 68(3), pages 902-911, 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:apmaco:v:409:y:2021:i:c:s0096300321004999. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.