IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v265y2015icp1067-1089.html
   My bibliography  Save this article

Global properties of delayed-HIV dynamics models with differential drug efficacy in cocirculating target cells

Author

Listed:
  • Elaiw, A.M.
  • Almuallem, N.A.

Abstract

The objective of this work is to investigate the qualitative behaviors of three HIV dynamical models with two types of cocirculating target cells and intracellular discrete time delay. In the two types of target cells, the drug efficacy is assumed to be different. The models take into account both short-lived infected cells and long-lived chronically infected cells. The incidence rate of infection is given by bilinear and saturation functional response in the first and second model, respectively, while it is given by a general function in the third model. Lyapunov functionals are constructed and LaSalle’s invariance principle is applied to prove the global asymptotic stability of all equilibria of the models. In the first two models, we have derived the basic reproduction number R0. It has been proven that the disease-free equilibrium is globally asymptotically stable (GAS) when R0 ≤ 1, and the endemic equilibrium is GAS when R0 > 1. For the third model, we have derived R0 and established a set of sufficient conditions for global stability of both disease-free and endemic equilibria of the model. At the end theoretical results have been checked by numerical simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:1067-1089
    DOI: 10.1016/j.amc.2015.06.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315007870
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.06.011?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 & 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Ahmed M. Elaiw & Safiya F. Alshehaiween & Aatef D. Hobiny, 2019. "Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions," Mathematics, MDPI, vol. 7(9), pages 1-27, September.
    2. Elaiw, A.M. & Al Agha, A.D., 2021. "Global dynamics of SARS-CoV-2/cancer model with immune responses," Applied Mathematics and Computation, Elsevier, vol. 408(C).
    3. Elaiw, Ahmed M. & Alshehaiween, Safiya F. & Hobiny, Aatef D., 2020. "Impact of B-cell impairment on virus dynamics with time delay and two modes of transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    4. Elaiw, Ahmed M. & Alshaikh, Matuka A., 2020. "Global stability of discrete pathogen infection model with humoral immunity and cell-to-cell transmission," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    5. Elaiw, A.M. & Hobiny, A.D. & Al Agha, A.D., 2020. "Global dynamics of reaction-diffusion oncolytic M1 virotherapy with immune response," Applied Mathematics and Computation, Elsevier, vol. 367(C).
    6. 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).

    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. 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. Ahmed M. Elaiw & Noura H. AlShamrani, 2020. "HTLV/HIV Dual Infection: Modeling and Analysis," Mathematics, MDPI, vol. 9(1), pages 1-32, December.
    11. 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.
    12. 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.
    13. Chia Hsiang Chen & Vincent Gau & Donna D Zhang & Joseph C Liao & Fei-Yue Wang & Pak Kin Wong, 2010. "Statistical Metamodeling for Revealing Synergistic Antimicrobial Interactions," PLOS ONE, Public Library of Science, vol. 5(11), pages 1-7, November.
    14. Christian E. Galarza & Luis M. Castro & Francisco Louzada & Victor H. Lachos, 2020. "Quantile regression for nonlinear mixed effects models: a likelihood based perspective," Statistical Papers, Springer, vol. 61(3), pages 1281-1307, June.
    15. Ahmed M. Elaiw & Safiya F. Alshehaiween & Aatef D. Hobiny, 2019. "Global Properties of a Delay-Distributed HIV Dynamics Model Including Impairment of B-Cell Functions," Mathematics, MDPI, vol. 7(9), pages 1-27, September.
    16. 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.
    17. 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.
    18. 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).
    19. 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.
    20. 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.

    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:265:y:2015:i:c:p:1067-1089. 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.