IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v212y2023icp159-181.html
   My bibliography  Save this article

Dynamic analysis of HIV model with a general incidence, CTLs immune response and intracellular delays

Author

Listed:
  • Chen, Chong
  • Zhou, Yinggao

Abstract

An HIV model with a general incidence, CTLs immune response and intracellular delays is considered. By using Lyapunov functions and LaSalle’s invariance principle, it is shown that when time delay is equal to zero or not, the reproductive number R0 is a threshold determining the global dynamics. These theoretical results are supported with numerical simulations. In order to effectively control the spread of HIV, A multi-pathways HIV-1 infection model without time delay is analyzed with three controls. The necessary conditions for optimal control are given by Pontryagin’s Maximum Principle. The optimality system is derived and solved numerically using the Euler procedure. Finally, numerical simulation shows the role of the best treatment in controlling the severity of HIV.

Suggested Citation

  • Chen, Chong & Zhou, Yinggao, 2023. "Dynamic analysis of HIV model with a general incidence, CTLs immune response and intracellular delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 159-181.
    • Handle: RePEc:eee:matcom:v:212:y:2023:i:c:p:159-181
    DOI: 10.1016/j.matcom.2023.04.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423001970
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.04.029?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. ., 2021. "A Labor Perspective on Globalization," Chapters, in: Neoliberalism and the Road to Inequality and Stagnation, chapter 16, pages 253-270, Edward Elgar Publishing.
    2. Lin, Jiazhe & Xu, Rui & Tian, Xiaohong, 2017. "Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 516-530.
    3. ., 2021. "Global climate change," Chapters, in: The Global Rise of the Modern Plug-In Electric Vehicle, chapter 5, pages 143-181, Edward Elgar Publishing.
    4. ., 2021. "Labor in The Global Economy," Chapters, in: Neoliberalism and the Road to Inequality and Stagnation, chapter 17, pages 271-273, Edward Elgar Publishing.
    5. HyunJun Na & Murat Sakir Erogul, 2021. "A global review of female entrepreneurial finance," International Journal of Globalisation and Small Business, Inderscience Enterprises Ltd, vol. 12(1), pages 59-82.
    6. Alex Sigal & Jocelyn T. Kim & Alejandro B. Balazs & Erez Dekel & Avi Mayo & Ron Milo & David Baltimore, 2011. "Cell-to-cell spread of HIV permits ongoing replication despite antiretroviral therapy," Nature, Nature, vol. 477(7362), pages 95-98, September.
    7. Dhar, Mausumi & Samaddar, Shilpa & Bhattacharya, Paritosh & Upadhyay, Ranjit Kumar, 2019. "Viral dynamic model with cellular immune response: A case study of HIV-1 infected humanized mice," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 524(C), pages 1-14.
    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. Noura H. AlShamrani & Reham H. Halawani & Ahmed M. Elaiw, 2023. "Effect of Impaired B-Cell and CTL Functions on HIV-1 Dynamics," Mathematics, MDPI, vol. 11(20), pages 1-39, October.

    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. Ma, Yuanlin & Yu, Xingwang, 2020. "The effect of environmental noise on threshold dynamics for a stochastic viral infection model with two modes of transmission and immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Bai, Ning & Xu, Rui, 2022. "Backward bifurcation and stability analysis in a within-host HIV model with both virus-to-cell infection and cell-to-cell transmission, and anti-retroviral therapy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 162-185.
    3. Waffenschmidt, Brigitte, 2021. "Nachhaltigkeit: Modewort oder Erwartung der Generation Y an ihre Arbeitgeber," EconStor Research Reports 246810, ZBW - Leibniz Information Centre for Economics.
    4. Suhail Ahmad & Tahar Tayachi & Sahibzada Ghiasul Haq & Wangari Wang’ombe & Fawad Ahmad, 2022. "Entrepreneurial-Specific Characteristics and Access to Finance of SMEs in Khyber Pakhtunkhwa, Pakistan," Sustainability, MDPI, vol. 14(16), pages 1-14, August.
    5. Ary José A. Souza-Jr., 2022. "Subjective well-being and climate change: Evidence for Portugal," Working Papers REM 2022/0213, ISEG - Lisbon School of Economics and Management, REM, Universidade de Lisboa.
    6. Wang, Zi & Yuan, Ruizhi & Luo, Jun & Liu, Martin J., 2022. "Redefining “masstige” luxury consumption in the post-COVID era," Journal of Business Research, Elsevier, vol. 143(C), pages 239-254.
    7. Ruiqing Shi & Ting Lu & Cuihong Wang, 2019. "Dynamic Analysis of a Fractional-Order Model for Hepatitis B Virus with Holling II Functional Response," Complexity, Hindawi, vol. 2019, pages 1-13, August.
    8. 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.
    9. Das, Parthasakha & Das, Pritha & Mukherjee, Sayan, 2020. "Stochastic dynamics of Michaelis–Menten kinetics based tumor-immune interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    10. Zhang, Lidong & Wang, Jinliang & Zhang, Ran, 2024. "Mathematical analysis for an age-space structured HIV model with latency," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 595-617.
    11. Mann Manyombe, M.L. & Mbang, J. & Chendjou, G., 2021. "Stability and Hopf bifurcation of a CTL-inclusive HIV-1 infection model with both viral and cellular infections, and three delays," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    12. Gerlagh, Reyer, 2022. "Climate, Technology, Family Size; on the Crossroad between Two Ultimate Externalities," Other publications TiSEM b6d5b02f-4624-46fd-836a-b, Tilburg University, School of Economics and Management.
    13. 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).
    14. Günerhan, Hatıra & Dutta, Hemen & Dokuyucu, Mustafa Ali & Adel, Waleed, 2020. "Analysis of a fractional HIV model with Caputo and constant proportional Caputo operators," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    15. 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).
    16. Liu, Lili & Ma, Xiaomin & Li, Yazhi & Liu, Xianning, 2023. "Mathematical analysis of global dynamics and optimal control of treatment for an age-structured HBV infection model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    17. Lin, Jiazhe & Xu, Rui & Tian, Xiaohong, 2017. "Threshold dynamics of an HIV-1 virus model with both virus-to-cell and cell-to-cell transmissions, intracellular delay, and humoral immunity," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 516-530.
    18. Hattaf, Khalid, 2020. "Global stability and Hopf bifurcation of a generalized viral infection model with multi-delays and humoral immunity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    19. 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).
    20. Simba, Amon & Martins Ogundana, Oyedele & Braune, Eric & Dana, Léo–Paul, 2023. "Community financing in entrepreneurship: A focus on women entrepreneurs in the developing world," Journal of Business Research, Elsevier, vol. 163(C).

    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:212:y:2023:i:c:p:159-181. 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.