IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i11p1857-d826793.html
   My bibliography  Save this article

Global Stability of a Humoral Immunity COVID-19 Model with Logistic Growth and Delays

Author

Listed:
  • Ahmed M. Elaiw

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut Branch, Assiut 4293073, Egypt)

  • Abdullah J. Alsaedi

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
    Department of Mathematics, University College in Al-Jamoum, Umm Al-Qura University, Makkah 21955, Saudi Arabia)

  • Afnan Diyab Al Agha

    (Department of Mathematical Science, College of Engineering, University of Business and Technology, Jeddah 21361, Saudi Arabia)

  • Aatef D. Hobiny

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

The mathematical modeling and analysis of within-host or between-host coronavirus disease 2019 (COVID-19) dynamics are considered robust tools to support scientific research. Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the cause of COVID-19. This paper proposes and investigates a within-host COVID-19 dynamics model with latent infection, the logistic growth of healthy epithelial cells and the humoral (antibody) immune response. Time delays can affect the dynamics of SARS-CoV-2 infection predicted by mathematical models. Therefore, we incorporate four time delays into the model: (i) delay in the formation of latent infected epithelial cells, (ii) delay in the formation of active infected epithelial cells, (iii) delay in the activation of latent infected epithelial cells, and (iv) maturation delay of new SARS-CoV-2 particles. We establish that the model’s solutions are non-negative and ultimately bounded. This confirms that the concentrations of the virus and cells should not become negative or unbounded. We deduce that the model has three steady states and their existence and stability are perfectly determined by two threshold parameters. We use Lyapunov functionals to confirm the global stability of the model’s steady states. The analytical results are enhanced by numerical simulations. The effect of time delays on the SARS-CoV-2 dynamics is investigated. We observe that increasing time delay values can have the same impact as drug therapies in suppressing viral progression. This offers some insight useful to develop a new class of treatment that causes an increase in the delay periods and then may control SARS-CoV-2 replication.

Suggested Citation

  • Ahmed M. Elaiw & Abdullah J. Alsaedi & Afnan Diyab Al Agha & Aatef D. Hobiny, 2022. "Global Stability of a Humoral Immunity COVID-19 Model with Logistic Growth and Delays," Mathematics, MDPI, vol. 10(11), pages 1-28, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1857-:d:826793
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/11/1857/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/11/1857/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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).
    2. Khan, Hasib & Ahmad, Farooq & Tunç, Osman & Idrees, Muhammad, 2022. "On fractal-fractional Covid-19 mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    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. Elaiw, A.M. & Alsaedi, A.J. & Hobiny, A.D. & Aly, S., 2023. "Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    2. Ahmed M. Elaiw & Abdulsalam S. Shflot & Aatef D. Hobiny & Shaban A. Aly, 2023. "Global Dynamics of an HTLV-I and SARS-CoV-2 Co-Infection Model with Diffusion," Mathematics, MDPI, vol. 11(3), pages 1-33, January.

    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. Hussain, Shah & Tunç, Osman & Rahman, Ghaus ur & Khan, Hasib & Nadia, Elissa, 2023. "Mathematical analysis of stochastic epidemic model of MERS-corona & application of ergodic theory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 207(C), pages 130-150.
    2. Elaiw, A.M. & Alsaedi, A.J. & Hobiny, A.D. & Aly, S., 2023. "Stability of a delayed SARS-CoV-2 reactivation model with logistic growth and adaptive immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 616(C).
    3. Li, Ruqi & Song, Yurong & Wang, Haiyan & Jiang, Guo-Ping & Xiao, Min, 2023. "Reactive–diffusion epidemic model on human mobility networks: Analysis and applications to COVID-19 in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 609(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:gam:jmathe:v:10:y:2022:i:11:p:1857-:d:826793. 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.