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

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  • 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
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    References listed on IDEAS

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    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).
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    Cited by:

    1. 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.
    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).

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