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Deterministic and Stochastic Nonlinear Model for Transmission Dynamics of COVID-19 with Vaccinations Following Bayesian-Type Procedure

Author

Listed:
  • Mohammadi Begum Jeelani

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Rahim Ud Din

    (Department of Mathematics, University of Malakand, Chakdra 18800, Khyber Pakhtunkhwa, Pakistan)

  • Ghaliah Alhamzi

    (Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia)

  • Manel Hleili

    (Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia)

  • Hussam Alrabaiah

    (College of Engineering, Ain University, Al Ain 112612, United Arab Emirates
    Department of Mathematics, Tafila Technical University, Tafila 66110, Jordan)

Abstract

We develop a mathematical model for the SARAS-CoV-2 double variant transmission characteristics with variant 1 vaccination to address this novel aspect of the disease. The model is theoretically examined, and adequate requirements are derived for the stability of its equilibrium points. The model includes the single variant 1 and variant 2 endemic equilibria in addition to the endemic and disease-free equilibria. Various approaches are used for the global and local stability of the model. For both strains, we determine the basic reproductive numbers R 1 and R 2 . To investigate the occurrence of the layers (waves), we expand the model to include some analysis based on the second-order derivative. The model is then expanded to its stochastic form, and numerical outcomes are computed. For numerical purposes, we use the nonstandard finite difference method. Some error analysis is also recorded.

Suggested Citation

  • Mohammadi Begum Jeelani & Rahim Ud Din & Ghaliah Alhamzi & Manel Hleili & Hussam Alrabaiah, 2024. "Deterministic and Stochastic Nonlinear Model for Transmission Dynamics of COVID-19 with Vaccinations Following Bayesian-Type Procedure," Mathematics, MDPI, vol. 12(11), pages 1-28, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:11:p:1662-:d:1402363
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