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A New Mathematical Model of COVID-19 with Quarantine and Vaccination

Author

Listed:
  • Ihtisham Ul Haq

    (Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan)

  • Numan Ullah

    (Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan)

  • Nigar Ali

    (Department of Mathematics, University of Malakand, Chakdara 18800, Pakistan)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, Collage of Arts and Science, Prince Sattam Bin Abdulaziz University, Al-Kharj 16278, Saudi Arabia)

Abstract

A mathematical model revealing the transmission mechanism of COVID-19 is produced and theoretically examined, which has helped us address the disease dynamics and treatment measures, such as vaccination for susceptible patients. The mathematical model containing the whole population was partitioned into six different compartments, represented by the SVEIQR model. Important properties of the model, such as the nonnegativity of solutions and their boundedness, are established. Furthermore, we calculated the basic reproduction number, which is an important parameter in infection models. The disease-free equilibrium solution of the model was determined to be locally and globally asymptotically stable. When the basic reproduction number R 0 is less than one, the disease-free equilibrium point is locally asymptotically stable. To discover the approximative solution to the model, a general numerical approach based on the Haar collocation technique was developed. Using some real data, the sensitivity analysis of R 0 was shown. We simulated the approximate results for various values of the quarantine and vaccination populations using Matlab to show the transmission dynamics of the Coronavirus-19 disease through graphs. The validation of the results by the Simulink software and numerical methods shows that our model and adopted methodology are appropriate and accurate and could be used for further predictions for COVID-19.

Suggested Citation

  • Ihtisham Ul Haq & Numan Ullah & Nigar Ali & Kottakkaran Sooppy Nisar, 2022. "A New Mathematical Model of COVID-19 with Quarantine and Vaccination," Mathematics, MDPI, vol. 11(1), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:142-:d:1017179
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    References listed on IDEAS

    as
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    4. Marek B. Trawicki, 2017. "Deterministic Seirs Epidemic Model for Modeling Vital Dynamics, Vaccinations, and Temporary Immunity," Mathematics, MDPI, vol. 5(1), pages 1-19, January.
    5. Chen, Yuyang & Bi, Kaiming & Zhao, Songnian & Ben-Arieh, David & Wu, Chih-Hang John, 2017. "Modeling individual fear factor with optimal control in a disease-dynamic system," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 531-545.
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