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A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor

Author

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  • Amar Nath Chatterjee

    (Department of Mathematics, K.L.S. College, Magadh University, Nawada 805110, Bihar, India
    These authors contributed equally to this work.)

  • Fahad Al Basir

    (Department of Mathematics, Asansol Girls’ College, Asansol 713304, West Bengal, India
    These authors contributed equally to this work.)

  • Bashir Ahmad

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

  • Ahmed Alsaedi

    (Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

During the past several years, the deadly COVID-19 pandemic has dramatically affected the world; the death toll exceeds 4.8 million across the world according to current statistics. Mathematical modeling is one of the critical tools being used to fight against this deadly infectious disease. It has been observed that the transmission of COVID-19 follows a fading memory process. We have used the fractional order differential operator to identify this kind of disease transmission, considering both fear effects and vaccination in our proposed mathematical model. Our COVID-19 disease model was analyzed by considering the Caputo fractional operator. A brief description of this operator and a mathematical analysis of the proposed model involving this operator are presented. In addition, a numerical simulation of the proposed model is presented along with the resulting analytical findings. We show that fear effects play a pivotal role in reducing infections in the population as well as in encouraging the vaccination campaign. Furthermore, decreasing the fractional-order parameter α value minimizes the number of infected individuals. The analysis presented here reveals that the system switches its stability for the critical value of the basic reproduction number R 0 = 1 .

Suggested Citation

  • Amar Nath Chatterjee & Fahad Al Basir & Bashir Ahmad & Ahmed Alsaedi, 2022. "A Fractional-Order Compartmental Model of Vaccination for COVID-19 with the Fear Factor," Mathematics, MDPI, vol. 10(9), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:9:p:1451-:d:802426
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    References listed on IDEAS

    as
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    Cited by:

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    3. Xuan Leng & Asad Khan & Anwarud Din, 2023. "Probability Analysis of a Stochastic Non-Autonomous SIQRC Model with Inference," Mathematics, MDPI, vol. 11(8), pages 1-18, April.

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