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Modeling and Dynamics of the Fractional Order SARS‐CoV‐2 Epidemiological Model

Author

Listed:
  • Tahir Khan
  • Roman Ullah
  • Ali Yousef
  • Gul Zaman
  • Qasem M. Al-Mdallal
  • Yasser Alraey

Abstract

We propose a theoretical study to investigate the spread of the SARS‐CoV‐2 virus, reported in Wuhan, China. We develop a mathematical model based on the characteristic of the disease and then use fractional calculus to fractionalize it. We use the Caputo-Fabrizio operator for this purpose. We prove that the considered model has positive and bounded solutions. We calculate the threshold quantity of the proposed model and discuss its sensitivity analysis to find the role of every epidemic parameter and the relative impact on disease transmission. The threshold quantity (reproductive number) is used to discuss the steady states of the proposed model and to find that the proposed epidemic model is stable asymptotically under some constraints. Both the global and local properties of the proposed model will be performed with the help of the mean value theorem, Barbalat’s lemma, and linearization. To support our analytical findings, we draw some numerical simulations to verify with graphical representations.

Suggested Citation

  • Tahir Khan & Roman Ullah & Ali Yousef & Gul Zaman & Qasem M. Al-Mdallal & Yasser Alraey, 2022. "Modeling and Dynamics of the Fractional Order SARS‐CoV‐2 Epidemiological Model," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:3846904
    DOI: 10.1155/2022/3846904
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    References listed on IDEAS

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    1. Zain Ul Abadin Zafar & Zahir Shah & Nigar Ali & Ebraheem O. Alzahrani & Meshal Shutaywi, 2021. "Mathematical And Stability Analysis Of Fractional Order Model For Spread Of Pests In Tea Plants," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(01), pages 1-14, February.
    2. Tuan, Nguyen Huy & Mohammadi, Hakimeh & Rezapour, Shahram, 2020. "A mathematical model for COVID-19 transmission by using the Caputo fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    3. Zafar, Zain Ul Abadin & Ali, Nigar & Baleanu, Dumitru, 2021. "Dynamics and numerical investigations of a fractional-order model of toxoplasmosis in the population of human and cats," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
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