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A Detailed Study of a Fractal‐Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination

Author

Listed:
  • Kamal Shah
  • Muhammad Sinan
  • Thabet Abdeljawad
  • M.A. El-Shorbagy
  • Bahaaeldin Abdalla
  • Marwan S. Abualrub

Abstract

This article is devoted to investigate a mathematical model consisting on susceptible, exposed, infected, quarantined, vaccinated, and recovered compartments of COVID‐19. The concerned model describes the transmission mechanism of the disease dynamics with therapeutic measures of vaccination of susceptible people along with the cure of the infected population. In the said study, we use the fractal‐fractional order derivative to understand the dynamics of all compartments of the proposed model in more detail. Therefore, the first model is formulated. Then, two equilibrium points disease‐free (DF) and endemic are computed. Furthermore, the basic threshold number is also derived. Some sufficient conditions for global asymptotical stability are also established. By using the next‐generation matrix method, local stability analysis is developed. We also attempt the sensitivity analysis of the parameters of the proposed model. Finally, for the numerical simulations, the Adams–Bashforth method is used. Using some available data, the results are displayed graphically using various fractal‐fractional orders to understand the mechanism of the dynamics. In addition, we compare our numerical simulation with real data in the case of reported infected cases.

Suggested Citation

  • Kamal Shah & Muhammad Sinan & Thabet Abdeljawad & M.A. El-Shorbagy & Bahaaeldin Abdalla & Marwan S. Abualrub, 2022. "A Detailed Study of a Fractal‐Fractional Transmission Dynamical Model of Viral Infectious Disease with Vaccination," Complexity, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:complx:v:2022:y:2022:i:1:n:7236824
    DOI: 10.1155/2022/7236824
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    References listed on IDEAS

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    1. Abdeljawad, Thabet & Al-Mdallal, Qasem M. & Jarad, Fahd, 2019. "Fractional logistic models in the frame of fractional operators generated by conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 94-101.
    2. A. A. M. Arafa & M. Khalil & A. Sayed, 2019. "A Non-Integer Variable Order Mathematical Model of Human Immunodeficiency Virus and Malaria Coinfection with Time Delay," Complexity, Hindawi, vol. 2019, pages 1-13, March.
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