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

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 susc...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2022, Vol.2022 (1)
Main Authors: Shah, Kamal, Sinan, Muhammad, Abdeljawad, Thabet, El-Shorbagy, M.A., Abdalla, Bahaaeldin, Abualrub, Marwan S.
Format: Article
Language:English
Subjects:
Compartments
Coronaviruses
Dynamic models
Epidemiology
Fractal models
Fractional calculus
Immunization
Infectious diseases
Matrix methods
Parameter sensitivity
Sensitivity analysis
Stability analysis
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2022/7236824