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

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...

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Bibliographic Details
Published in:Complexity (New York, N.Y.) N.Y.), 2022-01, Vol.2022 (1)
Main Authors: Khan, Tahir, Ullah, Roman, Yousef, Ali, Zaman, Gul, Al-Mdallal, Qasem M., Alraey, Yasser
Format: Article
Language:English
Subjects:
Constraint modelling
Coronaviruses
COVID-19
Differential calculus
Disease control
Disease transmission
Epidemics
Fractional calculus
Graphical representations
Infections
Infectious diseases
Pandemics
Parameter sensitivity
Public health
Sensitivity analysis
Severe acute respiratory syndrome coronavirus 2
System theory
Viral diseases
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Summary: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.
ISSN:1076-2787
1099-0526
DOI:10.1155/2022/3846904