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# A Theoretical Investigation of the SARS-CoV-2 Model via Fractional Order Epidemiological Model

Tahir Khan1, Rahman Ullah1, Thabet Abdeljawad2,3,*, Manar A. Alqudah4, Faizullah Faiz5

1 Department of Mathematics and Statistics, Woman University, Swabi, Khyber Pakhtunkhwa, 23501, Pakistan
2 Department of Mathematics and Sciences, Prince Sultan University, Riyadh, 11586, Saudi Arabia
3 Department of Medical Research, China Medical University, Taichung, 40402, Taiwan
4 Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P. O. Box 84428, Riyadh, 11671, Saudi Arabia
5 Department of Basic Sciences and Humanities, College of Electrical and Mechanical Engineering, National University of Sciences and Technology (NUST), Islamabad, 44320, Pakistan

* Corresponding Author: Thabet Abdeljawad. Email:

Computer Modeling in Engineering & Sciences 2023, 135(2), 1295-1313. https://doi.org/10.32604/cmes.2022.022177

## Abstract

We propose a theoretical study investigating the spread of the novel coronavirus (COVID-19) reported in Wuhan City of China in 2019. We develop a mathematical model based on the novel corona virus's characteristics and then use fractional calculus to fractionalize it. Various fractional order epidemic models have been formulated and analyzed using a number of iterative and numerical approaches while the complications arise due to singular kernel. We use the well-known Caputo-Fabrizio operator for the purposes of fictionalization because this operator is based on the non-singular kernel. Moreover, to analyze the existence and uniqueness, we will use the well-known fixed point theory. We also prove that the considered model has positive and bounded solutions. We also draw some numerical simulations to verify the theoretical work via graphical representations. We believe that the proposed epidemic model will be helpful for health officials to take some positive steps to control contagious diseases.

## Keywords

Khan, T., Ullah, R., Abdeljawad, T., Alqudah, M. A., Faiz, F. (2023). A Theoretical Investigation of the SARS-CoV-2 Model via Fractional Order Epidemiological Model. CMES-Computer Modeling in Engineering & Sciences, 135(2), 1295–1313.

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