Assessing the potential impact of COVID-19 Omicron variant: Insight through a fractional piecewise model

Xiao-Ping Li; Mahmoud H DarAssi; Muhammad Altaf Khan; C W Chukwu; Mohammad Y Alshahrani; Mesfer Al Shahrani; Muhammad Bilal Riaz

doi:10.1016/j.rinp.2022.105652

Assessing the potential impact of COVID-19 Omicron variant: Insight through a fractional piecewise model

Results Phys. 2022 Jul:38:105652. doi: 10.1016/j.rinp.2022.105652. Epub 2022 May 30.

Authors

Xiao-Ping Li¹, Mahmoud H DarAssi², Muhammad Altaf Khan³, C W Chukwu⁴, Mohammad Y Alshahrani⁵, Mesfer Al Shahrani⁵, Muhammad Bilal Riaz^{6

7

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Affiliations

¹ School of Mathematics and Information Science, Xiangnan University, Chenzhou, 423000, Hunan, PR China.
² Department of Basic Sciences, Princess Sumaya University for Technology, Amman 11941, Jordan.
³ Institute for Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, South Africa.
⁴ Division of Infectious Diseases and Global Public Health, University of California, San Diego, CA, USA.
⁵ Department of Clinical Laboratory Sciences, College of Applied Medical Sciences, King Khalid University, P.O. Box 61413, Abha, 9088, Saudi Arabia.
⁶ Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, 1/15 Stefanowskiego St., 90-924 Lodz, Poland.
⁷ Department of Mathematics, University of Management and Technology, 54770, Lahore, Pakistan.

Abstract

We consider a new mathematical model for the COVID-19 disease with Omicron variant mutation. We formulate in details the modeling of the problem with omicron variant in classical differential equations. We use the definition of the Atangana-Baleanu derivative and obtain the extended fractional version of the omicron model. We study mathematical results for the fractional model and show the local asymptotical stability of the model for infection-free case if $R_{0} < 1$ . We show the global asymptotically stable of the model for the disease free case when $R_{0} \leq 1$ . We show the existence and uniqueness of solution of the fractional model. We further extend the fractional order model into piecewise differential equation system and give a numerical algorithm for their numerical simulation. We consider the real cases of COVID-19 in South Africa of the third wave March 2021-Sep 2021 and estimate the model parameters and get $R_{0} \approx 1.4004$ . The real parameters values are used to show the graphical results for the fractional and piecewise model.

Keywords: COVID-19; Fractional model; Numerical simulation; Omicron; Piecewise model.