A mathematical model for SARS-CoV-2 in variable-order fractional derivative

Mahmoud H DarAssi; Mohammad A Safi; Muhammad Altaf Khan; Alireza Beigi; Ayman A Aly; Mohammad Y Alshahrani

doi:10.1140/epjs/s11734-022-00458-0

A mathematical model for SARS-CoV-2 in variable-order fractional derivative

Eur Phys J Spec Top. 2022;231(10):1905-1914. doi: 10.1140/epjs/s11734-022-00458-0. Epub 2022 Feb 3.

Authors

Mahmoud H DarAssi¹, Mohammad A Safi², Muhammad Altaf Khan³, Alireza Beigi⁴, Ayman A Aly⁵, Mohammad Y Alshahrani⁶

Affiliations

¹ Department of Basic Sciences, Princess Sumaya University for Technology, Amman, 11941 Jordan.
² Department of Mathematics Faculty of science, The Hashemite University, P. O. Box 330127, Zarqa, 13133 Jordan.
³ Institute for Ground Water Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa.
⁴ School of Mechatronic Systems Engineering, Simon Fraser University, 102 Avenue, Surrey, BC V3T 0A3, 250-13450 Canada.
⁵ Department of Mechanical Engineering, College of Engineering, Taif University, P.O.Box 11099, Taif, 21944 Saudi Arabia.
⁶ Department of Clinical Laboratory Sciences, College of Applied Medical Sciences, King Khalid University, P.O. Box 61413, Abha, 9088 Saudi Arabia.

Abstract

A new coronavirus mathematical with hospitalization is considered with the consideration of the real cases from March 06, 2021 till the end of April 30, 2021. The essential mathematical results for the model are presented. We show the model stability when $R_{0} < 1$ in the absence of infection. We show that the system is stable locally asymptotically when $R_{0} < 1$ at infection free state. We also show that the system is globally asymptotically stable in the disease absence when $R_{0} < 1$ . Data have been used to fit accurately to the model and found the estimated basic reproduction number to be $R_{0} = 1.2036$ . Some graphical results for the effective parameters are drawn for the disease elimination. In addition, a variable-order model is introduced, and so as to handle the outbreak effectively and efficiently, a genetic algorithm is used to produce high-quality control. Numerical simulations clearly show that decision-makers may develop helpful and practical strategies to manage future waves by implementing optimum policies.