Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function

Amir Khan; Rahat Zarin; Usa Wannasingha Humphries; Ali Akgül; Anwar Saeed; Taza Gul

doi:10.1186/s13662-021-03546-y

Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function

Adv Differ Equ. 2021;2021(1):387. doi: 10.1186/s13662-021-03546-y. Epub 2021 Aug 19.

Authors

Amir Khan^{1

2}, Rahat Zarin³, Usa Wannasingha Humphries¹, Ali Akgül⁴, Anwar Saeed⁵, Taza Gul⁶

Affiliations

¹ Department of Mathematics, Faculty of Science, King Mongkut's University of Technology, Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok, 10140 Thailand.
² Department of Mathematics and Statistics, University of Swat, Khyber Pakhtunkhawa, Pakistan.
³ Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan.
⁴ Department of Mathematics, Art and Science Faculty of Science, Siirt University, TR-56100 Siirt, Turkey.
⁵ Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140 Thailand.
⁶ Mathematics Department, City University of Science and Information Technology, Peshawar, Pakistan.

Abstract

In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana-Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray-Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik-Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.

Keywords: Mittag-Leffler function; Numerical simulations; Optimal control; Pandemic model; Sensitivity analysis; Stability analysis.