A fractional order Covid-19 epidemic model with Mittag-Leffler kernel

Hasib Khan; Muhammad Ibrahim; Abdel-Haleem Abdel-Aty; M Motawi Khashan; Farhat Ali Khan; Aziz Khan

doi:10.1016/j.chaos.2021.111030

A fractional order Covid-19 epidemic model with Mittag-Leffler kernel

Chaos Solitons Fractals. 2021 Jul:148:111030. doi: 10.1016/j.chaos.2021.111030. Epub 2021 May 12.

Authors

Hasib Khan¹, Muhammad Ibrahim¹, Abdel-Haleem Abdel-Aty^{2

3}, M Motawi Khashan⁴, Farhat Ali Khan⁵, Aziz Khan⁶

Affiliations

¹ Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan.
² Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, Bisha 61922, Saudi Arabia.
³ Physics Department, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt.
⁴ Department of Basic Sciences, Common First Year, King Saud University, Riyadh 11451, Saudi Arabia.
⁵ Department of Pharmacy, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, Khyber Pakhtunkhwa, Pakistan.
⁶ Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.

Abstract

In this article, we are studying fractional-order COVID-19 model for the analytical and computational aspects. The model consists of five compartments including; $` ` S_{c}^{″}$ which denotes susceptible class, $` ` E_{c}^{″}$ represents exposed population, $` ` I_{c}^{″}$ is the class for infected people who have been developed with COVID-19 and can cause spread in the population. The recovered class is denoted by $` ` R_{c}^{″}$ and $` ` V_{c}^{″}$ is the concentration of COVID-19 virus in the area. The computational study shows us that the spread will be continued for long time and the recovery reduces the infection rate. The numerical scheme is based on the Lagrange's interpolation polynomial and the numerical results for the suggested model are similar to the integer order which gives us the applicability of the numerical scheme and effectiveness of the fractional order derivative.

Keywords: 35R11; Primary 26A33; Secondary 34A08.