Fractional order mathematical modeling of COVID-19 transmission

Shabir Ahmad; Aman Ullah; Qasem M Al-Mdallal; Hasib Khan; Kamal Shah; Aziz Khan

doi:10.1016/j.chaos.2020.110256

Fractional order mathematical modeling of COVID-19 transmission

Chaos Solitons Fractals. 2020 Oct:139:110256. doi: 10.1016/j.chaos.2020.110256. Epub 2020 Sep 2.

Authors

Shabir Ahmad¹, Aman Ullah¹, Qasem M Al-Mdallal², Hasib Khan³, Kamal Shah¹, Aziz Khan⁴

Affiliations

¹ Department of Mathematics, University of Malakand, Dir(L), Khyber Pakhtunkhwa, Pakistan.
² Department of Mathematical Sciences, United Arab Emirates University, P.o Box 15551, Al Ain, Abu Dhabi, UAE.
³ Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Khyber Pakhtunkhwa, Pakistan.
⁴ Department of Mathematics and General Sciences, Prince Sultan University, P.O. Box 66833, 11586 Riyadh, Saudi Arabia.

Abstract

In this article, the mathematical model with different compartments for the transmission dynamics of coronavirus-19 disease (COVID-19) is presented under the fractional-order derivative. Some results regarding the existence of at least one solution through fixed point results are derived. Then for the concerned approximate solution, the modified Euler method for fractional-order differential equations (FODEs) is utilized. Initially, we simulate the results by using some available data for different fractional-order to show the appropriateness of the proposed method. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

Keywords: Approximate solutions; Caputo’s fractional derivative; Corona virus COVID-19; Fractional Euler’s method.