Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

Kottakkaran Sooppy Nisar; Shabir Ahmad; Aman Ullah; Kamal Shah; Hussam Alrabaiah; Muhammad Arfan

doi:10.1016/j.rinp.2020.103772

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data

Results Phys. 2021 Feb:21:103772. doi: 10.1016/j.rinp.2020.103772. Epub 2020 Dec 29.

Authors

Kottakkaran Sooppy Nisar¹, Shabir Ahmad², Aman Ullah², Kamal Shah², Hussam Alrabaiah³, Muhammad Arfan¹

Affiliations

¹ Department of Mathematics, College of Arts and Science, Wadi Aldawaser, 11991, Prince Sattam Bin Abdulaziz University, Saudi Arabia.
² Department of Mathematics, University of Malakand, Chakdara, Dir(L), Khyber Pakhtunkhawa, Pakistan.
³ Mathematics Department, Tafila Technical University, Tafila, Jordan.

Abstract

We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams-Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. 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 solution; Fixed point theory; Fractional derivative; Numerical simulations; SIRD mathematical model.