Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator

Saleh S Redhwan; Mohammed S Abdo; Kamal Shah; Thabet Abdeljawad; S Dawood; Hakim A Abdo; Sadikali L Shaikh

doi:10.1016/j.rinp.2020.103610

Mathematical modeling for the outbreak of the coronavirus (COVID-19) under fractional nonlocal operator

Results Phys. 2020 Dec:19:103610. doi: 10.1016/j.rinp.2020.103610. Epub 2020 Nov 16.

Authors

Saleh S Redhwan¹, Mohammed S Abdo², Kamal Shah³, Thabet Abdeljawad^{4

5

6}, S Dawood², Hakim A Abdo⁷, Sadikali L Shaikh⁸

Affiliations

¹ Department of Mathematics, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S), India.
² Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen.
³ Department of Mathematics, University of Malakand, Chakdara Dir (Lower), Khyber Pakhtunkhawa, Pakistan.
⁴ Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, Saudi Arabia.
⁵ Department of Medical Research, China Medical University, Taichung 40402, Taiwan.
⁶ Department of Computer Science and Information Engineering, Asia University, Taichung, Taiwan.
⁷ Department of Computer Science and information technology, Dr. Babasaheb Ambedkar Marathwada University, Aurangabad, (M.S), India.
⁸ Department of Mathematics, Maulana Azad College of arts, Science and Commerce, RozaBagh, Aurangabad, Maharashtra, 431001, India.

Abstract

A mathematical model for the spread of the COVID-19 disease based on a fractional Atangana-Baleanu operator is studied. Some fixed point theorems and generalized Gronwall inequality through the AB fractional integral are applied to obtain the existence and stability results. The fractional Adams-Bashforth is used to discuss the corresponding numerical results. A numerical simulation is presented to show the behavior of the approximate solution in terms of graphs of the spread of COVID-19 in the Chinese city of Wuhan. We simulate our table for the data of Wuhan from February 15, 2020 to April 25, 2020 for 70 days. Finally, we present a debate about the followed simulation in characterizing how the transmission dynamics of infection can take place in society.

Keywords: Adams–Bashforth technique; Atangana–Baleanu operator; COVID-19; Fixed point technique; Generalized Gronwall inequality; Stability and existence theory.