Study of transmission dynamics of COVID-19 mathematical model under ABC fractional order derivative

Sabri T M Thabet; Mohammed S Abdo; Kamal Shah; Thabet Abdeljawad

doi:10.1016/j.rinp.2020.103507

Study of transmission dynamics of COVID-19 mathematical model under ABC fractional order derivative

Results Phys. 2020 Dec:19:103507. doi: 10.1016/j.rinp.2020.103507. Epub 2020 Oct 12.

Authors

Sabri T M Thabet¹, Mohammed S Abdo², Kamal Shah³, Thabet Abdeljawad^{4

5

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Affiliations

¹ Department of Mathematics, University of Aden, Aden, Yemen.
² Department of Mathematics, Hodeidah University, Al-Hodeidah, Yemen.
³ Department of Mathematics, University of Malakand Chakdara, Dir(L), Pakhtunkhwa, 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.

Abstract

The current research work is devoted to address some results related to the existence and stability as well as numerical finding of a novel Coronavirus disease (COVID-19) by using a mathematical model. By using fixed point results we establish existence results for the proposed model under Atangana-Baleanu-Caputo (ABC) derivative with fractional order. Further, using the famous numerical technique due to Adams Bashforth, we simulate the concerned results for two famous cities of China known as Wuhan and Huanggang which are interconnected cities. The graphical presentations are given to observe the transmission dynamics from February 1 a=2020 to April 20, 2020 through various fractional order. The concerned dynamics is global in nature due to the various values of fractional order.

Keywords: 26A33; 34A08; 97M70; ABC derivative; Adams Bashforth method; COVID-19; Fixed point theorem.