A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

Nguyen Huy Tuan; Hakimeh Mohammadi; Shahram Rezapour

doi:10.1016/j.chaos.2020.110107

A mathematical model for COVID-19 transmission by using the Caputo fractional derivative

Chaos Solitons Fractals. 2020 Nov:140:110107. doi: 10.1016/j.chaos.2020.110107. Epub 2020 Jul 11.

Authors

Nguyen Huy Tuan¹, Hakimeh Mohammadi², Shahram Rezapour^{3

4

5}

Affiliations

¹ Division of Applied Mathematics, Thu Dau Mot University, Binh Duong Province, Vietnam.
² Department of Mathematics, Miandoab Branch, Islamic Azad University, Miandoab, Iran.
³ Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam.
⁴ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
⁵ Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, Iran.

Abstract

We present a mathematical model for the transmission of COVID-19 by the Caputo fractional-order derivative. We calculate the equilibrium points and the reproduction number for the model and obtain the region of the feasibility of system. By fixed point theory, we prove the existence of a unique solution. Using the generalized Adams-Bashforth-Moulton method, we solve the system and obtain the approximate solutions. We present a numerical simulation for the transmission of COVID-19 in the world, and in this simulation, the reproduction number is obtained as $R_{0} = 1 : 610007996,$ which shows that the epidemic continues.

Keywords: 34A08; 65P99; COVID-19; Equilibrium point; Fixed point; Fractional mathematical model; Numerical result.