SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

Shahram Rezapour; Hakimeh Mohammadi; Mohammad Esmael Samei

doi:10.1186/s13662-020-02952-y

SEIR epidemic model for COVID-19 transmission by Caputo derivative of fractional order

Adv Differ Equ. 2020;2020(1):490. doi: 10.1186/s13662-020-02952-y. Epub 2020 Sep 14.

Authors

Shahram Rezapour^{1

2

3}, Hakimeh Mohammadi⁴, Mohammad Esmael Samei⁵

Affiliations

¹ Institute of Research and Development, Duy Tan University, Da Nang, 550000 Vietnam.
² Faculty of Natural Sciences, Duy Tan University, Da Nang, 550000 Vietnam.
³ Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan.
⁴ Department of Mathematics, Miandoab Branch, Islamic Azad University, Miandoab, Iran.
⁵ Department of Mathematics, Bu-Ali Sina University, 65178 Hamedan, Iran.

Abstract

We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibrium points is investigated. We prove the existence of a unique solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. To predict the transmission of COVID-19 in Iran and in the world, we provide a numerical simulation based on real data.

Keywords: COVID-19; Equilibrium point; Numerical simulation; SEIR model.