Mathematical analysis of COVID-19 by using SIR model with convex incidence rate

Rahim Ud Din; Ebrahem A Algehyne

doi:10.1016/j.rinp.2021.103970

Mathematical analysis of COVID-19 by using SIR model with convex incidence rate

Results Phys. 2021 Apr:23:103970. doi: 10.1016/j.rinp.2021.103970. Epub 2021 Feb 19.

Authors

Rahim Ud Din¹, Ebrahem A Algehyne²

Affiliations

¹ Department of Mathematics, University of Malakand, Khyber Pakhtunkhwa, Pakistan.
² Department of Mathematics, Faculty of Science, University of Tabuk, P.O.Box 741, Tabuk 71491, Saudi Arabia.

Abstract

This paper is about a new COVID-19 SIR model containing three classes; Susceptible S(t), Infected I(t), and Recovered R(t) with the Convex incidence rate. Firstly, we present the subject model in the form of differential equations. Secondly, "the disease-free and endemic equilibrium" is calculated for the model. Also, the basic reproduction number $R_{0}$ is derived for the model. Furthermore, the Global Stability is calculated using the Lyapunov Function construction, while the Local Stability is determined using the Jacobian matrix. The numerical simulation is calculated using the Non-Standard Finite Difference (NFDS) scheme. In the numerical simulation, we prove our model using the data from Pakistan. "Simulation" means how S(t), I(t), and R(t) protection, exposure, and death rates affect people with the elapse of time.

Keywords: Basic reproduction number; COVID-19; Global stability; Local stability; Nonstandard finite difference scheme; SIR COVID model.