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

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 R0 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

• SIR COVID model
• Basic reproduction number
• Global stability
• Local stability
• COVID-19
• Nonstandard finite difference scheme