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

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

Rahim Ud Din  1 , Ebrahem A Algehyne  2
Affiliations

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

Rahim Ud Din et al. Results Phys. 2021 Apr.

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.

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Conflict of interest statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Figures

Fig. 1
Fig. 1
Dynamical behavior in of susceptible population of the considered model.
Fig. 2
Fig. 2
Dynamical behavior of infected population of the considered model.
Fig. 3
Fig. 3
Dynamical behavior of recovered population of the considered model.
Fig. 4
Fig. 4
Dynamical behavior in of susceptible population of the considered model.
Fig. 5
Fig. 5
Dynamical behavior of infected population of the considered model.
Fig. 6
Fig. 6
Dynamical behavior of recovered population of the considered model.
None
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