Using Non-Standard Finite Difference Scheme to Study Classical and Fractional Order SEIVR Model

Abstract

In this study, we considered a model for novel COVID-19 consisting on five classes, namely S, susceptible; E, exposed; I, infected; V, vaccinated; and R, recovered. We derived the expression for the basic reproductive rate R0 and studied disease-free and endemic equilibrium as well as local and global stability. In addition, we extended the nonstandard finite difference scheme to simulate our model using some real data. Moreover, keeping in mind the importance of fractional order derivatives, we also attempted to extend our numerical results for the fractional order model. In this regard, we considered the proposed model under the concept of a fractional order derivative using the Caputo concept. We extended the nonstandard finite difference scheme for fractional order and simulated our results. Moreover, we also compared the numerical scheme with the traditional RK4 both in CPU time as well as graphically. Our results have close resemblance to those of the RK4 method. Also, in the case of the infected class, we compared our simulated results with the real data.