Study of Integer and Fractional Order Covid-19 Mathematical Model

Abstract

In this paper, we study a nonlinear mathematical model which addresses the transmission dynamics of COVID-19. The considered model consists of susceptible ([Formula: see text]), exposed ([Formula: see text]), infected ([Formula: see text]), and recovered ([Formula: see text]) individuals. For simplicity, the model is abbreviated as [Formula: see text]. Immigration rates of two kinds are involved in susceptible and infected individuals. First of all, the model is formulated. Then via classical analysis, we investigate its local and global stability by using the Jacobian matrix and Lyapunov function method. Further, the fundamental reproduction number [Formula: see text] is computed for the said model. Then, we simulate the model through the Runge–Kutta method of order two abbreviated as RK2. Finally, we switch over to the fractional order model and investigate its numerical simulations corresponding to different fractional orders by using the fractional order version of the aforementioned numerical method. Finally, graphical presentations are given for the approximate solution of various compartments of the proposed model. Also, a comparison with real data has been shown.

Stability and numerical analysis via non-standard finite difference scheme of a nonlinear classical and fractional order model

“…In near past, the researchers [52] of the fields observe that this virus change their behavior each time. As we know that this virus change their behavior time to time.…”

A novel finite difference scheme for numerical solution of fractional order population growth model

“…But to understand the superiority of the solutions obtained from the fractional derivative model compared to the classical model, one should refer to the sources related to case studies. Where by adjusting the parameters of the model based on the real data, it is shown that the fractional model can approximate the proposed problem more accurately [16][17][18][19]30]. Table 1.…”

A generalized fractional hepatitis B virus infection modelwith both cell-to-cell and virus-to-cell transmissions

“…As in the previous numerical simulations, we can notice also in the present numerical simulations represented by Figs. [8][9][10][11][12], that all curves representing the different compartments converge to their steady states for different values of α. We can remark that for smaller values of fractional derivative order, all curves of the model converge very quickly to their corresponding steady states and the convergence becomes extremely sluggish with increasing fractional derivative order α, indicating a lengthy memory.…”

“…Fractional order equations provide a more realistic representation of the dynamics of disease because they take into consideration the memory effect, which means that the current and the past behavior of the state determine the future state of the fractional operator of a given function [4]. The dynamic of the transmission of several infectious diseases is described by many works using this derivation [5][6][7][8][9][10][11][12][13][14][15][16]. Recently Yang et al [17], studied a fractional epidemic model of HBV adaptive immunity.…”