STUDY OF INTEGER AND FRACTIONAL ORDER COVID-19 MATHEMATICAL MODEL
Rujira Ouncharoen, Kamal Shah, Rahim Ud Din, Thabet Abdeljawad, Ali Ahmadian, Soheil Salahshour, Thanin Sitthiwirattham
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.