Rujira OuncharoenKamal ShahRahim Ud DinThabet AbdeljawadA.L.I. AhmadianSoheil SalahshourThanin Sitthiwirattham2025-03-102025-03-102023Fractals0218348X10.1142/S0218348X234004672-s2.0-85157977181https://repository.dusit.ac.th//handle/123456789/4576In this paper, we study a nonlinear mathematical model which addresses the transmission dynamics of COVID-19. The considered model consists of susceptible (S), exposed (E), infected (I), and recovered (R) individuals. For simplicity, the model is abbreviated as SEIR. 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 R0 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. © 2023 The Author(s).All Open Access; Hybrid Gold Open AccessDynamical SystemFractional Order RK2 MethodGlobal StabilityLyapunov FunctionThe Basic Reproduction NumberArticleScopus