Research Specifications

In this paper, applying Caputo fractional derivative operator, the SCIRS epidemic model of Covid-19 has been presented. First, the well-definedness of the model (positive invariance) has been checked. We then calculate the equilibrium points of the system and the reproduction number and discuss the local and global stability of the equilibria based on values of the reproduction number. For the global stability of the rest points, the Liapunov’s second method and LaSalle’s invariance principle are used. The Pontryagin minimization principle is utilized to derive the optimal control conditions, with a focus on minimizing both the infection rate and the cost associated with vaccination implementation. Applying fixed point theory, the existence and uniqueness of the solutions of the model has been proven. Additionally, by using MATLAB and fractional Euler method, a numerical method has been applied to simulate the solutions based on real data and predict the transmission of Covid-19.