Abstract: The SIR model with unspecified parameters is a significant concern for researchers in the fields of epidemiology and the medical treatment of sick individuals. In this paper, an effective strategy based on the variational homotopy perturbation method, the Yang transform, and the multi-step approach, known as the Multi-step Yang transform variational homotopy perturbation method (MSYTVHPM), is used to solve the fractional order SIR epidemic model. The fractional derivative is defined in the Caputo sense. Using the multi-step Yang transform variational homotopy perturbation approach, we may achieve an analytic solution to the SIR model in the form of a convergent power series. We apply the suggested method to the fractional SIR model and compare the outcomes with those obtained using the fourth-order Runge-Kutta method to demonstrate its effectiveness. The graphical results show that the multi-step Yang transform variational homotopy perturbation method can be considered as an alternative technique for solving many real-life problems involving differential equations of any order.

Keywords: Fractional SIR model, Yang transform, Variational Iteration method, Homotopy perturbation method, Multi-step, Caputo derivative

Pages: 137-146