Analytic solution for SIR epidemic model with multi-parameter fractional derivative

Abstract

In this paper, we construct a general framework for presenting an approximate analytic solution of the SIR epidemic model that contains a multi-parameter of a fractional derivative ${}^C{D}_{a^{+}}^{\alpha ,\rho }$ in the sense of Caputo using the homotopy analysis method. Basic ideas of both fractional derivatives and the application of the semi-analytical method for this type of system of fractional differential equation are presented. The study presents the effect of the new parameters on the solution behaviors. The new parameters of the fractional derivative give the researchers additional tools to fit the data with appropriate parameters. A particular case for $\alpha =\rho =1$ compares with the fourth Runge Kutta method, the Adams Bashforth Moulton predictor correcter scheme, and the Bernstein wavelet method to show and confirm this effectiveness method.