The SIR model with unknown parameters is an important issue for scientists in the study of
epidemiology and medical care for the injured people. In this work, an efficient technique
based on the generalized Taylor series, called the residual power series method, is applied
to solve the SIR epidemic model of fractional order. The fractional derivative is described in
the Caputo sense. The use of the residual power series method enables us to get an
analytic solution of the SIR model in the form of a convergent power series in addition to the …

This study presents the dynamics of a fraction-order SIR epidemic model using the residual
power series (RPS) method. The proposed SIR model is described by coupled non-linear
ordinary differential equations (NLDEs) with fractional order, where the fractionalorder
derivative is defined in the Caputo sense. The RPS method is a semi-analytical method
based on the generalized Taylor series, which provides the approximate solution in the form
of a convergent series that usually converges to the exact solution. The solution obtained …