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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 approximate solution. To show the efficiency of the proposed technique, we apply it to the fractional SIR model and compare the results with the fourth-order Runge-Kutta method. The numerical and graphical results show that the residual power series method can be considered as an alternative technique for solving many real-life problems involving differential equations of any order.

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