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In this article, a general model for Influenza of two groups is presented as a fractional order model. The fractional derivatives for this model which consist of eight differential equations are defined in the sense of Caputo definition. To obtain an efficient numerical method, the fraction order derivatives are approximated by the shifted Jacobi polynomials. The proposed scheme reduces the solution of the main problem to the solution of a system of nonlinear algebraic equations. Comparative studies between the proposed method and both the fourth-order Runge-Kutta method and the generalized Euler method are done.

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