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The article presents the solution of the fractional Susceptible-Infected-Recovered model by modified variational iteration method. By using initial values, the explicit solutions of fractional SIR model for different values of fractional derivatives have been deduced. Modified variational iteration method performs extremely well in terms of efficiency that accelerates rapid convergence of series solution and also overcome the problem of crucial way of determining the Lagrange multipliers that arises in classical VIM method. Main feature of the present paper is to demonstrate the efficiency of modified variation method and exhibit system behavior for different fractional orders that are depicted graphically.