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All epidemic models include a system of non-linear differential equation. Mostly the analytical solution of epidemic model is difficult to obtain. There are many different methods to solve non-linear differential equation, one of them is homotopy analysis method. The homotopy analysis method is an analytic approximation method using series solution for highly non-linear equations. The advantage of this method is a guarantee the convergence of approximation power series solution by choosing suitable values of the auxiliary parameter. In this paper, we consider three epidemic models in a closed population without demographics;  SI ,  SIR , and  SEIR  models. We find the solutions of the models by homotopy analysis method and then compare the numerical results with fourth order Runge-Kutta method. The homotopy analysis method gives a good result for the solution of the epidemic models with a few iterations and the solutions obtained from this method are good as compared to fourth order Runge-Kutta numerical method.

The Comparison of Fourth Order Runge-Kutta and Homotopy Analysis Method for Solving Three Basic Epidemic Models