Abstract
Delay differential equations (DDEs) are functional differential equations arising in many applications from different fields of study. For instance: Medicine, Biology, Engineering, Population Dynamics, Economics, Control Theory, and many others. However, analytical approximation of the models described by different nonlinear systems of such equations is tough to obtain due to the lack of direct and simplified approach to evaluating nonlinear terms. The study focused on the new analytical method for solving SIRS Disease Model. The method was from the Homotopy Analysis Method and the Natural Transform, where He’s Polynomial was modified to compute nonlinear terms. The convergence analysis of the proposed method was provided to guarantee the convergence of the approximate solution of the model. Again, the technique produces a solution in a polynomial series, and by selecting the optimal value of auxiliary parameters, a better approximation is achieved using different time-delay values. Therefore some figures are used to demonstrate the accuracy of the result based on the residual error function. Hence, the approach provides the easiest means for the analytical treatment of such a model and can also be applied to other nonlinear problems.

Key words: Natural Transform; Homotopy Analysis Method; Modified He's Polynomial; SIRS Disease Model