Analytical Solution of the Effect of Awareness Program by Media on the Spread of an Infectious Disease by Homotopy Perturbation Method

In this paper, the nonlinear dynamical system modeling the effect of awareness program by media on spread of infectious disease is considered. The model is mathematically formulated by the deterministic compartmental model consisting of susceptible population, infected population, aware population and cumulative density of awareness spread by the media. Homotopy perturbation method is used to obtain the approximate solution of the governing nonlinear differential equation, which consists in determining the series solution convergent to the exact solution or enabling to built the approximate solution of the problem. Numerical solutions are obtained and the results are discussed graphically using Maple. The method allows to determine the solution in form of the continuous function, and shows the significance of awareness program driven by media in spread of an infectious disease, but due to immigration, the disease may remain endemic . The simulation analysis of the model with different parameter values confirms the analytical results.

کلیدواژه ها:

Nonlinear system of Differential Equation ، Approximate Solution ، Homotopy Perturbation method ، numerical simulation