A review of Approximate-analytical Solution for an Epidemic Model

In this paper, Homotopy analysis method (HAM) and Adomian decomposition method (ADM) are employed to solve a system of nonlinear equations. The model is the problem of the spread of a non-fatal disease in a population with a constant size, over the period of the epidemic. Mathematical modeling of the problem leads to a system of nonlinear ordinary differential equations. This system has been solved by HAM. Suitable values of the auxiliary parameter ℏ are determined, by using ℏ-curves. Approximate solutions are plotted and a comparison is made between the HAM results and the ADM. Also, we express the role of various parameters of biological mode.

Keywords:

Homotopy analysis method , Adomian decomposition method , System of nonlinear ordinary differential equations , epidemic model