Adomian decomposition approach to a SIR epidemic model with constant vaccination strategy

Over the years, diligent vaccination campaigns have resulted in high levels of permanent immunity against the childhood disease among the population. In this article, a SIR model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is developed. The qualitative analysis reveals the vaccination reproductive number for disease control and eradication. Adomian decomposition method is also employed to compute an approximation to the solution of the non-linear system of differential equations governing the problem. Maple is used to carry out the computations. Graphical results are presented and discussed quantitatively to illustrate the solution.