Solution of a Vaccination Based SIR Epidemic Model by Homotopy Analysis Method

Modeling infectious diseases helped out to understand and overcome epidemics. This paper is based on epidemic model SIR, which fits well to many epidemiological diseases. Basic idea of Homotopy Analysis Method (HAM)is discussed and employed to compute an approximation to the solution of nonlinear system of differential equations. The effect of vaccination on the dynamics of childhood disease described by SIR model is monitored using HAM. The qualitative analysis reveals the vaccination reproduction number for disease control and eradication. MATLAB is used to carry out the computations. Graphical results are presented and discussed quantitatively.