• Theoretical Analysis of A SIR Epidemic Model With Constant Vaccination Strategy

Abstract

A SIR (Susceptible-Infected-Removed) model that monitors the temporal dynamics of a childhood disease in the presence of preventive vaccine is discussed. The aim of epidemic modeling is to understand and if possible control the spread of disease. To do this, it tries to relate disease dynamics at the population level to basic properties of the host and pathogen populations and of the infection process. Epidemic models thus express scientific hypotheses. In this paper, a powerful analytical method, called Homotopy analysis method (HAM) is used to solve the system of nonlinear differential equations. Furthermore, in this work the numerical simulation of the problem is also reported using Scilab/Matlab program. Our analytical results are compared with simulation results. A good agreement between analytical and numerical results is noted.