Stability Analysis of SIR Model with Vaccination

摘要

This paper aims to study a SIR model with and without vaccination. A reproduction number R_(0) is defined and it is obtained that the disease-free equilibrium point is unstable if and the non-trivial endemic equilibrium point exist if in the absence of vaccination. Further, a new reproduction number is defined for the model in which vaccination is introduced. The linear stability and the global stability of both the models are discussed and the comparison of both the models is done regarding the existence of the disease-free equilibrium point and endemic equilibrium point. Finally, a numerical example is given in support of the result.