The Mathematical modelling of infectious disease is very important for public health management. Since the vaccinated individuals (immune class) are protected from infection for a time interval but not forever, they may be converted into susceptible with a specific rate. Again the infected individuals take some times to become infectious, call this time delay or latent period. Here two SIR models are taken into consideration for analysis where the newly entered individuals have been vaccinated with specific rate and the vaccinated individuals are taken as immune class, one model in absence of delay and other in presence of delay. The analysis of the two models show that if vaccination is administered to the newly entering individuals then the system will be asymptotically stable in both cases depending on certain conditions. The number of susceptible will increase more rapidly in presence of delay compare to the absence of delay. In both models the disease free equilibrium point will be asymptotically stable when the basic reproduction number less than one and the endemic equilibrium point will be asymptotically stable when basic reproduction number greater than one.
