The Mathematical modeling of infectious disease is currently a major research topic in the public health domain. In some cases the infected individuals may not be infectious at the time of infection. To become infectious, the infected individuals take some times which is known as latent period or delay. Here the two SIR models are taken into consideration for present analysis where the newly entered individuals have been vaccinated with a specific rate. The analysis of these models show that if vaccination is administered to the newly entering individuals then the system will be asymptotically stable in both cases i.e. with delay and without delay.
