The final size and critical times of an SIVR epidemic model

To understand the impact of vaccination, we consider an SIVR (susceptible–infected–vaccinated–recovered) model that combines impulsive vaccination into the classical SIR model. The final size is firstly defined and estimated, and then the peak value and peak time are considered. Finally, the critical time for a given infected number is studied, and it can be used to define and estimate the stopping time. Our results extend those for the well-understood SIR model.