In this note, we consider a mathematical model of infectious disease epidemic which takes waning of immunity and vaccination to susceptible individuals into account. The model consists of three compartments, namely the compartment S of susceptible individuals, I of infected and infectious individuals, and R of individuals who have acquired immunity through vaccination or recovery from the disease. An individual can pass from S to R by vaccination, and from R to S by loss of immunity. Denoting by ω the rate of passage from S to R, we shall call this model the ω-SIRS model. After discussing the behavior of solutions of the system of ordinary differential equations which describes our model, we investigate the stability of two steady states — the disease free steady state and the endemic steady state. It is shown that the mean waiting time before the vaccination of an arbitrarily chosen susceptible individual has to be below some upper bound, in order that the disease free steady state be stable, in other words the disease be successfully eliminated from the community by mass vaccination. This upper bound is a function of the basic reproduction number, the rate of waning of immunity, the mortality rate, and the fraction of newborns (or immigrants) that are vaccinated. Finally we briefly discuss an improved model with an additional compartment E of infected but still latent individuals, and show that this improvement does not essentially affect the steady states.

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