Summary: We study the use of a pulse vaccination strategy to eradicate infectious diseases modelizable by SIR epidemic models. We demonstrate the global asymptotic stability of the eradication solution [which was conjectured by L. Stone
et al., Math. Comput. Modelling 31, 207-215 (2000; Zbl 1043.92527
), for pulse vaccination in the classical SIR model] for a general model in which non-permanent immunization, variations of the total population size, and the emerging problem of vaccine failures are considered. As a strategy using a second inoculation as a standard practice, we propose a model to describe a modification of this strategy including the second inoculation and we study its local asymptotic stability.