Pulse vaccination strategy in the sir epidemic model: Global asymptotic stable eradication in presence of vaccine failures

In this paper, we study the use of a pulse vaccination strategy to eradicate infectious diseases modelizable by SIR epidemic model. We demonstrate the global asymptotic stability of the eradication solution (which was conjectured by Agur and coworkers in [1] for pulse vaccination in the classical SIR model) for a general model in which nonpermanent immunization, variations of the total population size, and the emerging problem of the vaccine failures are considered. As a strategy using a second inoculation is 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.