Vaccination policies and nonlinear force of infection: generalization of an observation by Alexander and Moghadas (2004)

It has been recently showed in [M.E. Alexander, S.M. Moghadas, Periodicity in an epidemic model with a generalized non-linear incidence, Math. Biosci. 189 (2004) 75-96] that one of the possible causes of unexpected failures of some vaccination campaigns may be the nonlinearity of the force of infection. The aim of this paper is to give a simple and biologically meaningful sufficient condition for the globally stable eradication of diseases whose spreading is described via a generic class of SIR and SEIR epidemic models ruled by nonlinear force of infection. We consider a scenario in which there are both traditional and pulse vaccination strategies.