Subcritical Bifurcation and Global Dynamics in an Imperfect Pulse Vaccination Model

Abstract

In this talk we investigate an SIVS epidemic model with imperfect vaccine, thus vaccinated individuals can also contract the infection. We consider pulse vaccination... It is known that in some vaccination models, backward bifurcation occurs and multiple subthreshold endemic equilibria exist, thus the behaviour of solution depends on the initial value [1]. We know that pulse vaccination can be more effective than constant vaccination, thus it is an interesting question to study whether backward bifurcation can arise in a pulse vaccination model. We prove that backward bifurcation can occur in pulse vaccination model. First, we find a disease-free periodic solution, which is locally asymptotically stable in the whole phase space if \(R_c 1\), then the infection is strongly uniformly persistent in the population.