We consider models for a disease with acute and chronic infective stages, and variable infectivity
and recovery rates, within the context of a vaccination campaign. Models for SIRS and SIS
disease cycles exhibit backward bifurcations under certain conditions, which complicate the
criteria for success of the vaccination campaign by making it possible to have stable endemic
states when R0 < 1. We also show the extent to which the forms of the infectivity and recovery
functions affect the possibility of backward bifurcations. SIR and SI models examined do not
exhibit this behavior.