Oscillations and hysteresis in an epidemic model with information-dependent imperfect vaccination

Abstract

We investigate a behavioral epidemic model including a partially effective vaccination at all ages. The vaccination is information-dependent, in the sense that the vaccination rate of susceptibles depends on the current and the past information available about the disease prevalence in the population. The weight given to the past history is described by an exponential kernel. The proposed model presents both the possibility of backward bifurcation and that of oscillations triggered by behavioral memory. Furthermore, a forward hysteresis scenario may take place where multiple endemic states are possible when the basic reproduction number P0 is greater than one. Finally, a stable endemic state may destabilize via Hopf bifurcation not only when P0>1 but also when P0<1, depending on the interplay between some relevant information-related parameters.