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

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 P-0 is greater than one. Finally, a stable endemic state may destabilize via Hopf bifurcation not only when P-0 > 1 but also when P-0 < 1, depending on the interplay between some relevant information-related parameters. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.