Spatiotemporal quasiperiodicity induced by all-ages vaccine hesitancy in an SIR model

In this work, in the context of a spatiotemporal Susceptible–Infectious–Removed (SIR) model with vaccination across all-ages, we consider the synergy between vaccine hesitancy and the intrinsic nonlocal spatial and temporal nature of the information used by agents to make their decisions. First, we analytically investigate the stability of the spatially homogeneous endemic equilibrium: we prove that the proposed model has either Hopf instability or Turing instability, but it cannot have Turing–Hopf instability. Second, we numerically show that, in the presence of both spatial and temporal nonlocality, the model may exhibit spatiotemporal quasi-periodicity. This phenomenon, to the best of our knowledge, was never been observed before in the context of behavioural epidemiology of infectious diseases. In other cases, instead, the triggering of other interesting spatiotemporal patterns is observed.