Behavioral SIR models with incidence-based social-distancing

Most available behavioral epidemiology models have linked the behavioral responses of individuals to infection prevalence. However, this is a crude approximation of reality because prevalence is typically an unobserved quantity. This work considers a general endemic SIR epidemiological model where behavioral responses are incidence-based i.e., the agents perceptions of risks are based on available information on infection incidence. The differences of this modeling approach with respect to the standard ‘prevalence-based’ formulations are discussed and its dynamical implications are investigated. Both current and delayed behavioral responses are considered. We show that depending on the form of the ‘memory’ (i.e., in mathematical language, of the information delaying kernel), the endemic equilibrium can either be globally stable or destabilized via Hopf bifurcations yielding to stable recurrent oscillations. These oscillations can have a very long inter-epidemic periods and a very wide amplitude. Finally, a numerical investigation of the interplay between these behavior-related oscillations and seasonality of the contact rate reveals a strong synergic effect yielding to a dramatic amplification of oscillations.