The interplay between voluntary vaccination and reduction of risky behavior: a general behavior-implicit SIR model for vaccine preventable infections

The onset in the last 15 years of behavioral epidemiology has opened many new avenues for epidemiological modelers. In this manuscript we first review two classes of behavioral epidemiology models for vaccine preventable diseases, namely behaviour-implicit SIR models with prevalence-dependent vaccination (at birth and among older individuals), and prevalence-dependent contact rate. Subsequently, we briefly propose a general framework of behavior–dependent nonlinear and linear Forces of Infection (FoI) valid for a vast family of infectious diseases, and including delays and ‘epidemic memory’ effects. Finally and mainly, we develop a new general behavioral SIR model. This model combines the two aforementioned types of behavioral phenomena, previously considered only separately, into a single unified model for behavioral responses. The resulting model allows to develop a general phenomenological theory of the effects of behavioral responses within SIR models for endemic infections. In particular, the model allows to complete the picture about the complicate interplay between different behavioral responses acting on different epidemiological parameters in triggering sustained oscillations of vaccine coverage, risky behavior, and infection prevalence.