Oscillations in SIR behavioural epidemic models: The interplay between behaviour and overexposure to infection

Oscillations in epidemic models including human behaviour indicate that the human factor might play a key role in the occurrence of periodically high levels of incidence and prevalence of the disease. Such phenomena can be captured even with minimal models, i.e. basic SIR or SEIR models with a reduced mathematical complexity. In such models, the effects of information-dependent changes in contact patterns are strongly affected by the function used to describe the memory of the population. In particular, the endemic equilibrium cannot be destabilized in case of exponentially fading memory but sustained oscillations are possible when the memory of the population is described by certain unimodal functions. In this work, we introduce a behavioural SIR-like model with information-dependent social distancing to investigate the interplay between individuals’ behaviour and overexposure to infection due to unconscious exposure to contagion. We use spectral analysis to show that sustained oscillations may take place even with exponentially fading memory. We show that this result holds both in case of prevalence-based and incidence-based social distancing. Furthermore, we show that the individual's behavioural response to information may stabilize the oscillations induced by overexposure.