The impact of fear and behaviour response to established and novel diseases

We analyze a disease transmission model that allows individuals to acquire fear and change their behaviour to reduce transmission. Fear is acquired through contact with infected individuals and through the influence of fearful individuals. We analyze the model in two limits: First, an Established Disease Limit (EDL), where the spread of the disease is much faster than the spread of fear, and second, a Novel Disease Limit (NDL), where the spread of the disease is comparable to that of fear. For the EDL, we show that the relative rate of fear acquisition to disease transmission controls the size of the fearful population at the end of a disease outbreak, and that the fear-induced contact reduction behaviour has very little impact on disease burden. Conversely, we show that in the NDL, disease burden can be controlled by fear-induced behaviour depending on the rate of fear loss. Specifically, fear-induced behaviour introduces a contact parameter $p$, which if too large prevents the contact reduction from effectively managing the epidemic. We analytically identify a critical prophylactic behaviour parameter $p=p_c$ where this happens leading to a discontinuity in epidemic prevalence. We show that this change in disease burden introduces delayed epidemic waves.