  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 multiple epidemic waves.
