  We study equilibrium distancing during epidemics. Distancing reduces the
individual's probability of getting infected but comes at a cost. It creates a
single-peaked epidemic, flattens the curve and decreases the size of the
epidemic. We examine more closely the effects of distancing on the outset, the
peak and the final size of the epidemic. First, we define a behavioral basic
reproduction number and show that it is concave in the transmission rate. The
infection, therefore, spreads only if the transmission rate is in the
intermediate region. Second, the peak of the epidemic is non-monotonic in the
transmission rate. A reduction in the transmission rate can lead to an increase
of the peak. On the other hand, a decrease in the cost of distancing always
flattens the curve. Third, both an increase in the infection rate as well as an
increase in the cost of distancing increase the size of the epidemic. Our
results have important implications on the modeling of interventions. Imposing
restrictions on the infection rate has qualitatively different effects on the
trajectory of the epidemics than imposing assumptions on the cost of
distancing. The interventions that affect interactions rather than the
transmission rate should, therefore, be modeled as changes in the cost of
distancing.
