Epidemics with behavior

We study social distancing in an epidemiological model. Distancing reduces the individual's probability of getting infected but comes at a cost. Equilibrium distancing flattens the curve and decreases the final size of the epidemic. We examine the effects of distancing on the outset, the peak, and the final size of the epidemic. First, the prevalence increases beyond the initial value 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 increase the peak. However, a decrease in the cost of distancing always flattens the curve. Third, both a reduction in the transmission rate as well as a reduction in the cost of distancing decrease the final size of the epidemic. Our results suggest that public policies that decrease the transmission rate can lead to unintended negative consequences in the short run but not in the long run. Therefore, it is important to distinguish between interventions that affect the transmission rate and interventions that affect contact rates. (c) 2022 Elsevier Inc. All rights reserved.