Optimal Control of an Epidemic through Social Distancing

We analyze how to optimally engage in social distancing in order to minimize the spread of an infectious disease. We identify conditions under which any optimal policy is single-peaked, i.e., first engages in increasingly more social distancing and subsequently decreases its intensity. We show that an optimal policy might delay measures that decrease the transmission rate substantially to create herd-immunity and that engaging in social distancing sub-optimally early can increase the number of fatalities. Finally, we find that optimal social distancing can be an effective measure and can substantially reduce the death rate of a disease.