We analyze how to optimally engage in social distancing (SD) in order to minimize the spread of an infectious disease. We identify conditions under which the optimal policy is single-peaked, i.e., ﬁrst engages in increasingly more social distancing and subsequently decreases its intensity. We show that the 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 in substantially reducing the death rate of a disease.
Kruse, Thomas and Strack, Philipp, "Optimal Control of an Epidemic through Social Distancing" (2020). Cowles Foundation Discussion Papers. 18.