Optimal Control of an Epidemic through Social Distancing
28 Pages Posted: 4 Jun 2020 Last revised: 29 Jul 2020
Date Written: July 28, 2020
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.
Keywords: Social Distancing, SIR model, Time-Optimal Control of an Epidemic
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