Optimal Control of an Epidemic through Social Distancing

33 Pages Posted: 4 Jun 2020 Last revised: 25 Jul 2022

See all articles by Thomas Kruse

Thomas Kruse

Justus-Liebig-University Giessen

Philipp Strack

Yale, Department of Economics

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.

Funding Information: Philipp Strack was supported by a Sloan fellowship.

Conflict of Interests: MISSING

Keywords: Social Distancing, SIR model, Time-Optimal Control of an Epidemic

Suggested Citation

Kruse, Thomas and Strack, Philipp, Optimal Control of an Epidemic through Social Distancing (July 28, 2020). Available at SSRN: https://ssrn.com/abstract=3581295 or http://dx.doi.org/10.2139/ssrn.3581295

Thomas Kruse

Justus-Liebig-University Giessen ( email )

Licher Str. 64
Giessen, 35394

Philipp Strack (Contact Author)

Yale, Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States

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