Optimal Control of an Epidemic through Social Distancing

28 Pages Posted: 23 Apr 2020 Last revised: 5 Aug 2020

See all articles by Thomas Kruse

Thomas Kruse

Justus Liebig University Giessen

Philipp Strack

Yale, Department of Economics

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Date Written: April 23, 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

Suggested Citation

Kruse, Thomas and Strack, Philipp, Optimal Control of an Epidemic through Social Distancing (April 23, 2020). Cowles Foundation Discussion Paper No. 2229, Available at SSRN: https://ssrn.com/abstract=3583186 or http://dx.doi.org/10.2139/ssrn.3583186

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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