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Optimal Control of an Epidemic through Social Distancing

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Abstract
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.

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  • Thomas Kruse & Philipp Strack, 2020. "Optimal Control of an Epidemic through Social Distancing," Cowles Foundation Discussion Papers 2229, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2229
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    15. repec:reg:rpubli:282 is not listed on IDEAS
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    Cited by:

    1. Giovanni Dieguez & Cristiane Batistela & José R. C. Piqueira, 2023. "Controlling COVID-19 Spreading: A Three-Level Algorithm," Mathematics, MDPI, vol. 11(17), pages 1-39, September.
    2. Carnehl, Christoph & Fukuda, Satoshi & Kos, Nenad, 2023. "Epidemics with behavior," Journal of Economic Theory, Elsevier, vol. 207(C).
    3. Phelan, Thomas & Toda, Alexis Akira, 2022. "Optimal epidemic control in equilibrium with imperfect testing and enforcement," Journal of Economic Theory, Elsevier, vol. 206(C).
    4. Miclo, Laurent & Spiro, Daniel & Weibull, Jörgen, 2022. "Optimal epidemic suppression under an ICU constraint: An analytical solution," Journal of Mathematical Economics, Elsevier, vol. 101(C).
    5. Rahul Deb & Mallesh Pai & Akhil Vohra & Rakesh Vohra, 2022. "Testing alone is insufficient," Review of Economic Design, Springer;Society for Economic Design, vol. 26(1), pages 1-21, March.
    6. Stephen C. Newbold & David Finnoff & Linda Thunström & Madison Ashworth & Jason F. Shogren, 2020. "Effects of Physical Distancing to Control COVID-19 on Public Health, the Economy, and the Environment," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 705-729, August.
    7. Alessandro Ramponi & Maria Elisabetta Tessitore, 2024. "Optimal Social and Vaccination Control in the SVIR Epidemic Model," Mathematics, MDPI, vol. 12(7), pages 1-17, March.
    8. Andersson, Tommy & Erlanson , Albin & Spiro, Daniel & Östling, Robert, 2020. "Optimal Trade-Off between Economic Activity and Health during an Epidemic," Working Papers 2020:8, Lund University, Department of Economics.
    9. Andrew Atkeson, 2020. "On Using SIR Models to Model Disease Scenarios for COVID-19," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 41(01), pages 1-35, June.
    10. Federico, Salvatore & Ferrari, Giorgio, 2021. "Taming the spread of an epidemic by lockdown policies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    11. Laurent Miclo & Daniel Spiro & Jörgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint ," Working Papers hal-02563023, HAL.
    12. Linus Nyiwul, 2021. "Epidemic Control and Resource Allocation: Approaches and Implications for the Management of COVID-19," Studies in Microeconomics, , vol. 9(2), pages 283-305, December.
    13. Alessandro Ramponi & Maria Elisabetta Tessitore, 2022. "The economic cost of social distancing during a pandemic: an optimal control approach in the SVIR model," Papers 2208.04908, arXiv.org.
    14. Laurent Miclo & Daniel Spiro & Jorgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint," Papers 2005.01327, arXiv.org.
    15. Li, Shilin & Li, Tongtong & Yang, Jinqiang, 2022. "Optimal consumption and portfolio choices in the stochastic SIS model," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    16. Baril-Tremblay, Dominique & Marlats, Chantal & Ménager, Lucie, 2021. "Self-isolation," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    17. Federico, Salvatore & Ferrari, Giorgio & Torrente, Maria-Laura, 2022. "Optimal Vaccination in a SIRS Epidemic Model," Center for Mathematical Economics Working Papers 667, Center for Mathematical Economics, Bielefeld University.
    18. Adriani, Fabrizio & Ladley, Dan, 2021. "Social distance, speed of containment and crowding in/out in a network model of contagion," Journal of Economic Behavior & Organization, Elsevier, vol. 190(C), pages 597-625.
    19. Federico, Salvatore & Ferrari, Giorgio, 2020. "Taming the Spread of an Epidemic by Lockdown Policies," Center for Mathematical Economics Working Papers 639, Center for Mathematical Economics, Bielefeld University.
    20. Huberts, Nick F.D. & Thijssen, Jacco J.J., 2023. "Optimal timing of non-pharmaceutical interventions during an epidemic," European Journal of Operational Research, Elsevier, vol. 305(3), pages 1366-1389.
    21. Avram, Florin & Freddi, Lorenzo & Goreac, Dan, 2022. "Optimal control of a SIR epidemic with ICU constraints and target objectives," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    22. Terrence Iverson & Larry Karp & Alessandro Peri, 2022. "Optimal social distancing and the economics of uncertain vaccine arrival," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(5), pages 1071-1100, October.

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    Keywords

    Social Distancing; SIR model; Time-Optimal Control of an Epidemic;
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