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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 in order to minimize the spread of an infectious disease. We identify conditions under which any optimal policy is single-peaked, i.e., first engages in increasingly more social distancing and subsequently decreases its intensity. We show that an 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 and can substantially reduce 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 2229R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2020.
    • Handle: RePEc:cwl:cwldpp:2229r
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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. 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).
    3. 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.
    4. 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.
    5. Laurent Miclo & Daniel Spiro & Jörgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint ," Working Papers hal-02563023, HAL.
    6. 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.
    7. 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.
    8. Laurent Miclo & Daniel Spiro & Jorgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint," Papers 2005.01327, arXiv.org.
    9. 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).
    10. Baril-Tremblay, Dominique & Marlats, Chantal & Ménager, Lucie, 2021. "Self-isolation," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    11. 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.
    12. 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.
    13. Tommy Andersson & Albin Erlanson & Daniel Spiro & Robert Ostling, 2020. "Optimal Trade-Off Between Economic Activity and Health During an Epidemic," Papers 2005.07590, arXiv.org.
    14. Phelan, Thomas & Toda, Alexis Akira, 2022. "Optimal epidemic control in equilibrium with imperfect testing and enforcement," Journal of Economic Theory, Elsevier, vol. 206(C).
    15. Carnehl, Christoph & Fukuda, Satoshi & Kos, Nenad, 2023. "Epidemics with behavior," Journal of Economic Theory, Elsevier, vol. 207(C).
    16. 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).
    17. 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.
    18. Federico, Salvatore & Ferrari, Giorgio, 2021. "Taming the spread of an epidemic by lockdown policies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    19. 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.
    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. 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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