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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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    1. Miclo, Laurent & Weibull, Jörgen W. & Spiro, Daniel, 2020. "Optimal epidemic suppression under an ICU constraint," TSE Working Papers 20-1111, Toulouse School of Economics (TSE).
    2. Fernando Alvarez & David Argente, 2020. "A Simple Planning Problem for COVID-19 Lockdown," Working Papers 2020-34, Becker Friedman Institute for Research In Economics.
    3. Viscusi, W Kip & Aldy, Joseph E, 2003. "The Value of a Statistical Life: A Critical Review of Market Estimates throughout the World," Journal of Risk and Uncertainty, Springer, vol. 27(1), pages 5-76, August.
    4. Mohammad Akbarpour & Cody Cook & Aude Marzuoli & Simon Mongey & Abhishek Nagaraj & Matteo Saccarola & Pietro Tebaldi & Shoshana Vasserman & Hanbin Yang, 2020. "Socioeconomic Network Heterogeneity and Pandemic Policy Response," NBER Working Papers 27374, National Bureau of Economic Research, Inc.
    5. Alexis Akira Toda, 2020. "Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact," Papers 2003.11221, arXiv.org, revised Mar 2020.
    6. Facundo Piguillem & Liyan Shi, 2022. "Optimal Covid-19 Quarantine and Testing Policies [‘Optimal targeted lockdowns in a multigroup sir model’]," The Economic Journal, Royal Economic Society, vol. 132(647), pages 2534-2562.
    7. Damien de Walque & Jed Friedman & Roberta Gatti & Aaditya Mattoo, 2020. "How Two Tests Can Help Contain COVID-19 and Revive the Economy," World Bank Publications - Reports 33583, The World Bank Group.
    8. Rowthorn, Robert & Toxvaerd, Flavio, 2012. "The Optimal Control of Infectious Diseases via Prevention and Treatment," CEPR Discussion Papers 8925, C.E.P.R. Discussion Papers.
    9. James H. Stock, 2020. "Data Gaps and the Policy Response to the Novel Coronavirus," NBER Working Papers 26902, National Bureau of Economic Research, Inc.
    10. Gonzalez-Eiras, Martin & Niepelt, Dirk, 2020. "On the Optimal "Lockdown" During an Epidemic," CEPR Discussion Papers 14612, C.E.P.R. Discussion Papers.
    11. Andrew Atkeson, 2020. "What Will Be the Economic Impact of COVID-19 in the US? Rough Estimates of Disease Scenarios," NBER Working Papers 26867, National Bureau of Economic Research, Inc.
    12. Laurent Miclo & Daniel Spiro & Jörgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint ," Working Papers hal-02563023, HAL.
    13. Veronica Guerrieri & Guido Lorenzoni & Ludwig Straub & Iván Werning, 2022. "Macroeconomic Implications of COVID-19: Can Negative Supply Shocks Cause Demand Shortages?," American Economic Review, American Economic Association, vol. 112(5), pages 1437-1474, May.
    14. repec:reg:rpubli:282 is not listed on IDEAS
    15. Daron Acemoglu & Victor Chernozhukov & Ivàn Werning & Michael D. Whinston, 2020. "A Multi-Risk SIR Model with Optimally Targeted Lockdown," CeMMAP working papers CWP14/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
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    Cited by:

    1. Carnehl, Christoph & Fukuda, Satoshi & Kos, Nenad, 2021. "Epidemics With Behavior," CEPR Discussion Papers 16429, C.E.P.R. Discussion Papers.
    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. 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.
    5. 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.
    6. Thomas Phelan & Alexis Akira Toda, 2021. "Optimal Epidemic Control in Equilibrium with Imperfect Testing and Enforcement," Papers 2104.04455, arXiv.org, revised Oct 2022.
    7. 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.
    8. Federico, Salvatore & Ferrari, Giorgio, 2021. "Taming the spread of an epidemic by lockdown policies," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    9. Laurent Miclo & Daniel Spiro & Jörgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint ," Working Papers hal-02563023, HAL.
    10. 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.
    11. 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.
    12. Laurent Miclo & Daniel Spiro & Jorgen Weibull, 2020. "Optimal epidemic suppression under an ICU constraint," Papers 2005.01327, arXiv.org.
    13. Baril-Tremblay, Dominique & Marlats, Chantal & Ménager, Lucie, 2021. "Self-isolation," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    14. 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.
    15. 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.
    16. 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.
    17. 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).

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    Keywords

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