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Closed-Form Solutions for Optimal Social Distancing in a SIR Model of Covid-19 Suppression

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  • Reyer Gerlagh

Abstract

I present a stylized suspected-infected-recovered (SIR) model of Covid-19, with symptomatic versus asymptomatic patients, and social distancing intervention. The optimal suppress strategy has low-infection rates, enabling assumptions that support closed-form solutions. The model predicts high costs of social distancing in comparison to health costs of the disease; it separates public versus private benefits of social distancing, and determines the required level of group immunity for relaxing social distance intervention. I extend the model with heterogeneous population for preferences over social contacts, health costs, and transmission. Heterogeneity in transmission intensity offers most opportunities for reduced costs under a differentiated social distancing policy.

Suggested Citation

  • Reyer Gerlagh, 2020. "Closed-Form Solutions for Optimal Social Distancing in a SIR Model of Covid-19 Suppression," CESifo Working Paper Series 8335, CESifo.
    • Handle: RePEc:ces:ceswps:_8335
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    References listed on IDEAS

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    1. Goyal, Sanjeev & Vigier, Adrien, 2015. "Interaction, protection and epidemics," Journal of Public Economics, Elsevier, vol. 125(C), pages 64-69.
    2. David Berger & Kyle Herkenhoff & Chengdai Huang & Simon Mongey, 2022. "Testing and Reopening in an SEIR Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 1-21, January.
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    5. Gonzalez-Eiras, Martin & Niepelt, Dirk, 2020. "On the Optimal "Lockdown" During an Epidemic," CEPR Discussion Papers 14612, C.E.P.R. Discussion Papers.
    6. David Berger & Kyle Herkenhoff & Chengdai Huang & Simon Mongey, 2022. "Testing and Reopening in an SEIR Model," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 43, pages 1-21, January.
    7. 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.
    8. 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.
    9. Marcus R. Keogh‐Brown & Simon Wren‐Lewis & W. John Edmunds & Philippe Beutels & Richard D. Smith, 2010. "The possible macroeconomic impact on the UK of an influenza pandemic," Health Economics, John Wiley & Sons, Ltd., vol. 19(11), pages 1345-1360, November.
    10. Toxvaerd, F.M.O, 2020. "Equilibrium Social Distancing," Cambridge Working Papers in Economics 2021, Faculty of Economics, University of Cambridge.
    11. Fenichel, Eli P., 2013. "Economic considerations for social distancing and behavioral based policies during an epidemic," Journal of Health Economics, Elsevier, vol. 32(2), pages 440-451.
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    Cited by:

    1. Martin F. Quaas & Jasper N. Meya & Hanna Schenk & Björn Bos & Moritz A. Drupp & Till Requate, 2020. "The Social Cost of Contacts: Theory and Evidence for the Covid-19 Pandemic in Germany," CESifo Working Paper Series 8347, CESifo.
    2. Stefan Pollinger, 2023. "Optimal Contact Tracing and Social Distancing Policies to Suppress A New Infectious Disease," The Economic Journal, Royal Economic Society, vol. 133(654), pages 2483-2503.
    3. Björn Bos & Moritz A. Drupp & Jasper N. Meya & Martin F. Quaas, 2020. "Moral Suasion and the Private Provision of Public Goods: Evidence from the COVID-19 Pandemic," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 76(4), pages 1117-1138, August.
    4. Epp, Markus & Jäger, Marius, 2021. "Network Exposure in the Propagation of the COVID-19 Pandemic," VfS Annual Conference 2021 (Virtual Conference): Climate Economics 242465, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    Covid-19; SIR model; suppression; (differentiated) social distancing;
    All these keywords.

    JEL classification:

    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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