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A Macroeconomic SIR Model for COVID-19

Author

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  • Erhan Bayraktar

    (Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
    These authors contributed equally to this work.)

  • Asaf Cohen

    (Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
    These authors contributed equally to this work.)

  • April Nellis

    (Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
    These authors contributed equally to this work.)

Abstract

The COVID-19 pandemic and subsequent lockdowns highlight the close and delicate relationship between a country’s public health and economic health. Models that combine macroeconomic factors with traditional epidemic dynamics to calculate the impacts of a disease outbreak are therefore extremely useful for policymakers seeking to evaluate the best course of action in such a crisis. We developed a macroeconomic SIR model that considers herd immunity, behavior-dependent transmission rates, remote workers, and the indirect externalities of lockdowns. It is formulated as an exit time control problem where a social planner is able to prescribe separate levels of the lockdown low-risk and high-risk portions of the adult population. The model predicts that by considering the possibility of reaching herd immunity, high-risk individuals are able to leave lockdown sooner than in models where herd immunity is not considered. Additionally, a behavior-dependent transmission rate (which represents increased personal caution in response to increased infection levels) can lower both output loss and total mortality. Overall, the model-determined optimal lockdown strategy, combined with individual actions to slow virus transmission, is able to reduce total mortality to one-third of the model-predicted no-lockdown level of mortality.

Suggested Citation

  • Erhan Bayraktar & Asaf Cohen & April Nellis, 2021. "A Macroeconomic SIR Model for COVID-19," Mathematics, MDPI, vol. 9(16), pages 1-24, August.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1901-:d:611506
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    References listed on IDEAS

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    1. Timothy C Reluga, 2010. "Game Theory of Social Distancing in Response to an Epidemic," PLOS Computational Biology, Public Library of Science, vol. 6(5), pages 1-9, May.
    2. Fernando Alvarez & David Argente & Francesco Lippi, 2021. "A Simple Planning Problem for COVID-19 Lock-down, Testing, and Tracing," American Economic Review: Insights, American Economic Association, vol. 3(3), pages 367-382, September.
    3. James H Fowler & Seth J Hill & Remy Levin & Nick Obradovich, 2021. "Stay-at-home orders associate with subsequent decreases in COVID-19 cases and fatalities in the United States," PLOS ONE, Public Library of Science, vol. 16(6), pages 1-15, June.
    4. Alexander W. Bartik & Marianne Bertrand & Zoe Cullen & Edward L. Glaeser & Michael Luca & Christopher Stanton, 2020. "The impact of COVID-19 on small business outcomes and expectations," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 117(30), pages 17656-17666, July.
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    Cited by:

    1. Francis Kuriakose & Deepa Kylasam Iyer, 2024. "Initial conditions and cross-country macroeconomic impact during Covid-19," International Journal of Trade and Global Markets, Inderscience Enterprises Ltd, vol. 19(1), pages 4-27.
    2. Vinicius Albani & Matheus Grasselli & Weijie Pang & Jorge P. Zubelli, 2022. "The Interplay between COVID-19 and the Economy in Canada," JRFM, MDPI, vol. 15(10), pages 1-26, October.
    3. 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.

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