IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i16p1901-d611506.html
   My bibliography  Save this article

A Macroeconomic SIR Model for COVID-19

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/16/1901/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/16/1901/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Carnehl, Christoph & Fukuda, Satoshi & Kos, Nenad, 2023. "Epidemics with behavior," Journal of Economic Theory, Elsevier, vol. 207(C).
    2. Christoph Carnehl & Satoshi Fukuda & Nenad Kos, 2022. "Time-varying Cost of Distancing: Distancing Fatigue and Lockdowns," Papers 2206.03847, arXiv.org, revised Sep 2023.
    3. McAdams, David & Song, Yangbo & Zou, Dihan, 2023. "Equilibrium social activity during an epidemic," Journal of Economic Theory, Elsevier, vol. 207(C).
    4. Allen, Kyle D. & Whitledge, Matthew D., 2022. "Further evidence on the effectiveness of community banks in the Paycheck Protection Program," Finance Research Letters, Elsevier, vol. 47(PA).
    5. Wang, Wei & Miao, Wei & Liu, Yongdong & Deng, Yiting & Cao, Yunfei, 2022. "The impact of COVID-19 on the ride-sharing industry and its recovery: Causal evidence from China," Transportation Research Part A: Policy and Practice, Elsevier, vol. 155(C), pages 128-141.
    6. Goodkin-Gold, Matthew & Kremer, Michael & Snyder, Christopher M. & Williams, Heidi, 2022. "Optimal vaccine subsidies for endemic diseases," International Journal of Industrial Organization, Elsevier, vol. 84(C).
    7. Mindes, Samuel C.H. & Lewin, Paul, 2021. "Self-employment through the COVID-19 pandemic: An analysis of linked monthly CPS data," Journal of Business Venturing Insights, Elsevier, vol. 16(C).
    8. Xiao Chen & Hanwei Huang & Jiandong Ju & Ruoyan Sun & Jialiang Zhang, 2022. "Endogenous cross-region human mobility and pandemics," CEP Discussion Papers dp1860, Centre for Economic Performance, LSE.
    9. Francesco Ciampi & Alessandro Giannozzi & Giacomo Marzi & Edward I. Altman, 2021. "Rethinking SME default prediction: a systematic literature review and future perspectives," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(3), pages 2141-2188, March.
    10. Ceddia, M.G. & Bardsley, N.O. & Goodwin, R. & Holloway, G.J. & Nocella, G. & Stasi, A., 2013. "A complex system perspective on the emergence and spread of infectious diseases: Integrating economic and ecological aspects," Ecological Economics, Elsevier, vol. 90(C), pages 124-131.
    11. Ahmad Al-Fadly, 2020. "Impact of COVID-19 on SMEs and employment," Entrepreneurship and Sustainability Issues, VsI Entrepreneurship and Sustainability Center, vol. 8(2), pages 629-648, December.
    12. Da Van Huynh & Thuy Thi Kim Truong & Long Hai Duong & Nhan Trong Nguyen & Giang Vu Huong Dao & Canh Ngoc Dao, 2021. "The COVID-19 Pandemic and Its Impacts on Tourism Business in a Developing City: Insight from Vietnam," Economies, MDPI, vol. 9(4), pages 1-17, November.
    13. Charlie Tchinda & Marcus Dejardin, 2021. "Are Business Policy Measures in Response to the COVID-19 Pandemic to Be Equally Valued? An Exploration According to SMEs Owners’ Business Expectations," Sustainability, MDPI, vol. 13(21), pages 1-42, October.
    14. Bisin, Alberto & Moro, Andrea, 2022. "Spatial‐SIR with network structure and behavior: Lockdown rules and the Lucas critique," Journal of Economic Behavior & Organization, Elsevier, vol. 198(C), pages 370-388.
    15. Hausmann, Ricardo & Schetter, Ulrich, 2022. "Horrible trade-offs in a pandemic: Poverty, fiscal space, policy, and welfare," World Development, Elsevier, vol. 153(C).
    16. Daniela Scur & Raffaella Sadun & John Van Reenen & Renata Lemos & Nicholas Bloom, 2021. "The World Management Survey at 18: lessons and the way forward," Oxford Review of Economic Policy, Oxford University Press and Oxford Review of Economic Policy Limited, vol. 37(2), pages 231-258.
    17. Dalina-Maria Andrei, 2022. "Objectives And Difficulties In Sme?S Sector In Romania," Management Strategies Journal, Constantin Brancoveanu University, vol. 56(2), pages 29-36.
    18. Yunhan Huang & Quanyan Zhu, 2022. "Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review," Dynamic Games and Applications, Springer, vol. 12(1), pages 7-48, March.
    19. Kapasia, Nanigopal & Paul, Pintu & Roy, Avijit & Saha, Jay & Zaveri, Ankita & Mallick, Rahul & Barman, Bikash & Das, Prabir & Chouhan, Pradip, 2020. "Impact of lockdown on learning status of undergraduate and postgraduate students during COVID-19 pandemic in West Bengal, India," Children and Youth Services Review, Elsevier, vol. 116(C).
    20. Brotherhood, Luiz & Cavalcanti, Tiago & Da Mata, Daniel & Santos, Cezar, 2022. "Slums and pandemics," Journal of Development Economics, Elsevier, vol. 157(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:16:p:1901-:d:611506. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.