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Article

A Macroeconomic SIR Model for COVID-19

Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2021, 9(16), 1901; https://doi.org/10.3390/math9161901
Submission received: 17 July 2021 / Revised: 2 August 2021 / Accepted: 5 August 2021 / Published: 10 August 2021
(This article belongs to the Special Issue The Mathematics of Pandemics: Applications for Insurance)

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.
Keywords: epidemic modeling; COVID-19; social planner’s problem; exit time control problem; value iterations epidemic modeling; COVID-19; social planner’s problem; exit time control problem; value iterations

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MDPI and ACS Style

Bayraktar, E.; Cohen, A.; Nellis, A. A Macroeconomic SIR Model for COVID-19. Mathematics 2021, 9, 1901. https://doi.org/10.3390/math9161901

AMA Style

Bayraktar E, Cohen A, Nellis A. A Macroeconomic SIR Model for COVID-19. Mathematics. 2021; 9(16):1901. https://doi.org/10.3390/math9161901

Chicago/Turabian Style

Bayraktar, Erhan, Asaf Cohen, and April Nellis. 2021. "A Macroeconomic SIR Model for COVID-19" Mathematics 9, no. 16: 1901. https://doi.org/10.3390/math9161901

APA Style

Bayraktar, E., Cohen, A., & Nellis, A. (2021). A Macroeconomic SIR Model for COVID-19. Mathematics, 9(16), 1901. https://doi.org/10.3390/math9161901

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