A Macroeconomic SIR Model for COVID-19

23 Pages Posted: 29 Jun 2020

See all articles by Erhan Bayraktar

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Asaf Cohen

University of Michigan at Ann arbor - Department of Mathematics

April Nellis

University of Michigan

Date Written: June 22, 2020

Abstract

The current COVID-19 pandemic and subsequent lockdowns have highlighted the close and delicate relationship between a country's public health and economic health. Macroeconomic models which use preexisting epidemic models 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 develop an SIR model of the COVID-19 pandemic which explicitly considers herd immunity, behavior-dependent transmission rates, remote workers, and indirect externalities of lockdown. This model is presented as an exit time control problem where the lockdown ends when the population achieves herd immunity, either naturally or via a vaccine. A social planner prescribes separate levels of lockdown for two separate sections of the adult population - those who are low-risk (ages 20-64) and those who are high-risk (ages 65 and over). These levels are determined via optimization of an objective function which assigns a macroeconomic cost to the level of lockdown and the number of deaths. We find that, by ending lockdowns once herd immunity is reached, high-risk individuals are able to leave lockdown significantly before the arrival of a vaccine without causing large increases in mortality. Additionally, if we incorporate a behavior-dependent transmission rate which represents increased personal caution in response to increased infection levels, both output loss and total mortality are lowered. Lockdown efficacy is further increased when there is less interaction between low- and high-risk individuals, and increased remote work decreases output losses. Overall, our model predicts that a lockdown which ends at the arrival of herd immunity, combined with individual actions to slow virus transmission, can reduce total mortality to one-third of the no-lockdown level, while allowing high-risk individuals to leave lockdown well before vaccine arrival.

Note: Funding: None to declare

Declaration of Interest: None to declare

Keywords: Epidemic modeling, COVID-19, planner problem, value iterations, exit time control problem

JEL Classification: E610, I12, I15, I18

Suggested Citation

Bayraktar, Erhan and Cohen, Asaf and Nellis, April, A Macroeconomic SIR Model for COVID-19 (June 22, 2020). Available at SSRN: https://ssrn.com/abstract=3633443 or http://dx.doi.org/10.2139/ssrn.3633443

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Asaf Cohen (Contact Author)

University of Michigan at Ann arbor - Department of Mathematics ( email )

Ann Arbor, MI 48109
United States

April Nellis

University of Michigan ( email )

Ann Arbor, MI 48109
United States

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