Capacitated SIR Model with an Application to COVID-19

31 Pages Posted: 22 Sep 2020 Last revised: 28 Jul 2021

See all articles by Ningyuan Chen

Ningyuan Chen

University of Toronto at Mississauga - Department of Management; University of Toronto - Rotman School of Management

Ming Hu

University of Toronto - Rotman School of Management

Chaoyu Zhang

University of Toronto - Rotman School of Management

Date Written: September 14, 2020

Abstract

The classical SIR model and its variants have seen great success in understanding and predicting infectious diseases' spread. To better capture the COVID-19 outbreak, we extend the SIR model to incorporate the limited testing capacity and account for asymptomatic people. Specifically, based on the SIR model, we impose a testing capacity and differentiate the infected people into symptomatic and asymptomatic. In this capacitated SIR model, we show first- and second-order structural properties of one measure, the number of uninfected people, with respect to the testing capacity, degree of testing people without symptoms (or level of a hospital panic run), testing turnaround time, and contact tracing accuracy. In particular, we show that the total number of infected cases is concavely decreasing in the testing capacity; the policies to increase the testing capacity, and reduce the degree of a panic run or decrease the testing turnaround time, are complementary. We use the COVID-19 data to calibrate our model and point out its public policy implications.

Note: Ethical approval statement: Our research only involves information freely available in the public domain without contact with any individuals.

Funding: None to declare

Declaration of Interest: None to declare

Keywords: COVID-19, testing capacity, compartmental model, SIR, structural result

JEL Classification: I18

Suggested Citation

Chen, Ningyuan and Hu, Ming and Zhang, Chaoyu, Capacitated SIR Model with an Application to COVID-19 (September 14, 2020). Available at SSRN: https://ssrn.com/abstract=3692751 or http://dx.doi.org/10.2139/ssrn.3692751

Ningyuan Chen (Contact Author)

University of Toronto at Mississauga - Department of Management ( email )


Canada

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada

Ming Hu

University of Toronto - Rotman School of Management ( email )

105 St. George st
Toronto, ON M5S 3E6
Canada
416-946-5207 (Phone)

HOME PAGE: http://ming.hu

Chaoyu Zhang

University of Toronto - Rotman School of Management ( email )

105 St. George Street
Toronto, Ontario M5S 3E6 M5S1S4
Canada

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