Capacitated SIR Model with an Application to COVID-19

Abstract

The classical SIR model and its variants have seen great success in understanding and predicting infectious diseases' spread. We extend the SIR model to incorporate the limited testing capacity, which is one of the most notable challenges in the current COVID-19 outbreak. Specifically, based on the SIR model, we impose a testing capacity that is shared among a mix of the infected and virus-free people. In this capacitated SIR model, we show first- and second-order structural properties of two measures, the total infections (confirmed or not) and the case number of undiagnosed infections, with respect to the testing capacity, degree of testing the uninfected (or level of hospital panic run), incubation/testing turnaround time, and infection rate. In particular, we show that in the early stage of a pandemic, the total number of infections is concavely decreasing in the testing capacity and concavely increasing in the degree of testing the uninfected/asymptomatic; the policies to increase the testing capacity and those to reduce the infection rate can be substitutable or complementary, depending on the chosen measure. We use the COVID-19 data to calibrate our model and point out its public policy implications. For example, CDC modified its testing guideline on August 25, 2020, to exclude people who do not have symptoms, and on September 18, 2020, reversed the course by reinforcing the need to test the asymptomatic. Our result suggests that such one-size-fits-all testing guidelines may not be appropriate for all states depending on their testing capacity, and implementing any unequivocal policy would have different impacts depending on the current degree of testing the uninfected/asymptomatic that varies largely across states.

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