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 epidemics' spread. We extend the SIR model to incorporate the limited testing capacity, which is by far one of the most notable challenges in the current COVID-19 outbreak. Specifically, on the SIR model, we impose a testing capacity that is shared among the infected and uninfected people. In this capacitated SIR model, we show first- and second-order structural properties of the total infection/confirmed cases 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 the total number of infection cases is concavely decreasing in the testing capacity. We use 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