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. 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.