Capacitated SIR Model with an Application to COVID-19 Testing

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. Building on the SIR model, we impose a testing capacity and differentiate the infected people into symptomatic and asymptomatic types. Using this capacitated SIR model, we show first- and second-order structural properties of one measure---the fraction of uninfected people---with respect to the testing capacity, testing accuracy, testing turnaround time, and contact tracing accuracy. Moreover, we study how to allocate limited testing capacity over time and across people with and without symptoms, and how to prioritize among the testing methods that have a different testing capacity, accuracy, and turnaround time. Moreover, using the COVID-19 data, we develop a sliding-window method to identify the non-stationarity of the model parameters and predict future infections.
The analytical results provide critical insights on managing testing capacities at both the strategic and operational levels. Moreover, the estimation results show that our parsimonious model can still have a strong predictive power.

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