Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays

Tamas G Molnar; Andrew W Singletary; Gabor Orosz; Aaron D Ames

doi:10.1109/LCSYS.2020.3040948

Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays

IEEE Control Syst Lett. 2020 Nov 26;5(5):1537-1542. doi: 10.1109/LCSYS.2020.3040948. eCollection 2021 Nov.

Authors

Tamas G Molnar^{1

2}, Andrew W Singletary², Gabor Orosz^{1

3}, Aaron D Ames²

Affiliations

¹ Department of Mechanical EngineeringUniversity of Michigan Ann Arbor MI 48109 USA.
² Department of Mechanical and Civil EngineeringCalifornia Institute of Technology Pasadena CA 91125 USA.
³ Department of Civil and Environmental EngineeringUniversity of Michigan Ann Arbor MI 48109 USA.

Abstract

We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and human interventions (such as quarantining or social distancing) as control input. We consider a generalized compartmental model that represents the form of the most popular epidemiological models and we design safety-critical controllers that formally guarantee safe evolution with respect to keeping certain populations of interest under prescribed safe limits. Furthermore, we discuss how measurement delays originated from incubation period and testing delays affect safety and how delays can be compensated via predictor feedback. We demonstrate our results by synthesizing active intervention policies that bound the number of infections, hospitalizations and deaths for epidemiological models capturing the spread of COVID-19 in the USA.

Keywords: COVID-19; epidemiology; safety-critical control; time delay.

Grants and funding

This work was supported in part by the National Science Foundation, CPS Award 1932091.