Safety-Critical Control of Active Interventions for COVID-19 Mitigation

Abstract

The world has recently undergone the most ambitious mitigation effort in a century [1], consisting of widespread quarantines aimed at preventing the spread of COVID-19 [2]. The use of influential epidemiological models [3]-[6] of COVID-19 helped to encourage decision makers to take drastic non-pharmaceutical interventions. Yet, inherent in these models are often assumptions that the active interventions are static, e.g., that social distancing is enforced until infections are minimized, which can lead to inaccurate predictions that are ever evolving as new data is assimilated. We present a methodology to dynamically guide the active intervention by shifting the focus from viewing epidemiological models as systems that evolve in autonomous fashion to control systems with an "input" that can be varied in time in order to change the evolution of the system. We show that a safety-critical control approach [7] to COVID-19 mitigation gives active intervention policies that formally guarantee the safe evolution of compartmental epidemiological models. This perspective is applied to current US data on cases while taking into account reduction of mobility, and we find that it accurately describes the current trends when time delays [8] associated with incubation and testing are incorporated. Optimal active intervention policies are synthesized to determine future mitigations necessary to bound infections, hospitalizations, and death, both at national and state levels. We therefore provide means in which to model and modulate active interventions with a view toward the phased reopenings that are currently beginning across the US and the world in a decentralized fashion. This framework can be converted into public policies, accounting for the fractured landscape of COVID-19 mitigation in a safety-critical fashion. INDEX TERMS Safety-Critical Control, Epidemiology, Non-Pharmaceutical Intervention, COVID-19 I. INTRODUCTION.

Safety-Critical Control of Compartmental Epidemiological Models With Measurement Delays

“…SIHRD model. The SIHRD model [10] adds two more outlet compartments to the SIR model: hospitalized population H and deceased population D. Their evolution is captured by three additional parameters: the hospitalization rate λ > 0, the recovery rate ν > 0 in hospitals and the death rate µ > 0. Equation (1) yields the SIHRD model for…”

“…1 shows the performance of the SIR model in capturing the spread of COVID-19 for the case of US national data. The parameters β 0 = 0.33 day −1 , γ = 0.2 day −1 and N = 33 × 10 6 of the SIR model and the control input u(t) were fitted following the algorithm in [10] to the recorded number of confirmed cases I + R [31] between March 25 and August 9, 2020 and to mobility data [32] about the medium time people spent home. The fitted control input (blue) follows the trend of the mobility data (gray) well in the beginning of the pandemic when stay-at-home orders came into action, and it deviates later when other means of mitigation (such as mask-wearing) became more significant.…”

“…The fitted control input (blue) follows the trend of the mobility data (gray) well in the beginning of the pandemic when stay-at-home orders came into action, and it deviates later when other means of mitigation (such as mask-wearing) became more significant. While the fitted model (blue) captures the data about confirmed cases (gray), the model also has predictive power (orange); see more details about forecasting in [10].…”

“…Viewing epidemiological models as control systems has been proposed in the literature recently [3]- [5], and various models with varying transmission rate [6]- [9] have appeared to quantify the level of human interventions in the case of COVID-19. Illustration of the SIR model as control system and its fit to US COVID-19 data [10]. Model parameters were estimated from compartmental data (right) by accounting for a measurement delay τ .…”

“…In this paper, we build on our recent work [10] and use a safety-critical control approach to synthesize control strategies that guide human interventions so that certain safety criteria (such as keeping infection, hospitalization and death below given limits) are fulfilled with minimal mitigation efforts. The approach is based on the framework of control barrier functions [11], [12] that leverages the theory of set invariance [13] for dynamical [14], [15] and control systems [16]- [18].…”