A Scenario-based Model Predictive Control Scheme for Pandemic Response through Non-pharmaceutical Interventions

Abstract

This paper presents a scenario-based model predictive control (MPC) scheme designed to control an evolving pandemic via non-pharmaceutical intervention (NPIs). The proposed approach combines predictions of possible pandemic evolution to decide on a level of severity of NPIs to be implemented over multiple weeks to maintain hospital pressure below a prescribed threshold, while minimizing their impact on society. Specifically, we first introduce a compartmental model which divides the population into Susceptible, Infected, Detected, Threatened, Healed, and Expired (SIDTHE) subpopulations and describe its positive invariant set. This model is expressive enough to explicitly capture the fraction of hospitalized individuals while preserving parameter identifiability w.r.t. publicly available datasets. Second, we devise a scenario-based MPC scheme with recourse actions that captures potential uncertainty of the model parameters. e.g., due to population behavior or seasonality. Our results show that the scenario-based nature of the proposed controller manages to adequately respond to all scenarios, keeping the hospital pressure at bay also in very challenging situations when conventional MPC methods fail.