Model Predictive Control Tailored to Epidemic Models

TL;DR

This paper develops a model predictive control framework tailored to epidemic models, specifically the SEIR model, to optimize social distancing and quarantine measures while ensuring infection levels stay within safe limits.

Contribution

It introduces a novel MPC approach that leverages the maximal robust positively invariant set of the SEIR model to effectively manage pandemic restrictions.

Findings

Infection decay is exponential within the invariant set.

A uniform bound exists on the time to reach the safe infection level.

Numerical case study validates the proposed control strategy.

Abstract

We propose a model predictive control (MPC) approach for minimising the social distancing and quarantine measures during a pandemic while maintaining a hard infection cap. To this end, we study the admissible and the maximal robust positively invariant set (MRPI) of the standard SEIR compartmental model with control inputs. Exploiting the fact that in the MRPI all restrictions can be lifted without violating the infection cap, we choose a suitable subset of the MRPI to define terminal constraints in our MPC routine and show that the number of infected people decays exponentially within this set. Furthermore, under mild assumptions we prove existence of a uniform bound on the time required to reach this terminal region (without violating the infection cap) starting in the admissible set. The findings are substantiated based on a numerical case study.