Epidemic Management with Admissible and Robust Invariant Sets

TL;DR

This paper analyzes epidemic models using set-based methods to ensure infection levels stay within safe limits through robust intervention strategies, applicable even under model uncertainties.

Contribution

It introduces a set-based framework for epidemic management, characterizing admissible and invariant sets for SIR and SEIR models with intervention bounds.

Findings

Admissible and invariant sets are characterized for epidemic models.

Intervention strategies can be designed to prevent infection caps under uncertainties.

Framework applies to both perfect and uncertain epidemic models.

Abstract

We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing, quarantining and vaccination. We describe the admissible and maximal robust positively invariant (MRPI) sets of these two models via the theory of barriers. We show how the sets may be used in the management of epidemics, for both perfect and imperfect/uncertain models, detailing how intervention strategies may be specified such that the hard infection cap is never breached, regardless of the basic reproduction number. The results are clarified with detailed examples.