Esterhuizen W, Lévine J, Streif S. Epidemic management with admissible and robust invariant sets.
PLoS One 2021;
16:e0257598. [PMID:
34559815 PMCID:
PMC8462746 DOI:
10.1371/journal.pone.0257598]
[Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/01/2021] [Accepted: 09/06/2021] [Indexed: 11/18/2022] Open
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.
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