Maintaining Hard Infection Caps in Epidemics via the Theory of Barriers

Willem Esterhuizen (1) , Tim Aschenbruck (1) , Jean Lévine (2) , Stefan Streif (1)

1 Chemnitz University of Technology / Technische Universität Chemnitz
2 CAS - Centre Automatique et Systèmes

Research in epidemiology often focusses on designing interventions that result in the number of infected individuals asymptotically approaching zero, without considering that this number may peak at high values during transients. Recent research has shown that a set-based approach could be used to address the problem, and we build on this idea by applying the theory of barriers to construct admissible and invariant sets for an epidemic model. We describe how these sets may be used to choose intervention strategies that maintain infection caps during epidemics. We also derive algebraic conditions of the model parameters that classify a system as being either comfortable, comfortable-viable, viable, or desperate.

Mots clés: State Constraints; Epidemic; Infection Cap; Admissible Set; Maximal Robust Positively Invariant Set (MRPI); Barrier

Domaines: Optimisation et contrôle [math.OC]

Willem Esterhuizen, Tim Aschenbruck, Jean Lévine, Stefan Streif. Maintaining Hard Infection Caps in Epidemics via the Theory of Barriers. 2019. ⟨hal-02388177⟩