Issue |
ESAIM: COCV
Volume 31, 2025
|
|
---|---|---|
Article Number | 9 | |
Number of page(s) | 40 | |
DOI | https://doi.org/10.1051/cocv/2024083 | |
Published online | 31 January 2025 |
Viability and control of a delayed SIR epidemic with an ICU state constraint
Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, via delle Scienze 206, 33100 Udine, Italy
* Corresponding author: matteo.dellarossa@uniud.it
Received:
23
January
2024
Accepted:
21
November
2024
This paper studies viability and control synthesis for a delayed SIR epidemic. The model integrates a constant delay representing an incubation/latency time. The control inputs model nonpharmaceutical interventions, while an intensive care unit (ICU) state-constraint is introduced to reflect the healthcare system’s capacity. The arising delayed control system is analyzed via functional viability tools, providing insights into fulfilling the ICU constraint through feedback control maps. In particular, we consider two scenarios: first, we consider the case of general continuous initial conditions. Then, as a further refinement of our analysis, we assume that the initial conditions satisfy a Lipschitz continuity property, consistent with the considered model. The study compares the (in general, sub-optimal) obtained control policies with the optimal ones for the delay-free case, emphasizing the impact of the delay parameter. The obtained results are supported and illustrated, in a concluding section, by numerical examples.
Mathematics Subject Classification: 34K35 / 49J21 / 49J53 / 92D30 / 93C23
Key words: SIR epidemic / state constraints / viability / optimal control / feedback control / delays / functional differential equations
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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