Optimality of Vaccination for an SIR Epidemic with an ICU Constraint

Matteo Della Rossa (), Lorenzo Freddi () and Dan Goreac ()
Additional contact information
Matteo Della Rossa: Università di Udine
Lorenzo Freddi: Università di Udine
Dan Goreac: Université Laval

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 1, No 8, 35 pages

Abstract: Abstract This paper studies an optimal control problem for a class of SIR epidemic models, in scenarios in which the infected population is constrained to be lower than a critical threshold imposed by the intensive care unit (ICU) capacity. The vaccination effort possibly imposed by the health-care deciders is classically modeled by a control input affecting the epidemic dynamic. After a preliminary viability analysis, the existence of optimal controls is established, and their structure is characterized by using a state-constrained version of Pontryagin’s theorem. The resulting optimal controls necessarily have a bang-bang regime with at most one switch. More precisely, the optimal strategies impose the maximum-allowed vaccination effort in an initial period of time, which can cease only once the ICU constraint can be satisfied without further vaccination. The switching times are characterized in order to identify conditions under which vaccination should be implemented or halted. The uniqueness of the optimal control is also discussed. Numerical examples illustrate our theoretical results and the corresponding optimal strategies. The analysis is eventually extended to the infinite horizon by $$\Gamma $$ Γ -convergence arguments.

Keywords: SIR epidemic; State constraints; Viability analysis; Optimal control; Feedback control; Vaccination; 49J15; 49J45; 92D30; 93C15 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-024-02598-w Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:204:y:2025:i:1:d:10.1007_s10957-024-02598-w

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-024-02598-w

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().