On the Optimal Vaccination Control of SIR Model with Erlang-Distributed Infectious Period

Luca Bolzoni () and Rossella Della Marca ()
Additional contact information
Luca Bolzoni: Istituto Zooprofilattico Sperimentale della Lombardia e dell’Emilia Romagna
Rossella Della Marca: SISSA – International School for Advanced Studies

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 20, 31 pages

Abstract: Abstract In this work, we investigate optimal vaccination strategies in SIR models with Erlang-distributed infectious period (the Erlang distribution is a gamma distribution with integer shape parameter). We consider the problem of minimizing the epidemic burden under either limited vaccination resources or linear costs of vaccination. By applying the Pontryagin’s minimum principle, we prove that both the optimal control problems admit only bang–bang solutions with at most one switch, the one-switch control being the case of reactive vaccination. We show that different assumptions on the infectious period distribution may lead to qualitatively and quantitatively different shapes of the optimal control. The main results are the following. We prove that in the absence of control the epidemic burden in SIR models is the same irrespectively of the infectious period distribution. However, when the vaccination resources are limiting, the optimal control problem leads to solutions where the epidemic burden is larger (and the time needed to complete vaccination campaigns is longer) in models with Erlang-distributed infectious periods with respect to exponential ones.

Keywords: SIR model; Epidemics; Non-exponential distribution; Erlang distribution; Vaccination; Optimal control; 49K15; 92D30 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10957-025-02645-0 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:205:y:2025:i:2:d:10.1007_s10957-025-02645-0

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

DOI: 10.1007/s10957-025-02645-0

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 ().