Bang-bang optimal control of vaccination in metapopulation epidemics with linear cost structures
File(s)
Accepted version
Author(s)
Machado Moschen, Lucas
Aronna, Maria Soledad
Moschen, Lucas
Type
Journal Article
Abstract
In this paper, we study optimal vaccination in a heterogeneous metapopulation epidemic model with state and mixed control-state constraints and a linear cost on the control, which better reflects real-world expenses compared to quadratic penalties. Within a general SIR / SEIR K-patch framework, we formulate the resulting control problem on a finite horizon, prove the existence of optimal control, and derive the necessary conditions via Pontryagin’s maximum principle extended to handle both shipment and per-region capacity limits. We use Pontryagin’s result to rule out the existence of singular arcs and obtain a complete characterization of the optimal policy as bang-bang, with at most one switching time per region per week. Numerical experiments on networks of 3 to 8 cities confirm that the predicted switching structure arises from the linear cost assumption, and we compare these findings with optimal quadratic-cost policies.
Date Issued
2025-05-30
Date Acceptance
2025-05-23
Citation
IEEE Control Systems, 2025
ISSN
1066-033X
Publisher
Institute of Electrical and Electronics Engineers
Journal / Book Title
IEEE Control Systems
Copyright Statement
Copyright © 2025, IEEE. This is the author’s accepted manuscript made available under a CC-BY licence in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy)
License URL
Publication Status
Published online
Date Publish Online
2025-05-30