Bang-Bang Optimal Control of Vaccination in Metapopulation Epidemics with Linear Cost Structures
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909631184371712 |
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| author | Moschen, Lucas Machado Aronna, Maria Soledad |
| author_facet | Moschen, Lucas Machado Aronna, Maria Soledad |
| contents | This paper investigates optimal vaccination strategies in a metapopulation epidemic model. We consider a linear cost to better capture operational considerations, such as the total number of vaccines or hospitalizations, in contrast to the standard quadratic cost assumption on the control. The model incorporates state and mixed control-state constraints, and we derive necessary optimality conditions based on Pontryagin's Maximum Principle. We use Pontryagin's result to rule out the possibility of the occurrence of singular arcs and to provide a full characterization of the optimal control. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_15154 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bang-Bang Optimal Control of Vaccination in Metapopulation Epidemics with Linear Cost Structures Moschen, Lucas Machado Aronna, Maria Soledad Optimization and Control Populations and Evolution 49K30, 49J30 (Primary) 92D30 (Secondary) I.2.8 This paper investigates optimal vaccination strategies in a metapopulation epidemic model. We consider a linear cost to better capture operational considerations, such as the total number of vaccines or hospitalizations, in contrast to the standard quadratic cost assumption on the control. The model incorporates state and mixed control-state constraints, and we derive necessary optimality conditions based on Pontryagin's Maximum Principle. We use Pontryagin's result to rule out the possibility of the occurrence of singular arcs and to provide a full characterization of the optimal control. |
| title | Bang-Bang Optimal Control of Vaccination in Metapopulation Epidemics with Linear Cost Structures |
| topic | Optimization and Control Populations and Evolution 49K30, 49J30 (Primary) 92D30 (Secondary) I.2.8 |
| url | https://arxiv.org/abs/2503.15154 |