Infinite horizon optimal control of a SIR epidemic under an ICU constraint
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916153455017984 |
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| author | Freddi, Lorenzo Goreac, Dan |
| author_facet | Freddi, Lorenzo Goreac, Dan |
| contents | The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem of a SIR epidemic on an infinite horizon. A state constraint related to intensive care units (ICU) capacity is imposed and the objective functional linearly depends on the state and the control. After preliminary asymptotic and viability analyses, a $Γ$-convergence argument is developed to reduce the problem to a finite horizon allowing to use a state constrained version of Pontryagin's theorem to characterize the structure of the optimal controls. Illustrating examples and numeric simulations are given according to the available data on Covid-19 epidemic in Italy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10513 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Infinite horizon optimal control of a SIR epidemic under an ICU constraint Freddi, Lorenzo Goreac, Dan Optimization and Control The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem of a SIR epidemic on an infinite horizon. A state constraint related to intensive care units (ICU) capacity is imposed and the objective functional linearly depends on the state and the control. After preliminary asymptotic and viability analyses, a $Γ$-convergence argument is developed to reduce the problem to a finite horizon allowing to use a state constrained version of Pontryagin's theorem to characterize the structure of the optimal controls. Illustrating examples and numeric simulations are given according to the available data on Covid-19 epidemic in Italy. |
| title | Infinite horizon optimal control of a SIR epidemic under an ICU constraint |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2306.10513 |