A simple planning problem for COVID-19 lockdown: a dynamic programming approach

A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Program...

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Autores principales: Calvia, Alessandro, Gozzi, Fausto, Lippi, Francesco, Zanco, Giovanni
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2023
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10105532/
https://www.ncbi.nlm.nih.gov/pubmed/37360773
http://dx.doi.org/10.1007/s00199-023-01493-1
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author Calvia, Alessandro
Gozzi, Fausto
Lippi, Francesco
Zanco, Giovanni
author_facet Calvia, Alessandro
Gozzi, Fausto
Lippi, Francesco
Zanco, Giovanni
author_sort Calvia, Alessandro
collection PubMed
description A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton–Jacobi–Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach.
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spelling pubmed-101055322023-04-17 A simple planning problem for COVID-19 lockdown: a dynamic programming approach Calvia, Alessandro Gozzi, Fausto Lippi, Francesco Zanco, Giovanni Econ Theory Research Article A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton–Jacobi–Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach. Springer Berlin Heidelberg 2023-04-15 /pmc/articles/PMC10105532/ /pubmed/37360773 http://dx.doi.org/10.1007/s00199-023-01493-1 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Research Article
Calvia, Alessandro
Gozzi, Fausto
Lippi, Francesco
Zanco, Giovanni
A simple planning problem for COVID-19 lockdown: a dynamic programming approach
title A simple planning problem for COVID-19 lockdown: a dynamic programming approach
title_full A simple planning problem for COVID-19 lockdown: a dynamic programming approach
title_fullStr A simple planning problem for COVID-19 lockdown: a dynamic programming approach
title_full_unstemmed A simple planning problem for COVID-19 lockdown: a dynamic programming approach
title_short A simple planning problem for COVID-19 lockdown: a dynamic programming approach
title_sort simple planning problem for covid-19 lockdown: a dynamic programming approach
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10105532/
https://www.ncbi.nlm.nih.gov/pubmed/37360773
http://dx.doi.org/10.1007/s00199-023-01493-1
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