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Optimal control for a SIR epidemic model with limited quarantine

Social distance, quarantines and total lock-downs are non-pharmaceutical interventions that policymakers have used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to societies in terms of social and economic costs, and they can be maintained only for a short pe...

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Autores principales: Balderrama, Rocío, Peressutti, Javier, Pinasco, Juan Pablo, Vazquez, Federico, Vega, Constanza Sánchez de la
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9307862/
https://www.ncbi.nlm.nih.gov/pubmed/35869150
http://dx.doi.org/10.1038/s41598-022-16619-z
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author Balderrama, Rocío
Peressutti, Javier
Pinasco, Juan Pablo
Vazquez, Federico
Vega, Constanza Sánchez de la
author_facet Balderrama, Rocío
Peressutti, Javier
Pinasco, Juan Pablo
Vazquez, Federico
Vega, Constanza Sánchez de la
author_sort Balderrama, Rocío
collection PubMed
description Social distance, quarantines and total lock-downs are non-pharmaceutical interventions that policymakers have used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to societies in terms of social and economic costs, and they can be maintained only for a short period of time. Here we investigate the optimal strategies that minimize the impact of an epidemic, by studying the conditions for an optimal control of a Susceptible-Infected-Recovered model with a limitation on the total duration of the quarantine. The control is done by means of the reproduction number [Formula: see text] , i.e., the number of secondary infections produced by a primary infection, which can be arbitrarily varied in time over a quarantine period T to account for external interventions. We also assume that the most strict quarantine (lower bound of [Formula: see text] ) cannot last for a period longer than a value [Formula: see text] . The aim is to minimize the cumulative number of ever-infected individuals (recovered) and the socioeconomic cost of interventions in the long term, by finding the optimal way to vary [Formula: see text] . We show that the optimal solution is a single bang-bang, i.e., the strict quarantine is turned on only once, and is turned off after the maximum allowed time [Formula: see text] . Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, [Formula: see text] and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations.
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spelling pubmed-93078622022-07-24 Optimal control for a SIR epidemic model with limited quarantine Balderrama, Rocío Peressutti, Javier Pinasco, Juan Pablo Vazquez, Federico Vega, Constanza Sánchez de la Sci Rep Article Social distance, quarantines and total lock-downs are non-pharmaceutical interventions that policymakers have used to mitigate the spread of the COVID-19 virus. However, these measures could be harmful to societies in terms of social and economic costs, and they can be maintained only for a short period of time. Here we investigate the optimal strategies that minimize the impact of an epidemic, by studying the conditions for an optimal control of a Susceptible-Infected-Recovered model with a limitation on the total duration of the quarantine. The control is done by means of the reproduction number [Formula: see text] , i.e., the number of secondary infections produced by a primary infection, which can be arbitrarily varied in time over a quarantine period T to account for external interventions. We also assume that the most strict quarantine (lower bound of [Formula: see text] ) cannot last for a period longer than a value [Formula: see text] . The aim is to minimize the cumulative number of ever-infected individuals (recovered) and the socioeconomic cost of interventions in the long term, by finding the optimal way to vary [Formula: see text] . We show that the optimal solution is a single bang-bang, i.e., the strict quarantine is turned on only once, and is turned off after the maximum allowed time [Formula: see text] . Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, [Formula: see text] and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations. Nature Publishing Group UK 2022-07-22 /pmc/articles/PMC9307862/ /pubmed/35869150 http://dx.doi.org/10.1038/s41598-022-16619-z Text en © The Author(s) 2022 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 Article
Balderrama, Rocío
Peressutti, Javier
Pinasco, Juan Pablo
Vazquez, Federico
Vega, Constanza Sánchez de la
Optimal control for a SIR epidemic model with limited quarantine
title Optimal control for a SIR epidemic model with limited quarantine
title_full Optimal control for a SIR epidemic model with limited quarantine
title_fullStr Optimal control for a SIR epidemic model with limited quarantine
title_full_unstemmed Optimal control for a SIR epidemic model with limited quarantine
title_short Optimal control for a SIR epidemic model with limited quarantine
title_sort optimal control for a sir epidemic model with limited quarantine
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9307862/
https://www.ncbi.nlm.nih.gov/pubmed/35869150
http://dx.doi.org/10.1038/s41598-022-16619-z
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