Optimal control for a SIR epidemic model with limited quarantine

Autores
Balderrama, Rocio Celeste; Peressutti, Javier Hector; Pinasco, Juan Pablo; Vazquez, Federico; Sanchez Fernandez de la Vega, Constanza Mariel
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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 σ(t) , 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 σ) cannot last for a period longer than a value τ. 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 σ(t). 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 τ. Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, τ and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations.
Fil: Balderrama, Rocio Celeste. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Peressutti, Javier Hector. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Fil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Fil: Vazquez, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: Sanchez Fernandez de la Vega, Constanza Mariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Materia
SIR
COVID-19
Quarantine
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/204060
Acceder
id CONICETDig_63966b1abb50d5d873091ae103605666
oai_identifier_str oai:ri.conicet.gov.ar:11336/204060
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Optimal control for a SIR epidemic model with limited quarantineBalderrama, Rocio CelestePeressutti, Javier HectorPinasco, Juan PabloVazquez, FedericoSanchez Fernandez de la Vega, Constanza MarielSIRCOVID-19Quarantinehttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1Social 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 σ(t) , 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 σ) cannot last for a period longer than a value τ. 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 σ(t). 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 τ. Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, τ and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations.Fil: Balderrama, Rocio Celeste. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Peressutti, Javier Hector. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; ArgentinaFil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; ArgentinaFil: Vazquez, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Sanchez Fernandez de la Vega, Constanza Mariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaNature2022-07info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/204060Balderrama, Rocio Celeste; Peressutti, Javier Hector; Pinasco, Juan Pablo; Vazquez, Federico; Sanchez Fernandez de la Vega, Constanza Mariel; Optimal control for a SIR epidemic model with limited quarantine; Nature; Scientific Reports; 12; 1; 7-2022; 1-262045-2322CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.nature.com/articles/s41598-022-16619-z#citeasinfo:eu-repo/semantics/altIdentifier/doi/10.1038/s41598-022-16619-zinfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:51:11Zoai:ri.conicet.gov.ar:11336/204060instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:51:11.412CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Optimal control for a SIR epidemic model with limited quarantine
title Optimal control for a SIR epidemic model with limited quarantine
spellingShingle Optimal control for a SIR epidemic model with limited quarantine
Balderrama, Rocio Celeste
SIR
COVID-19
Quarantine
title_short 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_sort Optimal control for a SIR epidemic model with limited quarantine
dc.creator.none.fl_str_mv Balderrama, Rocio Celeste
Peressutti, Javier Hector
Pinasco, Juan Pablo
Vazquez, Federico
Sanchez Fernandez de la Vega, Constanza Mariel
author Balderrama, Rocio Celeste
author_facet Balderrama, Rocio Celeste
Peressutti, Javier Hector
Pinasco, Juan Pablo
Vazquez, Federico
Sanchez Fernandez de la Vega, Constanza Mariel
author_role author
author2 Peressutti, Javier Hector
Pinasco, Juan Pablo
Vazquez, Federico
Sanchez Fernandez de la Vega, Constanza Mariel
author2_role author
author
author
author
dc.subject.none.fl_str_mv SIR
COVID-19
Quarantine
topic SIR
COVID-19
Quarantine
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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 σ(t) , 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 σ) cannot last for a period longer than a value τ. 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 σ(t). 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 τ. Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, τ and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations.
Fil: Balderrama, Rocio Celeste. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina
Fil: Peressutti, Javier Hector. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata. Instituto de Investigaciones Físicas de Mar del Plata. Universidad Nacional de Mar del Plata. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Físicas de Mar del Plata; Argentina
Fil: Pinasco, Juan Pablo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - San Luis. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi". Universidad Nacional de San Luis. Facultad de Ciencias Físico, Matemáticas y Naturales. Instituto de Matemática Aplicada de San Luis "Prof. Ezio Marchi"; Argentina
Fil: Vazquez, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
Fil: Sanchez Fernandez de la Vega, Constanza Mariel. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina
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 σ(t) , 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 σ) cannot last for a period longer than a value τ. 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 σ(t). 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 τ. Besides, we calculate the optimal time to begin and end the strict quarantine, which depends on T, τ and the initial conditions. We provide rigorous proofs of these results and check that are in perfect agreement with numerical computations.
publishDate 2022
dc.date.none.fl_str_mv 2022-07
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/204060
Balderrama, Rocio Celeste; Peressutti, Javier Hector; Pinasco, Juan Pablo; Vazquez, Federico; Sanchez Fernandez de la Vega, Constanza Mariel; Optimal control for a SIR epidemic model with limited quarantine; Nature; Scientific Reports; 12; 1; 7-2022; 1-26
2045-2322
CONICET Digital
CONICET
url http://hdl.handle.net/11336/204060
identifier_str_mv Balderrama, Rocio Celeste; Peressutti, Javier Hector; Pinasco, Juan Pablo; Vazquez, Federico; Sanchez Fernandez de la Vega, Constanza Mariel; Optimal control for a SIR epidemic model with limited quarantine; Nature; Scientific Reports; 12; 1; 7-2022; 1-26
2045-2322
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.nature.com/articles/s41598-022-16619-z#citeas
info:eu-repo/semantics/altIdentifier/doi/10.1038/s41598-022-16619-z
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv Nature
publisher.none.fl_str_mv Nature
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
_version_ 1842269078689939456
score 13.13397

Publicaciones similares