Critical Asymptotic Behaviour in the SIR model

Autores
Capanna, Monia
Año de publicación
2019
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between susceptibles and infected so that an infected individual is more likely to infect nearby sites than those further away. For fixed time, we prove that the density fields weakly converge to the solution of a PDE´s system, as the number of particles increases. We find an implicit expression for the final survivor density of the limit equation and we analyze the asymptotics of the microscopic system, by taking first the time and after the number of particles to infinity, showing a critical behaviour for some values of the parameters when the system is set in the mean field regime.
Fil: Capanna, Monia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Materia
INFECTION MODEL
INTERACTING PARTICLE SYSTEM
HYDRODYNAMIC LIMIT
ASYMPTOTIC ANALYSIS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/136258
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/136258
network_acronym_str CONICETDig
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network_name_str CONICET Digital (CONICET)
spelling Critical Asymptotic Behaviour in the SIR modelCapanna, MoniaINFECTION MODELINTERACTING PARTICLE SYSTEMHYDRODYNAMIC LIMITASYMPTOTIC ANALYSIShttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between susceptibles and infected so that an infected individual is more likely to infect nearby sites than those further away. For fixed time, we prove that the density fields weakly converge to the solution of a PDE´s system, as the number of particles increases. We find an implicit expression for the final survivor density of the limit equation and we analyze the asymptotics of the microscopic system, by taking first the time and after the number of particles to infinity, showing a critical behaviour for some values of the parameters when the system is set in the mean field regime.Fil: Capanna, Monia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaPolymat Publishing Company2019-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/136258Capanna, Monia; Critical Asymptotic Behaviour in the SIR model; Polymat Publishing Company; Markov Processes And Related Fields; 25; 5; 12-2019; 763-7961024-2953CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://math-mprf.org/journal/articles/id1557/info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1708.03905info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-22T12:12:38Zoai:ri.conicet.gov.ar:11336/136258instacron: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:34982025-10-22 12:12:38.826CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Critical Asymptotic Behaviour in the SIR model
title Critical Asymptotic Behaviour in the SIR model
spellingShingle Critical Asymptotic Behaviour in the SIR model
Capanna, Monia
INFECTION MODEL
INTERACTING PARTICLE SYSTEM
HYDRODYNAMIC LIMIT
ASYMPTOTIC ANALYSIS
title_short Critical Asymptotic Behaviour in the SIR model
title_full Critical Asymptotic Behaviour in the SIR model
title_fullStr Critical Asymptotic Behaviour in the SIR model
title_full_unstemmed Critical Asymptotic Behaviour in the SIR model
title_sort Critical Asymptotic Behaviour in the SIR model
dc.creator.none.fl_str_mv Capanna, Monia
author Capanna, Monia
author_facet Capanna, Monia
author_role author
dc.subject.none.fl_str_mv INFECTION MODEL
INTERACTING PARTICLE SYSTEM
HYDRODYNAMIC LIMIT
ASYMPTOTIC ANALYSIS
topic INFECTION MODEL
INTERACTING PARTICLE SYSTEM
HYDRODYNAMIC LIMIT
ASYMPTOTIC ANALYSIS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between susceptibles and infected so that an infected individual is more likely to infect nearby sites than those further away. For fixed time, we prove that the density fields weakly converge to the solution of a PDE´s system, as the number of particles increases. We find an implicit expression for the final survivor density of the limit equation and we analyze the asymptotics of the microscopic system, by taking first the time and after the number of particles to infinity, showing a critical behaviour for some values of the parameters when the system is set in the mean field regime.
Fil: Capanna, Monia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
description This article is devoted to the analysis of a particle system model for epidemics among a finite population with susceptible, infective and removed individuals (SIR). The infection mechanism depends on the relative distance between susceptibles and infected so that an infected individual is more likely to infect nearby sites than those further away. For fixed time, we prove that the density fields weakly converge to the solution of a PDE´s system, as the number of particles increases. We find an implicit expression for the final survivor density of the limit equation and we analyze the asymptotics of the microscopic system, by taking first the time and after the number of particles to infinity, showing a critical behaviour for some values of the parameters when the system is set in the mean field regime.
publishDate 2019
dc.date.none.fl_str_mv 2019-12
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/11336/136258
Capanna, Monia; Critical Asymptotic Behaviour in the SIR model; Polymat Publishing Company; Markov Processes And Related Fields; 25; 5; 12-2019; 763-796
1024-2953
CONICET Digital
CONICET
url http://hdl.handle.net/11336/136258
identifier_str_mv Capanna, Monia; Critical Asymptotic Behaviour in the SIR model; Polymat Publishing Company; Markov Processes And Related Fields; 25; 5; 12-2019; 763-796
1024-2953
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://math-mprf.org/journal/articles/id1557/
info:eu-repo/semantics/altIdentifier/url/https://arxiv.org/abs/1708.03905
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Polymat Publishing Company
publisher.none.fl_str_mv Polymat Publishing Company
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_ 1846782524836020224
score 12.982451

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