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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/136258
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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 Técnicas2025-09-29T10:40:16Zoai: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:34982025-09-29 10:40:16.245CONICET 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 |
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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 |
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1844614429997531136 |
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13.070432 |