On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate

Detalhes bibliográficos
Autor(a) principal: BÁEZ-SÁNCHEZ,ANDRES DAVID
Data de Publicação: 2020
Outros Autores: BOBKO,NARA
Tipo de documento: Artigo
Idioma: eng
Título da fonte: TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
Texto Completo: http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512020000300409
Resumo: ABSTRACT We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also the stability of the disease-free equilibrium. We show that, in contrast with classical SIR models, a system with a recovery-dependent infection rate can have multiple endemic stable equilibria (multistability) and multiple unstable saddle points of equilibria. We establish conditions for the occurrence of these phenomena and illustrate the results with some examples.
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spelling On equilibria stability in an epidemiological SIR model with recovery-dependent infection rateSIR epidemiological modelrecovery-dependent infection rateendemic equilibriamultistabilityABSTRACT We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also the stability of the disease-free equilibrium. We show that, in contrast with classical SIR models, a system with a recovery-dependent infection rate can have multiple endemic stable equilibria (multistability) and multiple unstable saddle points of equilibria. We establish conditions for the occurrence of these phenomena and illustrate the results with some examples.Sociedade Brasileira de Matemática Aplicada e Computacional2020-12-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersiontext/htmlhttp://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512020000300409TEMA (São Carlos) v.21 n.3 2020reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)instname:Sociedade Brasileira de Matemática Aplicada e Computacionalinstacron:SBMAC10.5540/tema.2020.021.03.0409info:eu-repo/semantics/openAccessBÁEZ-SÁNCHEZ,ANDRES DAVIDBOBKO,NARAeng2020-11-27T00:00:00Zoai:scielo:S2179-84512020000300409Revistahttp://www.scielo.br/temaPUBhttps://old.scielo.br/oai/scielo-oai.phpcastelo@icmc.usp.br2179-84511677-1966opendoar:2020-11-27T00:00TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacionalfalse
dc.title.none.fl_str_mv On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate
title On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate
spellingShingle On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate
BÁEZ-SÁNCHEZ,ANDRES DAVID
SIR epidemiological model
recovery-dependent infection rate
endemic equilibria
multistability
title_short On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate
title_full On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate
title_fullStr On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate
title_full_unstemmed On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate
title_sort On equilibria stability in an epidemiological SIR model with recovery-dependent infection rate
author BÁEZ-SÁNCHEZ,ANDRES DAVID
author_facet BÁEZ-SÁNCHEZ,ANDRES DAVID
BOBKO,NARA
author_role author
author2 BOBKO,NARA
author2_role author
dc.contributor.author.fl_str_mv BÁEZ-SÁNCHEZ,ANDRES DAVID
BOBKO,NARA
dc.subject.por.fl_str_mv SIR epidemiological model
recovery-dependent infection rate
endemic equilibria
multistability
topic SIR epidemiological model
recovery-dependent infection rate
endemic equilibria
multistability
description ABSTRACT We consider an epidemiological SIR model with an infection rate depending on the recovered population. We establish sufficient conditions for existence, uniqueness, and stability (local and global) of endemic equilibria and consider also the stability of the disease-free equilibrium. We show that, in contrast with classical SIR models, a system with a recovery-dependent infection rate can have multiple endemic stable equilibria (multistability) and multiple unstable saddle points of equilibria. We establish conditions for the occurrence of these phenomena and illustrate the results with some examples.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-01
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512020000300409
url http://old.scielo.br/scielo.php?script=sci_arttext&pid=S2179-84512020000300409
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.5540/tema.2020.021.03.0409
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv text/html
dc.publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
publisher.none.fl_str_mv Sociedade Brasileira de Matemática Aplicada e Computacional
dc.source.none.fl_str_mv TEMA (São Carlos) v.21 n.3 2020
reponame:TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
instname:Sociedade Brasileira de Matemática Aplicada e Computacional
instacron:SBMAC
instname_str Sociedade Brasileira de Matemática Aplicada e Computacional
instacron_str SBMAC
institution SBMAC
reponame_str TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
collection TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online)
repository.name.fl_str_mv TEMA (Sociedade Brasileira de Matemática Aplicada e Computacional. Online) - Sociedade Brasileira de Matemática Aplicada e Computacional
repository.mail.fl_str_mv castelo@icmc.usp.br
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