Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness

In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the rate of creation of the less aware individuals, which depend...

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Autores: Juher, David, Rojas Pérez, David, Saldaña Meca, Joan
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2023
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10256/22900
Acceso en línea:http://hdl.handle.net/10256/22900
Access Level:acceso abierto
Palabra clave:Epidèmies -- Models matemàtics
Teoria de la bifurcació
Epidemics -- Mathematical models
Bifurcation theory
Models estocàstics
Stochastic models
Cicles límits
Limit cycles
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spelling Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awarenessJuher, DavidRojas Pérez, DavidSaldaña Meca, JoanEpidèmies -- Models matemàticsTeoria de la bifurcacióEpidemics -- Mathematical modelsBifurcation theoryModels estocàsticsStochastic modelsCicles límitsLimit cyclesIn this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the rate of creation of the less aware individuals, which depend on the disease prevalence in a non-linear way. For the ODE model, the numerical computation of the limit cycles and the study of their stability are made by means of the Poincaré map. Moreover, sufficient conditions for the existence of an endemic equilibrium are also obtained. These conditions involve a rather natural relationship between the transmissibility of the disease and that of awareness. Finally, stochastic simulations of the model under a very low rate of imported cases are used to confirm the scenarios of bistability (endemic equilibrium and limit cycle) observed in the solutions of the ODE modelThis work is supported by the grants PID2019-104437GB-I00 and PID2020-118281GB-C31 funded by MCIN/AEI/, Spain 10.13039/501100011033. The authors are members of the Consolidated Research Groups 2021 SGR 00113 of the Generalitat de Catalunya. D.R. is a Serra Húnter FellowOpen Access funding provided thanks to the CRUE-CSIC agreement with ElsevierElsevierAgencia Estatal de Investigación2023info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionpeer-reviewedapplication/pdfhttp://hdl.handle.net/10256/22900http://hdl.handle.net/10256/22900Physica. D, Nonlinear phenomena, 2023, vol. 448, art.núm. 133714Articles publicats (D-IMAE)Juher, David Rojas Pérez, David JSaldaña Meca, Joan 2023 Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness Physica. D, Nonlinear phenomena 448 art.núm. 133714reponame:Recercat. Dipósit de la Recerca de Catalunyainstname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)Inglésinfo:eu-repo/semantics/altIdentifier/doi/10.1016/j.physd.2023.133714info:eu-repo/semantics/altIdentifier/issn/0167-2789info:eu-repo/semantics/altIdentifier/eissn/1872-8022PID2019-104437GB-I00info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104437GB-I00Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0info:eu-repo/semantics/openAccessoai:recercat.cat:10256/229002026-05-29T05:05:01Z
dc.title.none.fl_str_mv Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
title Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
spellingShingle Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
Juher, David
Epidèmies -- Models matemàtics
Teoria de la bifurcació
Epidemics -- Mathematical models
Bifurcation theory
Models estocàstics
Stochastic models
Cicles límits
Limit cycles
title_short Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
title_full Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
title_fullStr Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
title_full_unstemmed Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
title_sort Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness
dc.creator.none.fl_str_mv Juher, David
Rojas Pérez, David
Saldaña Meca, Joan
author Juher, David
author_facet Juher, David
Rojas Pérez, David
Saldaña Meca, Joan
author_role author
author2 Rojas Pérez, David
Saldaña Meca, Joan
author2_role author
author
dc.contributor.none.fl_str_mv Agencia Estatal de Investigación
dc.subject.none.fl_str_mv Epidèmies -- Models matemàtics
Teoria de la bifurcació
Epidemics -- Mathematical models
Bifurcation theory
Models estocàstics
Stochastic models
Cicles límits
Limit cycles
topic Epidèmies -- Models matemàtics
Teoria de la bifurcació
Epidemics -- Mathematical models
Bifurcation theory
Models estocàstics
Stochastic models
Cicles límits
Limit cycles
description In this paper we study the appearance of bifurcations of limit cycles in an epidemic model with two types of aware individuals. All the transition rates are constant except for the alerting decay rate of the most aware individuals and the rate of creation of the less aware individuals, which depend on the disease prevalence in a non-linear way. For the ODE model, the numerical computation of the limit cycles and the study of their stability are made by means of the Poincaré map. Moreover, sufficient conditions for the existence of an endemic equilibrium are also obtained. These conditions involve a rather natural relationship between the transmissibility of the disease and that of awareness. Finally, stochastic simulations of the model under a very low rate of imported cases are used to confirm the scenarios of bistability (endemic equilibrium and limit cycle) observed in the solutions of the ODE model
publishDate 2023
dc.date.none.fl_str_mv 2023
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
peer-reviewed
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10256/22900
http://hdl.handle.net/10256/22900
url http://hdl.handle.net/10256/22900
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1016/j.physd.2023.133714
info:eu-repo/semantics/altIdentifier/issn/0167-2789
info:eu-repo/semantics/altIdentifier/eissn/1872-8022
PID2019-104437GB-I00
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-104437GB-I00
dc.rights.none.fl_str_mv Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconeixement-NoComercial-SenseObraDerivada 4.0 Internacional
http://creativecommons.org/licenses/by-nc-nd/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv Physica. D, Nonlinear phenomena, 2023, vol. 448, art.núm. 133714
Articles publicats (D-IMAE)
Juher, David Rojas Pérez, David JSaldaña Meca, Joan 2023 Saddle-node bifurcation of limit cycles in an epidemic model with two levels of awareness Physica. D, Nonlinear phenomena 448 art.núm. 133714
reponame:Recercat. Dipósit de la Recerca de Catalunya
instname:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
instname_str Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
reponame_str Recercat. Dipósit de la Recerca de Catalunya
collection Recercat. Dipósit de la Recerca de Catalunya
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812455

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