An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns

This paper analyses an SIRS epidemic model with the vaccination of susceptible individuals and treatment of infectious ones. Both actions are governed by a designed control system whose inputs are the subpopulations of the epidemic model. In addition, the vaccination of a proportion of newborns is c...

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Autores: Alonso Quesada, Santiago, De la Sen Parte, Manuel, Nistal Riobello, Raúl
Tipo de documento: artigo
Data de publicação:2021
País:España
Recursos:Universidad del País Vasco
Repositório:Addi. Archivo Digital para la Docencia y la Investigación
OAI Identifier:oai:addi.ehu.eus:10810/54917
Acesso em linha:http://hdl.handle.net/10810/54917
Access Level:Acceso aberto
Palavra-chave:epidemic models
vaccination and treatment actions
feedback control
equilibrium points
stability
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spelling An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of NewbornsAlonso Quesada, SantiagoDe la Sen Parte, ManuelNistal Riobello, Raúlepidemic modelsvaccination and treatment actionsfeedback controlequilibrium pointsstabilityThis paper analyses an SIRS epidemic model with the vaccination of susceptible individuals and treatment of infectious ones. Both actions are governed by a designed control system whose inputs are the subpopulations of the epidemic model. In addition, the vaccination of a proportion of newborns is considered. The control reproduction number Rc of the controlled epidemic model is calculated, and its influence in the existence and stability of equilibrium points is studied. If such a number is smaller than a threshold value R¯¯¯c, then the model has a unique equilibrium point: the so-called disease-free equilibrium point at which there are not infectious individuals. Furthermore, such an equilibrium point is locally and globally asymptotically stable. On the contrary, if Rc>R¯¯¯c, then the model has two equilibrium points: the referred disease-free one, which is unstable, and an endemic one at which there are infectious individuals. The proposed control strategy provides several free-design parameters that influence both values Rc and R¯¯¯c. Then, such parameters can be appropriately adjusted for guaranteeing the non-existence of the endemic equilibrium point and, in this way, eradicating the persistence of the infectious disease.This research received support from the Spanish Government through grant RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE).MDPI2022202220212022info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10810/54917reponame:Addi. Archivo Digital para la Docencia y la Investigacióninstname:Universidad del País VascoInglésinfo:eu-repo/grantAgreement/MCIU/RTI2018-094336-B-I00/https://www.mdpi.com/2227-7390/10/1/36info:eu-repo/semantics/openAccess© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).oai:addi.ehu.eus:10810/549172026-06-18T09:23:17Z
dc.title.none.fl_str_mv An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns
title An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns
spellingShingle An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns
Alonso Quesada, Santiago
epidemic models
vaccination and treatment actions
feedback control
equilibrium points
stability
title_short An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns
title_full An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns
title_fullStr An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns
title_full_unstemmed An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns
title_sort An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns
dc.creator.none.fl_str_mv Alonso Quesada, Santiago
De la Sen Parte, Manuel
Nistal Riobello, Raúl
author Alonso Quesada, Santiago
author_facet Alonso Quesada, Santiago
De la Sen Parte, Manuel
Nistal Riobello, Raúl
author_role author
author2 De la Sen Parte, Manuel
Nistal Riobello, Raúl
author2_role author
author
dc.subject.none.fl_str_mv epidemic models
vaccination and treatment actions
feedback control
equilibrium points
stability
topic epidemic models
vaccination and treatment actions
feedback control
equilibrium points
stability
description This paper analyses an SIRS epidemic model with the vaccination of susceptible individuals and treatment of infectious ones. Both actions are governed by a designed control system whose inputs are the subpopulations of the epidemic model. In addition, the vaccination of a proportion of newborns is considered. The control reproduction number Rc of the controlled epidemic model is calculated, and its influence in the existence and stability of equilibrium points is studied. If such a number is smaller than a threshold value R¯¯¯c, then the model has a unique equilibrium point: the so-called disease-free equilibrium point at which there are not infectious individuals. Furthermore, such an equilibrium point is locally and globally asymptotically stable. On the contrary, if Rc>R¯¯¯c, then the model has two equilibrium points: the referred disease-free one, which is unstable, and an endemic one at which there are infectious individuals. The proposed control strategy provides several free-design parameters that influence both values Rc and R¯¯¯c. Then, such parameters can be appropriately adjusted for guaranteeing the non-existence of the endemic equilibrium point and, in this way, eradicating the persistence of the infectious disease.
publishDate 2021
dc.date.none.fl_str_mv 2021
2022
2022
2022
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10810/54917
url http://hdl.handle.net/10810/54917
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/MCIU/RTI2018-094336-B-I00/
https://www.mdpi.com/2227-7390/10/1/36
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv MDPI
publisher.none.fl_str_mv MDPI
dc.source.none.fl_str_mv reponame:Addi. Archivo Digital para la Docencia y la Investigación
instname:Universidad del País Vasco
instname_str Universidad del País Vasco
reponame_str Addi. Archivo Digital para la Docencia y la Investigación
collection Addi. Archivo Digital para la Docencia y la Investigación
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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