Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations

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In the present work, the existence of Uniformly Bound Solutions of a SI Mathematical Model with vital dynamics, with logistic growth for the Susceptibles, developed by Delay Differential Equations is constructed, and the behavior of the solutions will be studied (qualitative analysis) for the Infect...

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Detalles Bibliográficos
Autores: Pino Romero, Neisser, Salazar Fernández, Christian Ulises, López Cruz, Roxana
Formato: artículo
Fecha de Publicación:2019
Institución:Universidad Nacional de Trujillo
Repositorio:Revistas - Universidad Nacional de Trujillo
Lenguaje:español
OAI Identifier:oai:ojs.revistas.unitru.edu.pe:article/2446
Enlace del recurso:https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2446
Nivel de acceso:acceso abierto
Materia:Mathematical Epidemiology
Ordinary Differential Equations
Delay Differential Equations. Stationary Points
Local stability
Absolute Estability
Epidemiología Matemática
Ecuaciones Diferenciales Ordinarias
Ecuaciones Diferenciales con Retardo
Puntos Estacionarios
Estabilidad Local
Estabilidad Absoluta
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spelling Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential EquationsSolución Uniformemente Acotada y Estabilidad Asintótica del Punto Libre de Infección de un Modelo Matemático SI con Dinámica Vital (crecimiento logístico) mediante las Ecuaciones Diferenciales con RetardoPino Romero, NeisserSalazar Fernández, Christian UlisesLópez Cruz, RoxanaMathematical EpidemiologyOrdinary Differential EquationsDelay Differential Equations. Stationary PointsLocal stabilityAbsolute EstabilityEpidemiología MatemáticaEcuaciones Diferenciales OrdinariasEcuaciones Diferenciales con RetardoPuntos EstacionariosEstabilidad LocalEstabilidad AbsolutaIn the present work, the existence of Uniformly Bound Solutions of a SI Mathematical Model with vital dynamics, with logistic growth for the Susceptibles, developed by Delay Differential Equations is constructed, and the behavior of the solutions will be studied (qualitative analysis) for the Infection-Free Point where the necessary conditions for its asymptotic stability will be determined; and furthermore, that the Uniformly Bounded Solution of the Model tends to the steady state of the Infection-Free Point. In addition, it will be simulated computationally (approximate solutions) with initial populations and epidemiological rates of the model. The simulation will complement the qualitative analysis (behavior of solutions) to conclude trends of behaviors of the transmission of the disease overtime.En el presente trabajo, se construye la existencia de Soluciones Uniformemente Acotadas de un Modelo Matemático SI con dinámica vital, con crecimiento logístico para los Susceptibles, desarrollado mediante las Ecuaciones Diferenciales con Retardo, y se estudiará el comportamiento de las soluciones (análisis cualitativo) para el Punto Libre de Infección donde se determinará las condiciones necesarias para su estabilidad asintótica; y más aún, la Solución Uniformemente Acotada del Modelo tiende al estado estacionario del Punto Libre de Infección. Además, se simulará computacionalmente (soluciones aproximadas) con poblaciones iniciales y tasas epidemiológicas del modelo. La simulación complementará el análisis cualitativo (comportamiento de soluciones) para concluir tendencias de comportamientos de la transmisión de la enfermedad en el tiempo.National University of Trujillo - Academic Department of Mathematics2019-07-21info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdftext/htmlhttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/2446Selecciones Matemáticas; Vol. 6 No. 01 (2019): January - July; 66-76Selecciones Matemáticas; Vol. 6 Núm. 01 (2019): Enero-Julio; 66-76Selecciones Matemáticas; v. 6 n. 01 (2019): Enero-Julio; 66-762411-1783reponame:Revistas - Universidad Nacional de Trujilloinstname:Universidad Nacional de Trujilloinstacron:UNITRUspahttps://revistas.unitru.edu.pe/index.php/SSMM/article/view/2446/2484https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2446/2501Derechos de autor 2019 Selecciones Matemáticasinfo:eu-repo/semantics/openAccessoai:ojs.revistas.unitru.edu.pe:article/24462022-10-21T18:52:41Z
dc.title.none.fl_str_mv Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
Solución Uniformemente Acotada y Estabilidad Asintótica del Punto Libre de Infección de un Modelo Matemático SI con Dinámica Vital (crecimiento logístico) mediante las Ecuaciones Diferenciales con Retardo
title Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
spellingShingle Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
Pino Romero, Neisser
Mathematical Epidemiology
Ordinary Differential Equations
Delay Differential Equations. Stationary Points
Local stability
Absolute Estability
Epidemiología Matemática
Ecuaciones Diferenciales Ordinarias
Ecuaciones Diferenciales con Retardo
Puntos Estacionarios
Estabilidad Local
Estabilidad Absoluta
title_short Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
title_full Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
title_fullStr Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
title_full_unstemmed Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
title_sort Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
dc.creator.none.fl_str_mv Pino Romero, Neisser
Salazar Fernández, Christian Ulises
López Cruz, Roxana
author Pino Romero, Neisser
author_facet Pino Romero, Neisser
Salazar Fernández, Christian Ulises
López Cruz, Roxana
author_role author
author2 Salazar Fernández, Christian Ulises
López Cruz, Roxana
author2_role author
author
dc.subject.none.fl_str_mv Mathematical Epidemiology
Ordinary Differential Equations
Delay Differential Equations. Stationary Points
Local stability
Absolute Estability
Epidemiología Matemática
Ecuaciones Diferenciales Ordinarias
Ecuaciones Diferenciales con Retardo
Puntos Estacionarios
Estabilidad Local
Estabilidad Absoluta
topic Mathematical Epidemiology
Ordinary Differential Equations
Delay Differential Equations. Stationary Points
Local stability
Absolute Estability
Epidemiología Matemática
Ecuaciones Diferenciales Ordinarias
Ecuaciones Diferenciales con Retardo
Puntos Estacionarios
Estabilidad Local
Estabilidad Absoluta
description In the present work, the existence of Uniformly Bound Solutions of a SI Mathematical Model with vital dynamics, with logistic growth for the Susceptibles, developed by Delay Differential Equations is constructed, and the behavior of the solutions will be studied (qualitative analysis) for the Infection-Free Point where the necessary conditions for its asymptotic stability will be determined; and furthermore, that the Uniformly Bounded Solution of the Model tends to the steady state of the Infection-Free Point. In addition, it will be simulated computationally (approximate solutions) with initial populations and epidemiological rates of the model. The simulation will complement the qualitative analysis (behavior of solutions) to conclude trends of behaviors of the transmission of the disease overtime.
publishDate 2019
dc.date.none.fl_str_mv 2019-07-21
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2446
url https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2446
dc.language.none.fl_str_mv spa
language spa
dc.relation.none.fl_str_mv https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2446/2484
https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2446/2501
dc.rights.none.fl_str_mv Derechos de autor 2019 Selecciones Matemáticas
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Derechos de autor 2019 Selecciones Matemáticas
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
text/html
dc.publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
publisher.none.fl_str_mv National University of Trujillo - Academic Department of Mathematics
dc.source.none.fl_str_mv Selecciones Matemáticas; Vol. 6 No. 01 (2019): January - July; 66-76
Selecciones Matemáticas; Vol. 6 Núm. 01 (2019): Enero-Julio; 66-76
Selecciones Matemáticas; v. 6 n. 01 (2019): Enero-Julio; 66-76
2411-1783
reponame:Revistas - Universidad Nacional de Trujillo
instname:Universidad Nacional de Trujillo
instacron:UNITRU
instname_str Universidad Nacional de Trujillo
instacron_str UNITRU
institution UNITRU
reponame_str Revistas - Universidad Nacional de Trujillo
collection Revistas - Universidad Nacional de Trujillo
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 13.339478
Uniformly Bounded Solution and Asymptotic Stability of the Infection-Free Point of a SI Mathematical Model with Vital Dynamics (logistic growth) by Delay Differential Equations
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