Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates

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In this paper, we consider a modified SIR model, implementing a population of Pathogens interacting with a human population of Susceptibles, with which we will have 4 ordinary differential equations in our system. The objective of this work is to analyze the stability of the disease free point (loca...

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Detalles Bibliográficos
Autores: Huapaya Quispe, Javier, Barahona Mart´ınez, Willy, De La Cruz Marcacuzco, Roc´ıo
Formato: artículo
Fecha de Publicación:2021
Institución:Universidad Nacional Mayor de San Marcos
Repositorio:Revistas - Universidad Nacional Mayor de San Marcos
Lenguaje:español
OAI Identifier:oai:ojs.csi.unmsm:article/21869
Enlace del recurso:https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/21869
Nivel de acceso:acceso abierto
Materia:SIR model
Stability
Basic Reproduction Number
Routh Hurwitz Criterion
Next Generation Matrix
Numerical Simulation
Modelo SIR
Estabilidad
N´umero B´asico de Reproducci´on
Criterio de Routh Hurwitz
Matriz de la Pr´oxima Generaci´on
Simulaci´on Num´erica
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spelling Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission RatesAnálisis de Estabilidad Local de la Dinámica COVID-19 de un Modelo SIR con Tasas de Transmisión no LinealHuapaya Quispe, JavierBarahona Mart´ınez, WillyDe La Cruz Marcacuzco, Roc´ıoHuapaya Quispe, JavierBarahona Mart´ınez, WillyDe La Cruz Marcacuzco, Roc´ıoSIR modelStabilityBasic Reproduction NumberRouth Hurwitz CriterionNext Generation MatrixNumerical SimulationModelo SIREstabilidadN´umero B´asico de Reproducci´onCriterio de Routh HurwitzMatriz de la Pr´oxima Generaci´onSimulaci´on Num´ericaIn this paper, we consider a modified SIR model, implementing a population of Pathogens interacting with a human population of Susceptibles, with which we will have 4 ordinary differential equations in our system. The objective of this work is to analyze the stability of the disease free point (local and global) and the endemic equilibrium point (local) of this mathematical model. In addition, numerical simulations to the model are presented to contrast the effects of nonlinear transmission rates and other parameters.En este artículo, consideramos un modelo SIR modificado, implementando una población de Patógenos que interactúa con una población humana de Susceptibles, con lo cual tendremos en nuestro sistema 4 ecuaciones diferenciales ordinarias. El objetivo de este trabajo, es analizar la estabilidad del punto libre de enfermedad (local y global) y el punto de equilibrio endémico (local) de este modelo matemático. Además se presentan simulaciones numéricas al modelo para contrastar los efectos de las tasas de transmisión no lineal y otros parámetros.Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas2021-12-30info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/2186910.15381/pesquimat.v24i2.21869Pesquimat; Vol. 24 No. 2 (2021); 82-96Pesquimat; Vol. 24 Núm. 2 (2021); 82-961609-84391560-912Xreponame:Revistas - Universidad Nacional Mayor de San Marcosinstname:Universidad Nacional Mayor de San Marcosinstacron:UNMSMspahttps://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/21869/17593Derechos de autor 2021 Javier Huapaya Quispe, Willy Barahona Mart´ınez, Roc´ıo De La Cruz Marcacuzcohttp://creativecommons.org/licenses/by-nc-sa/4.0info:eu-repo/semantics/openAccessoai:ojs.csi.unmsm:article/218692021-12-30T12:10:20Z
dc.title.none.fl_str_mv Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
Análisis de Estabilidad Local de la Dinámica COVID-19 de un Modelo SIR con Tasas de Transmisión no Lineal
title Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
spellingShingle Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
Huapaya Quispe, Javier
SIR model
Stability
Basic Reproduction Number
Routh Hurwitz Criterion
Next Generation Matrix
Numerical Simulation
Modelo SIR
Estabilidad
N´umero B´asico de Reproducci´on
Criterio de Routh Hurwitz
Matriz de la Pr´oxima Generaci´on
Simulaci´on Num´erica
title_short Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
title_full Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
title_fullStr Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
title_full_unstemmed Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
title_sort Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
dc.creator.none.fl_str_mv Huapaya Quispe, Javier
Barahona Mart´ınez, Willy
De La Cruz Marcacuzco, Roc´ıo
Huapaya Quispe, Javier
Barahona Mart´ınez, Willy
De La Cruz Marcacuzco, Roc´ıo
author Huapaya Quispe, Javier
author_facet Huapaya Quispe, Javier
Barahona Mart´ınez, Willy
De La Cruz Marcacuzco, Roc´ıo
author_role author
author2 Barahona Mart´ınez, Willy
De La Cruz Marcacuzco, Roc´ıo
author2_role author
author
dc.subject.none.fl_str_mv SIR model
Stability
Basic Reproduction Number
Routh Hurwitz Criterion
Next Generation Matrix
Numerical Simulation
Modelo SIR
Estabilidad
N´umero B´asico de Reproducci´on
Criterio de Routh Hurwitz
Matriz de la Pr´oxima Generaci´on
Simulaci´on Num´erica
topic SIR model
Stability
Basic Reproduction Number
Routh Hurwitz Criterion
Next Generation Matrix
Numerical Simulation
Modelo SIR
Estabilidad
N´umero B´asico de Reproducci´on
Criterio de Routh Hurwitz
Matriz de la Pr´oxima Generaci´on
Simulaci´on Num´erica
description In this paper, we consider a modified SIR model, implementing a population of Pathogens interacting with a human population of Susceptibles, with which we will have 4 ordinary differential equations in our system. The objective of this work is to analyze the stability of the disease free point (local and global) and the endemic equilibrium point (local) of this mathematical model. In addition, numerical simulations to the model are presented to contrast the effects of nonlinear transmission rates and other parameters.
publishDate 2021
dc.date.none.fl_str_mv 2021-12-30
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://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/21869
10.15381/pesquimat.v24i2.21869
url https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/21869
identifier_str_mv 10.15381/pesquimat.v24i2.21869
dc.language.none.fl_str_mv spa
language spa
dc.relation.none.fl_str_mv https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/21869/17593
dc.rights.none.fl_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0
info:eu-repo/semantics/openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas
publisher.none.fl_str_mv Universidad Nacional Mayor de San Marcos, Facultad de Ciencias Matemáticas
dc.source.none.fl_str_mv Pesquimat; Vol. 24 No. 2 (2021); 82-96
Pesquimat; Vol. 24 Núm. 2 (2021); 82-96
1609-8439
1560-912X
reponame:Revistas - Universidad Nacional Mayor de San Marcos
instname:Universidad Nacional Mayor de San Marcos
instacron:UNMSM
instname_str Universidad Nacional Mayor de San Marcos
instacron_str UNMSM
institution UNMSM
reponame_str Revistas - Universidad Nacional Mayor de San Marcos
collection Revistas - Universidad Nacional Mayor de San Marcos
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1795238281169862656
score 13.987529
Local Stability Analysis of COVID-19 Dynamics of a SIR Model with Non-Linear Transmission Rates
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