Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students

In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invarianc...

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Autores:
Pérez, Edgardo
Tipo de recurso:
Fecha de publicación:
2020
Institución:
Universidad EAFIT
Repositorio:
Repositorio EAFIT
Idioma:
eng
OAI Identifier:
oai:repository.eafit.edu.co:10784/25811
Acceso en línea:
http://hdl.handle.net/10784/25811
Palabra clave:
Alcohol consumption
mathematical modeling
nonlinear dynamical systems
optimal control
basic reproduction number
numerical simulations
Consumo de alcohol
modelamiento matemático
sistemas dinámicos no lineales
control óptimo
número reproductivobásico
simulaciones numéricas
Rights
openAccess
License
Copyright © 2020 Edgardo Pérez
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spelling Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees2020-11-112021-02-19T16:41:44Z2020-11-112021-02-19T16:41:44Z1794-9165http://hdl.handle.net/10784/25811In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.En este trabajo, presentamos un modelo matemático no lineal, describiendola propagación de consumo de alcohol de alto riesgo entre estudiantesuniversitarios en Colombia. Probamos la existencia y estabilidad del estadode equilibrio libre de alcohol y el estado endémico por medio de funcionesde Lyapunov y el principio de invarianza de LaSalle. Además, aplicamoscontrol óptimo para estudiar el impacto de una medida preventiva sobrela propagación del comportamiento de consumo de alcohol entre losestudiantes universitarios. Finalmente, usamos simulaciones numéricas ydatos disponibles, proporcionados por la Oficina de las Naciones Unidascontra la Droga y el Delito (ONUDD) y el Ministerio de Justicia deColombia para validar el modelo matemático obtenido.application/pdfengUniversidad EAFIThttps://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6438/5067https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6438/5067Copyright © 2020 Edgardo Pérezinfo:eu-repo/semantics/openAccessAcceso abiertohttp://purl.org/coar/access_right/c_abf2Revista Ingeniería y Ciencias, Vol. 16 Núm. 32 (2020)Mathematical Modeling of the Spread of Alcoholism Among Colombian College StudentsMathematical Modeling of the Spread ofAlcoholism Among Colombian CollegeStudentsarticleinfo:eu-repo/semantics/articlepublishedVersioninfo:eu-repo/semantics/publishedVersionArtículohttp://purl.org/coar/version/c_970fb48d4fbd8a85http://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Alcohol consumptionmathematical modelingnonlinear dynamical systemsoptimal controlbasic reproduction numbernumerical simulationsConsumo de alcoholmodelamiento matemáticosistemas dinámicos no linealescontrol óptimonúmero reproductivobásicosimulaciones numéricasPérez, Edgardo67f24e3f-c229-4ef3-b0b0-78a128cfba54-1Universidad del SinúIngeniería y Ciencias1632195223THUMBNAILminaitura-ig_Mesa de trabajo 1.jpgminaitura-ig_Mesa de trabajo 1.jpgimage/jpeg265796https://repository.eafit.edu.co/bitstreams/9b55f347-2a07-42d7-99d6-f884a2e0963e/downloadda9b21a5c7e00c7f1127cef8e97035e0MD51ORIGINALdocument - 2021-04-28T221938.326.pdfdocument - 2021-04-28T221938.326.pdfPDF Completoapplication/pdf1252614https://repository.eafit.edu.co/bitstreams/77c6d0ff-0411-4481-bc17-00fd24505898/download54042a2f7f104a9f3ffdcec3c91ec802MD52articulo - copia.htmlarticulo - copia.htmlHTML Completotext/html375https://repository.eafit.edu.co/bitstreams/08f826ed-63e8-4ee2-aed0-39470f3397b2/download9ecd85497baaa921232727aa7c10dc5bMD5310784/25811oai:repository.eafit.edu.co:10784/258112024-12-04 11:47:19.99open.accesshttps://repository.eafit.edu.coRepositorio Institucional Universidad EAFITrepositorio@eafit.edu.co
dc.title.eng.fl_str_mv Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
dc.title.spa.fl_str_mv Mathematical Modeling of the Spread ofAlcoholism Among Colombian CollegeStudents
title Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
spellingShingle Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
Alcohol consumption
mathematical modeling
nonlinear dynamical systems
optimal control
basic reproduction number
numerical simulations
Consumo de alcohol
modelamiento matemático
sistemas dinámicos no lineales
control óptimo
número reproductivobásico
simulaciones numéricas
title_short Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
title_full Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
title_fullStr Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
title_full_unstemmed Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
title_sort Mathematical Modeling of the Spread of Alcoholism Among Colombian College Students
dc.creator.fl_str_mv Pérez, Edgardo
dc.contributor.author.spa.fl_str_mv Pérez, Edgardo
dc.contributor.affiliation.spa.fl_str_mv Universidad del Sinú
dc.subject.keyword.eng.fl_str_mv Alcohol consumption
mathematical modeling
nonlinear dynamical systems
optimal control
basic reproduction number
numerical simulations
topic Alcohol consumption
mathematical modeling
nonlinear dynamical systems
optimal control
basic reproduction number
numerical simulations
Consumo de alcohol
modelamiento matemático
sistemas dinámicos no lineales
control óptimo
número reproductivobásico
simulaciones numéricas
dc.subject.keyword.spa.fl_str_mv Consumo de alcohol
modelamiento matemático
sistemas dinámicos no lineales
control óptimo
número reproductivobásico
simulaciones numéricas
description In this paper, we present a nonlinear mathematical model, describing the spread of high-risk alcohol consumption behavior among college students in Colombia. We proved the existence and stability of the alcohol-free and drinking state equilibrium by means of Lyapunov function and LaSalle’s invariance principle. Also, we apply optimal control to study the impact of a preventive measure on the spread of drinking behavior among college students. Finally, we use numerical simulations and available data provided by the United Nations Office on Drugs and Crime (UNODC) and the Colombian Ministry of Justice to validate the obtained mathematical model.
publishDate 2020
dc.date.issued.none.fl_str_mv 2020-11-11
dc.date.available.none.fl_str_mv 2021-02-19T16:41:44Z
dc.date.accessioned.none.fl_str_mv 2021-02-19T16:41:44Z
dc.date.none.fl_str_mv 2020-11-11
dc.type.eng.fl_str_mv article
info:eu-repo/semantics/article
publishedVersion
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http://purl.org/coar/resource_type/c_2df8fbb1
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status_str publishedVersion
dc.identifier.issn.none.fl_str_mv 1794-9165
dc.identifier.uri.none.fl_str_mv http://hdl.handle.net/10784/25811
identifier_str_mv 1794-9165
url http://hdl.handle.net/10784/25811
dc.language.iso.none.fl_str_mv eng
language eng
dc.relation.isversionof.none.fl_str_mv https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6438/5067
dc.relation.uri.none.fl_str_mv https://publicaciones.eafit.edu.co/index.php/ingciencia/article/view/6438/5067
dc.rights.eng.fl_str_mv Copyright © 2020 Edgardo Pérez
dc.rights.coar.fl_str_mv http://purl.org/coar/access_right/c_abf2
dc.rights.accessrights.eng.fl_str_mv info:eu-repo/semantics/openAccess
dc.rights.local.spa.fl_str_mv Acceso abierto
rights_invalid_str_mv Copyright © 2020 Edgardo Pérez
Acceso abierto
http://purl.org/coar/access_right/c_abf2
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.coverage.spatial.none.fl_str_mv Medellín de: Lat: 06 15 00 N degrees minutes Lat: 6.2500 decimal degrees Long: 075 36 00 W degrees minutes Long: -75.6000 decimal degrees
dc.publisher.spa.fl_str_mv Universidad EAFIT
dc.source.spa.fl_str_mv Revista Ingeniería y Ciencias, Vol. 16 Núm. 32 (2020)
institution Universidad EAFIT
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