Publicación:
Impacto de la conciencia de los enfermos en la transmisión de enfermedades en un modelo SIR

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dc.audience
dc.contributor.advisorArenas Tawil, Abraham José
dc.contributor.authorNavarro Benítez, Daniela
dc.contributor.juryPérez Reyes, Edgardo Enrique
dc.contributor.juryBanquet Brango, Carlos Alberto
dc.date.accessioned2024-04-06T13:35:06Z
dc.date.available2027-02-04
dc.date.available2024-04-06T13:35:06Z
dc.date.issued2024-04-05
dc.description.abstractEn el presente trabajo, se llevó a cabo un análisis de un modelo matemático, el cual establece cinco subpoblaciones definidas como: susceptibles conscientes, susceptibles inconscientes, infectados consientes, infectados inconsciente y recuperados. Se realizó un análisis exhaustivo del nuevo sistema que permitió demostrar propiedades fundamentales del sistema que amplían la comprensión teórica de la propagación de enfermedades, tales como la existencia, unicidad, positividad y acotamiento de sus soluciones. Además, encontramos los puntos de equilibrio del modelo y se llevó a cabo un estudio detallado sobre la estabilidad local del punto de equilibrio que describe la ausencia de enfermedad en este sistema. Por último, se efectuaron simulaciones numéricas implementando el comando ode45 en el software MATLAB que permitieron comparar y sustentar la precisión de los resultados previamente obtenidos mediante métodos analíticos.spa
dc.description.abstractIn the present work, an analysis of a mathematical model was carried out, which establishes five subpopulations defined as: conscious susceptible, unconscious susceptible, conscious infected, unconscious infected and recovered. An exhaustive analysis of the system was carried out that allowed us to demonstrate fundamental properties of the system that expand the theoretical understanding of the spread of diseases, such as the existence, uniqueness, positivity and delimitation of its solutions. Furthermore, we found the equilibrium points of the model and a detailed study was carried out on the local stability of the equilibrium point that describes the absence of disease in this system. Finally, numerical simulations were carried out by implementing the $ode45$ command in the MATLAB software, which allowed us to compare and support the precision of the results previously obtained through analytical methods.
dc.description.degreelevelPregrado
dc.description.degreenameMatemático(a)
dc.description.modalityTrabajos de Investigación y/o Extensión
dc.description.tableofcontentsDeclaración de autoria....................6
dc.description.tableofcontentsAgradecimientos....................7
dc.description.tableofcontentsResumen....................8
dc.description.tableofcontentsAbstrat....................9
dc.description.tableofcontentsÍndice de figuras....................12
dc.description.tableofcontentsÍndice de tablas....................13
dc.description.tableofcontentsIntroducción....................14
dc.description.tableofcontentsPreliminares....................17
dc.description.tableofcontentsModelo propuesto....................20
dc.description.tableofcontentsExistencia , unicidad, positividad y acotación de las soluciones del modelo planteado....................24
dc.description.tableofcontentsPositividad y acotación....................24
dc.description.tableofcontentsPositividad....................25
dc.description.tableofcontentsAcotación....................27
dc.description.tableofcontentsExistencia y unicidad del sistema planteado....................28
dc.description.tableofcontentsAnálisis de estabilidad local....................34
dc.description.tableofcontentsExistencia de puntos críticos....................35
dc.description.tableofcontentsNúmero de reproducción básico R_{0}....................38
dc.description.tableofcontentsEstabilidad local del punto libre de enfermedad....................41
dc.description.tableofcontentsSimulaciones....................45
dc.description.tableofcontentsConclusiones y trabajos futuros....................53
dc.description.tableofcontentsConclusiones....................53
dc.description.tableofcontentsTrabajos futuros....................54
dc.description.tableofcontentsApendice A....................55
dc.description.tableofcontentsApendice B....................58
dc.description.tableofcontentsReferencias....................63
dc.format.mimetypeapplication/pdf
dc.identifier.instnameUniversidad de Córdoba
dc.identifier.reponameRepositorio universidad de Córdoba
dc.identifier.repourlhttps://repositorio.unicordoba.edu.co
dc.identifier.urihttps://repositorio.unicordoba.edu.co/handle/ucordoba/8275
dc.language.isospa
dc.publisherUniversidad de Córdoba
dc.publisher.facultyFacultad de Ciencias Básicas
dc.publisher.placeMontería, Córdoba, Colombia
dc.publisher.programMatemática
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dc.rightsCopyright Universidad de Córdoba, 2024
dc.rights.accessrightsinfo:eu-repo/semantics/embargoedAccess
dc.rights.coarhttp://purl.org/coar/access_right/c_f1cf
dc.rights.licenseAtribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subject.keywordsModels
dc.subject.keywordsUnconscious
dc.subject.keywordsInfectious diseases
dc.subject.keywordsAware
dc.subject.keywordsAwareness
dc.subject.keywordsStability
dc.subject.keywordsEndemic
dc.subject.keywordsDisease free
dc.subject.proposalModelos
dc.subject.proposalInconsciente
dc.subject.proposalEnfermedades infecciosas
dc.subject.proposalConsciente
dc.subject.proposalConciencia
dc.subject.proposalEstabilidad
dc.subject.proposalEndémico
dc.subject.proposalLibre de enfermedad
dc.titleImpacto de la conciencia de los enfermos en la transmisión de enfermedades en un modelo SIRspa
dc.typeTrabajo de grado - Pregrado
dc.type.coarhttp://purl.org/coar/resource_type/c_7a1f
dc.type.coarversionhttp://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.contentText
dc.type.driverinfo:eu-repo/semantics/bachelorThesis
dc.type.versioninfo:eu-repo/semantics/acceptedVersion
dspace.entity.typePublication
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