A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications

[EN] This paper provides a comprehensive probabilistic analysis of a full randomization of approximate SIR-type epidemiological models based on discrete-time Markov chain formulation. The randomization is performed by assuming that all input data (initial conditions, the contagion, and recovering ra...

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Autores: Cortés, J.-C.|||0000-0002-6528-2155, El-Labany, S.K., Navarro-Quiles, A., Selim, Mustafa M., Slama, H.
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/162100
Acceso en línea:https://riunet.upv.es/handle/10251/162100
Access Level:acceso abierto
Palabra clave:First probability density function
Random variable transformation technique
Randomized discrete-time Markov chains
Simulations
SIR epidemiological model
MATEMATICA APLICADA
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spelling A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applicationsCortés, J.-C.|||0000-0002-6528-2155El-Labany, S.K.Navarro-Quiles, A.Selim, Mustafa M.Slama, H.First probability density functionRandom variable transformation techniqueRandomized discrete-time Markov chainsSimulationsSIR epidemiological modelMATEMATICA APLICADA[EN] This paper provides a comprehensive probabilistic analysis of a full randomization of approximate SIR-type epidemiological models based on discrete-time Markov chain formulation. The randomization is performed by assuming that all input data (initial conditions, the contagion, and recovering rates involved in the transition matrix) are random variables instead of deterministic constants. In the first part of the paper, we determine explicit expressions for the so called first probability density function of each subpopulation identified as the corresponding states of the Markov chain (susceptible, infected, and recovered) in terms of the probability density function of each input random variable. Afterwards, we obtain the probability density functions of the times until a given proportion of the population remains susceptible, infected, and recovered, respectively. The theoretical analysis is completed by computing explicit expressions of important randomized epidemiological quantities, namely, the basic reproduction number, the effective reproduction number, and the herd immunity threshold. The study is conducted under very general assumptions and taking extensive advantage of the random variable transformation technique. The second part of the paper is devoted to apply our theoretical findings to describe the dynamics of the pandemic influenza in Egypt using simulated data excerpted from the literature. The simulations are complemented with valuable information, which is seldom displayed in epidemiological models. In spite of the nonlinear mathematical nature of SIR epidemiological model, our results show a strong agreement with the approximation via an appropriate randomized Markov chain. A justification in this regard is discussed.Spanish Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-P; Generalitat Valenciana, Grant/Award Number: APOSTD/2019/128; Ministerio de Economia y Competitividad, Grant/Award Number: MTM2017-89664-PJohn Wiley & SonsFacultad de Administración y Dirección de EmpresasDepartamento de Matemática AplicadaInstituto Universitario de Matemática MultidisciplinarGeneralitat ValencianaAgencia Estatal de InvestigaciónRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-09-30journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/162100reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-89664-P PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONESGeneralitat Valenciana https://doi.org/10.13039/501100003359 APOSTD%2F2019%2F128open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1621002026-06-13T07:49:27Z
dc.title.none.fl_str_mv A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications
title A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications
spellingShingle A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications
Cortés, J.-C.|||0000-0002-6528-2155
First probability density function
Random variable transformation technique
Randomized discrete-time Markov chains
Simulations
SIR epidemiological model
MATEMATICA APLICADA
title_short A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications
title_full A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications
title_fullStr A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications
title_full_unstemmed A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications
title_sort A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications
dc.creator.none.fl_str_mv Cortés, J.-C.|||0000-0002-6528-2155
El-Labany, S.K.
Navarro-Quiles, A.
Selim, Mustafa M.
Slama, H.
author Cortés, J.-C.|||0000-0002-6528-2155
author_facet Cortés, J.-C.|||0000-0002-6528-2155
El-Labany, S.K.
Navarro-Quiles, A.
Selim, Mustafa M.
Slama, H.
author_role author
author2 El-Labany, S.K.
Navarro-Quiles, A.
Selim, Mustafa M.
Slama, H.
author2_role author
author
author
author
dc.contributor.none.fl_str_mv Facultad de Administración y Dirección de Empresas
Departamento de Matemática Aplicada
Instituto Universitario de Matemática Multidisciplinar
Generalitat Valenciana
Agencia Estatal de Investigación
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv First probability density function
Random variable transformation technique
Randomized discrete-time Markov chains
Simulations
SIR epidemiological model
MATEMATICA APLICADA
topic First probability density function
Random variable transformation technique
Randomized discrete-time Markov chains
Simulations
SIR epidemiological model
MATEMATICA APLICADA
description [EN] This paper provides a comprehensive probabilistic analysis of a full randomization of approximate SIR-type epidemiological models based on discrete-time Markov chain formulation. The randomization is performed by assuming that all input data (initial conditions, the contagion, and recovering rates involved in the transition matrix) are random variables instead of deterministic constants. In the first part of the paper, we determine explicit expressions for the so called first probability density function of each subpopulation identified as the corresponding states of the Markov chain (susceptible, infected, and recovered) in terms of the probability density function of each input random variable. Afterwards, we obtain the probability density functions of the times until a given proportion of the population remains susceptible, infected, and recovered, respectively. The theoretical analysis is completed by computing explicit expressions of important randomized epidemiological quantities, namely, the basic reproduction number, the effective reproduction number, and the herd immunity threshold. The study is conducted under very general assumptions and taking extensive advantage of the random variable transformation technique. The second part of the paper is devoted to apply our theoretical findings to describe the dynamics of the pandemic influenza in Egypt using simulated data excerpted from the literature. The simulations are complemented with valuable information, which is seldom displayed in epidemiological models. In spite of the nonlinear mathematical nature of SIR epidemiological model, our results show a strong agreement with the approximation via an appropriate randomized Markov chain. A justification in this regard is discussed.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-09-30
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/162100
url https://riunet.upv.es/handle/10251/162100
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-89664-P PROBLEMAS DINAMICOS CON INCERTIDUMBRE SIMULABLE: MODELIZACION MATEMATICA, ANALISIS, COMPUTACION Y APLICACIONES
Generalitat Valenciana https://doi.org/10.13039/501100003359 APOSTD%2F2019%2F128
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv John Wiley & Sons
publisher.none.fl_str_mv John Wiley & Sons
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,301603

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