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

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

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dc.contributor.author Cortés, J.-C. es_ES
dc.contributor.author El-Labany, S.K. es_ES
dc.contributor.author Navarro-Quiles, A. es_ES
dc.contributor.author Selim, Mustafa M. es_ES
dc.contributor.author Slama, H. es_ES
dc.date.accessioned 2021-02-23T04:31:16Z
dc.date.available 2021-02-23T04:31:16Z
dc.date.issued 2020-09-30 es_ES
dc.identifier.issn 0170-4214 es_ES
dc.identifier.uri http://hdl.handle.net/10251/162100
dc.description.abstract [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. es_ES
dc.description.sponsorship 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-P es_ES
dc.language Inglés es_ES
dc.publisher John Wiley & Sons es_ES
dc.relation AEI/MTM2017-89664-P-AR es_ES
dc.relation GENERALITAT VALENCIANA/APOSTD/2019/128 es_ES
dc.relation.ispartof Mathematical Methods in the Applied Sciences es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject First probability density function es_ES
dc.subject Random variable transformation technique es_ES
dc.subject Randomized discrete-time Markov chains es_ES
dc.subject Simulations es_ES
dc.subject SIR epidemiological model es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1002/mma.6482 es_ES
dc.rights.accessRights Embargado es_ES
dc.date.embargoEndDate 2021-09-30 es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Cortés, J.; El-Labany, S.; Navarro-Quiles, A.; Selim, MM.; Slama, H. (2020). A comprehensive probabilistic analysis of SIR-type epidemiological models based on full randomized Discrete-Time Markov Chain formulation with applications. Mathematical Methods in the Applied Sciences. 43(14):8204-8222. https://doi.org/10.1002/mma.6482 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1002/mma.6482 es_ES
dc.description.upvformatpinicio 8204 es_ES
dc.description.upvformatpfin 8222 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 43 es_ES
dc.description.issue 14 es_ES
dc.relation.pasarela S\407906 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES


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