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dc.contributor.authorDe la Sen Parte, Manuel
dc.contributor.authorNistal Riobello, Raúl
dc.contributor.authorAlonso Quesada, Santiago
dc.contributor.authorIbeas Hernández, Asier
dc.date.accessioned2020-04-29T11:26:07Z
dc.date.available2020-04-29T11:26:07Z
dc.date.issued2019-07-08
dc.identifier.citationDiscrete Dynamics in Nature and Society 2019 : (2019) // Article ID 8959681es_ES
dc.identifier.issn1026-0226
dc.identifier.issn1607-887X
dc.identifier.urihttp://hdl.handle.net/10810/42956
dc.description.abstractA formal description of typical compartmental epidemic models obtained is presented by splitting the state into an infective substate, or infective compartment, and a noninfective substate, or noninfective compartment. A general formal study to obtain the reproduction number and discuss the positivity and stability properties of equilibrium points is proposed and formally discussed. Such a study unifies previous related research and it is based on linear algebraic tools to investigate the positivity and the stability of the linearized dynamics around the disease-free and endemic equilibrium points. To this end, the complete state vector is split into the dynamically coupled infective and noninfective compartments each one containing the corresponding state components. The study is then extended to the case of commensurate internal delays when all the delays are integer multiples of a base delay. Two auxiliary delay-free systems are defined related to the linearization processes around the equilibrium points which correspond to the zero delay, i.e., delay-free, and infinity delay cases. Those auxiliary systems are used to formulate stability and positivity properties independently of the delay sizes. Some examples are discussed to the light of the developed formal study.es_ES
dc.description.sponsorshipThe authors are grateful to the Spanish Government for Grants DPI2015-64766-R, RTI2018-094336-B-I00, and DPI2016-77271-R (MINECO/FEDER, UE).es_ES
dc.language.isoenges_ES
dc.publisherHindawies_ES
dc.relationinfo:eu-repo/grantAgreement/MINECO/DPI2015-64766-Res_ES
dc.relationinfo:eu-repo/grantAgreement/MINECO/RTI2018-094336-B-I00es_ES
dc.relationinfo:eu-repo/grantAgreement/MINECO/DPI2016-77271-Res_ES
dc.rightsinfo:eu-repo/semantics/openAccesses_ES
dc.rights.urihttp://creativecommons.org/licenses/by/3.0/es/*
dc.subjectsystemses_ES
dc.titleSome Formal Results on Positivity, Stability, and Endemic Steady-State Attainability Based on Linear Algebraic Tools for a Class of Epidemic Models with Eventual Incommensurate Delayses_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.rights.holder2019 M. De la Sen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.es_ES
dc.rights.holderAtribución 3.0 España*
dc.relation.publisherversionhttps://www.hindawi.com/journals/ddns/2019/8959681/es_ES
dc.identifier.doi10.1155/2019/8959681
dc.departamentoesElectricidad y electrónicaes_ES
dc.departamentoeuElektrizitatea eta elektronikaes_ES


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2019 M. De la Sen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Except where otherwise noted, this item's license is described as 2019 M. De la Sen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.