Some formal results on positivity, stability, and endemic steady-state attainability based on linear algebraic tools for a class of epidemic models with eventual incommensurate delays
De la Sen, Manuel (Universidad del País Vasco. Instituto de Investigación y Desarrollo de Procesos)
Nistal, Raul (Universidad del País Vasco. Instituto de Investigación y Desarrollo de Procesos)
Alonso-Quesada, Santiago (Universidad del País Vasco. Instituto de Investigación y Desarrollo de Procesos)
Ibeas, Asier (Universitat Autònoma de Barcelona. Departament de Telecomunicació i Enginyeria de Sistemes)

Fecha:	2019
Resumen:	A 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.
Ayudas:	Ministerio de Economía y Competitividad DPI2015-64766-R Agencia Estatal de Investigación RTI2018-094336-B-I00 Agencia Estatal de Investigación DPI2016-77271-R
Derechos:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.
Lengua:	Anglès
Documento:	Article ; recerca ; Versió publicada
Publicado en:	Discrete dynamics in nature and society, Vol. 2019 (2019) , art. 8959681, ISSN 1607-887X

DOI: 10.1155/2019/8959681

23 p, 2.1 MB

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