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
Joint Authors
Nistal, R.
Alonso-Quesada, Santiago
de La Sen, Manuel
Ibeas, Asier
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2019-07-08
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
de La Sen, Manuel& Nistal, R.& Alonso-Quesada, Santiago& Ibeas, Asier. 2019. 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. Discrete Dynamics in Nature and Society،Vol. 2019, no. 2019, pp.1-22.
https://search.emarefa.net/detail/BIM-1146629
Modern Language Association (MLA)
de La Sen, Manuel…[et al.]. 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. Discrete Dynamics in Nature and Society No. 2019 (2019), pp.1-22.
https://search.emarefa.net/detail/BIM-1146629
American Medical Association (AMA)
de La Sen, Manuel& Nistal, R.& Alonso-Quesada, Santiago& Ibeas, Asier. 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. Discrete Dynamics in Nature and Society. 2019. Vol. 2019, no. 2019, pp.1-22.
https://search.emarefa.net/detail/BIM-1146629
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1146629