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On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease
Joint Authors
Nistal, R.
Alonso-Quesada, S.
de La Sen, Manuel
Ibeas, Asier
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-02-19
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
This paper studies the nonnegativity and local and global stability properties of the solutions of a newly proposed SEIADR model which incorporates asymptomatic and dead-infective subpopulations into the standard SEIR model and, in parallel, it incorporates feedback vaccination plus a constant term on the susceptible and feedback antiviral treatment controls on the symptomatic infectious subpopulation.
A third control action of impulsive type (or “culling”) consists of the periodic retirement of all or a fraction of the lying corpses which can become infective in certain diseases, for instance, the Ebola infection.
The three controls are allowed to be eventually time varying and contain a total of four design control gains.
The local stability analysis around both the disease-free and endemic equilibrium points is performed by the investigation of the eigenvalues of the corresponding Jacobian matrices.
The global stability is formally discussed by using tools of qualitative theory of differential equations by using Gauss-Stokes and Bendixson theorems so that neither Lyapunov equation candidates nor the explicit solutions are used.
It is proved that stability holds as a parallel property to positivity and that disease-free and the endemic equilibrium states cannot be simultaneously either stable or unstable.
The periodic limit solution trajectories and equilibrium points are analyzed in a combined fashion in the sense that the endemic periodic solutions become, in particular, equilibrium points if the control gains converge to constant values and the control gain for culling the infective corpses is asymptotically zeroed.
American Psychological Association (APA)
de La Sen, Manuel& Ibeas, Asier& Alonso-Quesada, S.& Nistal, R.. 2017. On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease. Discrete Dynamics in Nature and Society،Vol. 2017, no. 2017, pp.1-22.
https://search.emarefa.net/detail/BIM-1151387
Modern Language Association (MLA)
de La Sen, Manuel…[et al.]. On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease. Discrete Dynamics in Nature and Society No. 2017 (2017), pp.1-22.
https://search.emarefa.net/detail/BIM-1151387
American Medical Association (AMA)
de La Sen, Manuel& Ibeas, Asier& Alonso-Quesada, S.& Nistal, R.. On a New Epidemic Model with Asymptomatic and Dead-Infective Subpopulations with Feedback Controls Useful for Ebola Disease. Discrete Dynamics in Nature and Society. 2017. Vol. 2017, no. 2017, pp.1-22.
https://search.emarefa.net/detail/BIM-1151387
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1151387