On the Stability and Equilibrium Points of Multistaged SI(n)R Epidemic Models
This paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as SI(n)R-model to study its stability. The model includes n successive stages of infectious subpopulations, each one acting at the exposed subpopulation of the next infectio...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/379576 |
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| author | Raul Nistal Manuel de la Sen Santiago Alonso-Quesada Asier Ibeas Aitor J. Garrido |
| author_facet | Raul Nistal Manuel de la Sen Santiago Alonso-Quesada Asier Ibeas Aitor J. Garrido |
| author_sort | Raul Nistal |
| collection | DOAJ |
| description | This paper relies on the concept of next generation matrix defined ad hoc for a new
proposed extended SEIR model referred to as SI(n)R-model to study its stability.
The model includes n successive stages of infectious subpopulations, each one acting
at the exposed subpopulation of the next infectious stage in a cascade global disposal
where each infectious population acts as the exposed subpopulation of the next infectious
stage. The model also has internal delays which characterize the time intervals of
the coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages. Since the susceptible subpopulation is common, and then
unique, to all the infectious stages, its coupled dynamic action on each of those stages
is modeled with an increasing delay as the infectious stage index increases from 1 to n.
The physical interpretation of the model is that the dynamics of the disease exhibits
different stages in which the infectivity and the mortality rates vary as the individual
numbers go through the process of recovery, each stage with a characteristic average
time. |
| format | Article |
| id | doaj-art-d47c7c0e3dbc480ba237ff365d311869 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-d47c7c0e3dbc480ba237ff365d3118692025-02-03T01:21:26ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2015-01-01201510.1155/2015/379576379576On the Stability and Equilibrium Points of Multistaged SI(n)R Epidemic ModelsRaul Nistal0Manuel de la Sen1Santiago Alonso-Quesada2Asier Ibeas3Aitor J. Garrido4Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, P.O. Box 644, Barrio Sarriena, Bilbao, Bizkaia, 48940 Leioa, SpainInstitute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, P.O. Box 644, Barrio Sarriena, Bilbao, Bizkaia, 48940 Leioa, SpainInstitute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, P.O. Box 644, Barrio Sarriena, Bilbao, Bizkaia, 48940 Leioa, SpainDepartment of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, SpainSchool of Industrial Technical Engineering, University of the Basque Country, Paseo Rafael Moreno 3, 48013 Bilbao, SpainThis paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as SI(n)R-model to study its stability. The model includes n successive stages of infectious subpopulations, each one acting at the exposed subpopulation of the next infectious stage in a cascade global disposal where each infectious population acts as the exposed subpopulation of the next infectious stage. The model also has internal delays which characterize the time intervals of the coupling of the susceptible dynamics with the infectious populations of the various cascade infectious stages. Since the susceptible subpopulation is common, and then unique, to all the infectious stages, its coupled dynamic action on each of those stages is modeled with an increasing delay as the infectious stage index increases from 1 to n. The physical interpretation of the model is that the dynamics of the disease exhibits different stages in which the infectivity and the mortality rates vary as the individual numbers go through the process of recovery, each stage with a characteristic average time.http://dx.doi.org/10.1155/2015/379576 |
| spellingShingle | Raul Nistal Manuel de la Sen Santiago Alonso-Quesada Asier Ibeas Aitor J. Garrido On the Stability and Equilibrium Points of Multistaged SI(n)R Epidemic Models Discrete Dynamics in Nature and Society |
| title | On the Stability and Equilibrium Points of Multistaged SI(n)R Epidemic Models |
| title_full | On the Stability and Equilibrium Points of Multistaged SI(n)R Epidemic Models |
| title_fullStr | On the Stability and Equilibrium Points of Multistaged SI(n)R Epidemic Models |
| title_full_unstemmed | On the Stability and Equilibrium Points of Multistaged SI(n)R Epidemic Models |
| title_short | On the Stability and Equilibrium Points of Multistaged SI(n)R Epidemic Models |
| title_sort | on the stability and equilibrium points of multistaged si n r epidemic models |
| url | http://dx.doi.org/10.1155/2015/379576 |
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