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Discrete Dynamics in Nature and Society
Volume 2015, Article ID 379576, 15 pages
Research Article

On the Stability and Equilibrium Points of Multistaged Epidemic Models

1Institute of Research and Development of Processes, University of the Basque Country, Campus of Leioa, P.O. Box 644, Barrio Sarriena, Bilbao, Bizkaia, 48940 Leioa, Spain
2Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, Bellaterra, 08193 Barcelona, Spain
3School of Industrial Technical Engineering, University of the Basque Country, Paseo Rafael Moreno 3, 48013 Bilbao, Spain

Received 1 October 2014; Revised 10 December 2014; Accepted 16 December 2014

Academic Editor: Qing-hua Ma

Copyright © 2015 Raul Nistal 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.


This paper relies on the concept of next generation matrix defined ad hoc for a new proposed extended SEIR model referred to as -model to study its stability. The model includes 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 . 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.