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Discrete Dynamics in Nature and Society
Volume 2011, Article ID 743067, 19 pages
Research Article

Observer-Based Vaccination Strategy for a True Mass Action SEIR Epidemic Model with Potential Estimation of All the Populations

1Institute of Research and Development of Processes, Faculty of Science and Technology, University of the Basque Country, P. O. Box 644, 48940 Bilbao, Spain
2Department of Telecommunications and Systems Engineering, Autonomous University of Barcelona, 08193 Bellaterra, Barcelona, Spain

Received 14 June 2011; Accepted 8 August 2011

Academic Editor: Vimal Singh

Copyright © 2011 M. De la Sen 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 presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among the susceptible and infected. The control objective is the asymptotically tracking of the removed-by-immunity population to the total population while achieving simultaneously the remaining population (i.e., susceptible plus infected plus infectious) to asymptotically converge to zero. A state observer is used to estimate the true various partial populations of the susceptible, infected, infectious, and immune which are assumed to be unknown. The model parameters are also assumed to be, in general, unknown. In this case, the parameters are replaced by available estimates to implement the vaccination action.