Journal of Mathematical Biology

, Volume 78, Issue 1–2, pp 225–256 | Cite as

State estimators for some epidemiological systems

  • A. Iggidr
  • M. O. SouzaEmail author


We consider a class of epidemiological models that includes most well-known dynamics for directly transmitted diseases, and some reduced models for indirectly transmitted diseases. We then propose a simple observer that can be applied to models in this class. The error analysis of this observer leads to a non-autonomous error equation, and a new bound for fundamental matrices is also presented. We analyse and implement this observer in two examples: the classical SIR model, and a reduced Bailey-Dietz model for vector-borne diseases. In both cases we obtain arbitrary exponential convergence of the observer. For the latter model, we also applied the observer to recover the number of susceptible using dengue infection data from a district in the city of Rio de Janeiro.


Dengue Epidemic models Observers State estimation 

Mathematics Subject Classification

92D30 34E13 34A30 93B07 93B40 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Université de Lorraine, CNRS, Inria, IECLMetzFrance
  2. 2.Instituto de Matemática e Estatística, Universidade Federal FluminenseNiteróiBrazil

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