IDENTIFIABILITY STUDY IN A MODEL DESCRIBING THE PROPAGATION OF THE CHIKUNGUNYA TO THE HUMAN POPULATION.
Résumé
In different fields of research, modeling has become a major issue for studying and predicting the possible evolution of a system, in particular in epidemiology. Indeed, according to the globalization of our societies and the genetic mutation of certain diseases or transmission vectors, several epidemics have appeared in the last years in regions not yet concerned by such a catastrophe. One can name, for example, the chikungunya epidemic on the Réunion Island in 2005-2006. In this paper, a model describing the propagation of the chikungunya to the human population is taken again from \cite{Moulay2010}. In such models, some parameters are not directly accessible from experiments and have to be estimated numerically from an iterative algorithm. However, before searching for their values, it is essential to verify the identifiability of model parameters to assess whether the set of unknown parameters can be uniquely determined from the data. Indeed, this study insures that numerical procedures can be successful and if the identifiability is not ensured, some supplementary data have to be added or the set of admissible data has to be reduced. A first identifiability study had been done in \cite{Moulay2012} in considering that the number of eggs can be easily counted. However, after discussing with epidemiologist searchers, it appears that it is the number of larvae who can be estimated weeks by weeks. Thus, this paper proposes to do an identifiability study with this assumption and thanks to an integration of one of the model equations, some easier equations linking the inputs, outputs and parameters are obtained permitting a simpler identifiability study.
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