Qualitative and Quantitative Identifiability Analysis of Nonlinear Chemical Kinetic Models

Identifiability analysis deals with the problem of uniqueness of the parameters when fitting a model to a set of observations. If the model is not qualitatively identifiable, then several or infinitely many parameter sets generate identical predictions of the observed quantities. Three rigorous approaches are evaluated. to study qualitative identifiability of nonlinear dynamic models, with emphasis on chemical kinetic modelling. Analysis of a large variety of systems of higher-order reactions shows that under reasonable experimental conditions such models are rarely unidentifiable in the qualitative sense, although there exist well-known examples of unidentifiable models for monomolecular reaction systems. Kinetic models are, however, frequently unidentifiable in a quantitative sense, when a particular sei of error-corrupted data does not allow for obtaining reliable estimates of the parameters. In such cases the goodness-of-fit depends only on some combinations of the parameters. Performing a logarithmic transformation, the well-known principal component analysis is shown to offer an efficient method for detecting and identifying nonlinear dependences among the parameters, thereby suggesting simpler models leading to meaningful estimates.