DAISY: An efficient tool to test global identifiability. Some case studies

Global identifiability is a fundamental prerequisite for model identification; it concerns the possibility of uniquely determining the model parameters from input-output data, under ideal conditions of noise-free observations and error- free model structure. In many biological, physiological and especially clinical studies, checking a priori global identifiability of the underlying model may save resources, time and effort in performing expensive and/or difficult experiments which may not be sufficiently informative for parameter identification. Recently we have proposed a software tool, DAISY (differential algebra for identifiability of systems), for automatically checking global identifiability of (linear and) nonlinear dynamic models described by differential equations involving polynomial or rational functions. DAISY does not require expertise on mathematical modeling by the experimenter and is believed to be a useful instrument for the medical/ biological investigator. In this paper we demonstrate the DAISY software checking the a priori global identifiability of two well-known nonlinear physiological models from the literature: a glucose minimal model which has been widely used in clinical studies to estimate the insulin sensitivity from an oral glucose tolerance test and a four-state HIV/AIDS model. Specific problems relating to the optimal input-output experimental configuration and to the role of the initial conditions in identifiability are discussed. Both these examples bring up the relevance of identifiability in physiological studies. In particular they lead to investigate some particular features of the software.