Differential algebra methods for the study of the structural identifiability of rational function state-space models in the biosciences

Abstract

In this paper methods from differential algebra are used to study the structural identifiability of biological and pharmacokinetics models expressed in state-space form and with a structure given by rational functions. The focus is on the examples presented and on the application of efficient, automatic methods to test for structural identifiability for various input–output experiments. Differential algebra methods are coupled with Gröbner bases, Lie derivatives and the Taylor series expansion in order to obtain efficient algorithms. In particular, an upper bound on the number of derivatives needed for the Taylor series approach for a structural identifiability analysis of rational function models is given.