Structural identifiability analysis via symmetries of differential equations

Results and derivations are presented for the generation of a local Lie algebra that represents the ‘symmetries’ of a set of coupled differential equations. The subalgebra preserving the observation defined on the model structure is found, thus giving all transformations of the system that preserve its structure. It is shown that this is equivalent to the similarity transformation approach (Evans, Chapman, Chappell, & Godfrey, 2002) for structural identifiability analysis and as such is a method of generating such transformations for this approach. This provides another method for performing structural identifiability analysis on nonlinear state-space models that has the possibility of extension to PDE type models. The analysis is easily automated and performed in Mathematica, and this is demonstrated by application of the technique to a number of practical examples from the literature.