Input-output equivalence and identifiability: some simple generalizations of the differential algebra approach

In this paper, we give an overview of the differential algebra approach to identifiability, and then note a very simple observation about input-output equivalence and identifiability, that describes the identifiability equivalence between input-output equivalent models. We then give several simple consequences of this observation that can be useful in showing identifiability, including examining non-first order ODE models, nondimensionalization and rescaling, model reducibility, and a modular approach to evaluating identifiability. We also examine how input-output equivalence can allow us to generate input output equations in the differential algebra approach through a wider range of methods (e.g. substitution and differential or standard Groebner basis approaches).