Testing structural identifiability by a simple scaling method

Successful mathematical modeling of biological processes relies on the expertise of the modeler to capture the essential mechanisms in the process at hand and on the ability to extract useful information from empirical data. The very structure of the model limits the ability to infer numerical values for the parameters, a concept referred to as structural identifiability. Most of the available methods to test the structural identifiability of a model are either too complex mathematically for the general practitioner to be applied or require involved calculations or numerical computation for complex non-linear models. In this work, we present a new analytical method to test structural identifiability of models based on ordinary differential equations, based on the invariance of the equations under the scaling transformation of its parameters. The method is based on rigorous mathematical results but it is easy and quick to apply, even to test the identifiability of sophisticated highly non-linear models. We illustrate our method by example and compare its performance with other existing methods in the literature.