A Differential Algebra Method for Eliminating Unidentifiability.

摘要

We present an algorithm to find globally identifiable parameter combinations in unidentifiable nonlinear ODE models. The method is based on a differential algebra approach to analyze identifiability and uses Gröbner Bases to find the identifiable parameter combinations. We prove that our method can be used to find a set of algebraically independent identifiable parameter combinations that can rationally reparameterize the input-output equations of the model. We demonstrate our algorithm on several unidentifiable biological models and find the associated reparameterizations of the models, rendering them identifiable. We also compare our results to those obtained from other methods. Our method can determine globally identifiable parameter combinations, whereas other methods can either determine only locally identifiable parameter combinations or find globally identifiable combinations in limited cases.;We also find an alternative approach to obtain the input-output equations of the model. We show that this alternative approach is easier to implement and demonstrate its application on both models with a single output or multiple outputs. We also prove a new result on the order of the input-output equations for systems with multiple outputs.;We finally present some details regarding the implementation of our algorithm and discuss techniques to efficiently find a set of algebraically independent identifiable parameter combinations.