Local Identifiability Analysis of NonLinear ODE Models: How to Determine All Candidate Solutions

Identifiability analysis aims at answering the theoretical question whether the inverse problem is solved, uniquely, by a particular value of the free parameters, or if there is a finite or infinite number of parameter vectors that generate identical output trajectories. Multiple solutions of locally identifiable parameters imply different time courses of unmeasured variables, and arbitrarily chosen solutions can lead to misinterpretations and to erroneous conclusions. We present theoretical background and applications to locally identifiable ODE models described by rational functions, showing that structural identifiability analysis reinforces the practical identifiability approach. In a first example using a three compartment model, we discuss the algorithm that allows to find all the equivalent parameter solutions. In the second example on HIV dynamics, we show how two solutions can provide two major different scenarios regarding the prediction of unobservable variables, which may lead to different treatment strategies. In conclusion, for locally identifiable models we propose an algorithmic approach which, for the first time, allows the calculation of all numerical model solutions, the possible rejection of non admissible parameters, and the simulation of the trajectories of unobservable variables.