Identifiability of deterministic differential models in state space: An implementation for a computer

In this work the problem of identifiability of parameters in models with an a priori known structure is considered. The models are assumed to be presented in strictly deterministic differential equations in state space, and in the general case the equations may be nonlinear. Although the methodology is applicable to a large variety of models, special attention, especially in examples, was paid to compartmental structures. Different approaches to the problem, found in literature, are reviewed. In particular, the method utilizing the Taylor series expansion of the solution of the differential equations, as functions of the unknown parameters, is described, and was elaborated a step further to obtain a simple criteria for local identifiability. The most prominent part of the present work is evidencing that the algorithms derived for evaluating local identifiability can be programmed for a computer. The models for which the described implementation can be applied can have polynomial nonlinearities in the state components, in time, and in the parameters. In addition, external binding equations and different initial conditions can be included in an analysis of a given model under a given experimentation. The measurements can be defined as direct observations of the state components, or, which is usual in compartmental systems, as sums of state components. The computer implementation has been utilized except for analyzing single models, also for performing a systematic study on biologically justified open three-compartment models with one compartment Langmuir saturative. The results of the analysis along with those obtained for the corresponding linear models showed that the nonlinearity often brings along local identifiability.