Ordinary differential equation models often contain a large number of parameters that must be determined from measurements by parameter estimation. For a parameter estimation procedure to be successful, there must be a unique set of parameters that can have produced the measured data. This is not the case if a model is not structurally identifiable with the given set of outputs selected as measurements. We describe the implementation of a recent probabilistic semi-numerical method for testing local structural identifiability based on computing the rank of a numerically instantiated Jacobian matrix (observability/identifiability matrix). To obtain this, matrix parameters and initial conditions are specialized to random integer numbers, inputs are specialized to truncated random integer coefficient power series, and the corresponding output of the state space system is computed in terms of a truncated power series, which then is utilized to calculate the elements of a Jacobian matrix. To reduce the memory requirements and increase the speed of the computations all operations are done modulo a large prime number. The method has been extended to handle parametrized initial conditions and is demonstrated to be capable of handling systems in the order of a hundred state variables and equally many parameters on a standard desktop computer.

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New experimental techniques in bioscience provide us with high-quality data allowing quantitative mathematical modelling. Parameter estimation is often necessary and, in connection with this, it is important to know whether all parameters can be uniquely estimated from available data, (i.e. whether the model is identifiable). Dealing essentially with models for metabolism, we show how the assumption of an algebraic relation between concentrations may cause parameters to be unidentifiable. If a sufficient data set is available, the problem with unidentifiability arises locally in individual rate expressions. A general method for reparameterisation to identifiable rate expressions is provided, together with a Mathematica code to help with the calculations. The general results are exemplified by four well-cited models for glycolysis.

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