Maple implementation of the algorithm for checking global identifiability for systems of ODEs presented in the paper Global Identifiability of Differential Models. Tested with Maple 2017 and Maple 2016.
The main function, which corresponds to Algorithm 1 from the paper, is GlobalIdentifiability(sigma, theta_l, p, method) with arguments
- sigma - a Maple table that describes a system of ODEs with the following entries
- x_vars - the list of state variables (x in the paper)
- x_eqs - the list of state equations (x' = f(x, mu, u) in the paper) in the same order as the variables in x_vars
- y_vars - the list of output variables (y in the paper)
- y_eqs - the list of output equations (y = g(x, mu, u) in the paper) in the same order as the variables in y_vars
- u_vars - the list of input variables (u in the paper)
- mu - the list of parameters that are not the initial conditions (mu in the paper)
- theta_l - a subset of locally identifiable parameters
- p - the probability of correctness, the default value is 0.99
- method - the method of checking the consistency in Step 4 of Algorithm 1 from the paper. Possible options are
- 1 - using saturation and Groebner bases, see item (1) in Remark 7 from the paper, this is usually faster
- 2 - without saturation, with checking memebership using Groebner bases, see item (2) in Remark 7 from the paper
Examples of usage can be found in the examples/ folder
- GlobalIdentifiabiliy.mpl contains the algorithm
- /examples folder contains examples from the paper
- example_paper.mpl contains the code for Example 5
- ChemicalReactionNetwork.mpl contains the code for Example 6
- Cholera.mpl contains the code for Example 7
The software is partially supported by the National Science Foundation.