SIAN (Structural Identifiability ANalyser)

Maple code for assessing identifiability/observability (local and global) for models defined by systems of ODEs presented. Mostly based on the paper Global Identifiability of Differential Models. Supplementary Maple code for the paper is available at https://github.com/pogudingleb/Global_Identifiability Tested with Maple 2016-2019.

How to download

• Using git checkout
• On https://github.com/pogudingleb/SIAN, press green button "Clone of download", and then "Dowload ZIP"

Usage

The main function is IdentifiabilityODE(system, parameters, p, infolevel, method, num_nodes) with required positional arguments system and parameters and optional keyword arguments p, infolevel, method, num_nodes.

• system - a system of ODEs in the state-space form. It should include equations of two types
  • ODEs with rational right-hand side defining the evolution of the state variables
  • equations of the form output_variable = rational_function(state_variables, parameters, inputs) defining the output variables
• parameters - a list of parameters and initial values whose identifiability is to be assessed. You can use GetParameters(system) if you want to check identifibaility of all the parameters and initial values
• p (optional) - the probability of correctness, the default value is 0.99. For technical reasons
• infolevel (optional) - the variable that regulates the amount of information printed. Options are (the default value is 1)
  • 0 - nothing is printed
  • 1 - information about the original system, main steps of the algorithm, and the summary of the results are printed
  • 2 - debugging mode, a lot of information is printed
• method (optional) - the method of checking the consistency in Step 4 of Algorithm 1 from the paper. Possible options are (the default value is 2)
  • 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
• num_nodes (optional) - the maximal number of processes created by the algorithm, the default value is 6.

Example IdentifiabilityODE(s, [a, b], infolevel = 2, num_nodes = 5). For more details on positional and keyword arguments in Maple, see here.

Multiple experiments One can use SIAN to assess identifiability of parameters from several independent experiments. This can be done using function GenerateReplica(sigma, N) which construct a system consisting of N copies of sigma sharing parameters appearing in ODEs but having different initial conditions and inputs. For an example of such assessment, see the SlowFast example.

Examples of usage can be found in the examples folder. One can run an example by

• either opening it as a Maple worksheet and executing it
• or from the command line by
  • going to examples directory
  • calling maple name_of_file.mpl

Files

• IdentifiabiliyODE.mpl contains the algorithm
• examples folder contains examples

References

• Global Identifiability of Differential Models - the original paper with underlying theory. Corresponds to version 0.5
• SIAN: software for structural identifiability analysis of ODE models (Bioinformatics, Volume 35, Issue 16, Pages 2873–2874, 2019) - an application note. Corresponds to version 1.1

The software is partially supported by the National Science Foundation.