Linear Compartmental Models: Input-Output Equations and Operations That Preserve Identifiability

This work focuses on the question of how identifiability of a mathematical model, that is, whether parameters can be recovered from data, is related to identifiability of its submodels. We look specifically at linear compartmental models and investigate when identifiability is preserved after adding or removing model components. In particular, we examine whether identifiability is preserved when an input, output, edge, or leak is added or deleted. Our approach, via differential algebra, is to analyze specific input-output equations of a model and the Jacobian of the associated coefficient map. We clarify a prior determinantal formula for these equations, and then use it to prove that, under some hypotheses, a model's input-output equations can be understood in terms of certain submodels we call "output-reachable". Our proofs use algebraic and combinatorial techniques.

• Publication year

  2018

• Venue

  SIAM Journal on Applied Mathematics

• Publication date

  2018-08-01

• Fields of study

  Biology, Mathematics, Computer Science

• Identifiers
  DOI 10.1137/18M1204826arXiv 1808.00335
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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