Bulletin of Mathematical Biology

, Volume 77, Issue 8, pp 1620–1651 | Cite as

Identifiability Results for Several Classes of Linear Compartment Models

  • Nicolette Meshkat
  • Seth Sullivant
  • Marisa Eisenberg
Original Article

Abstract

Identifiability concerns finding which unknown parameters of a model can be estimated, uniquely or otherwise, from given input–output data. If some subset of the parameters of a model cannot be determined given input–output data, then we say the model is unidentifiable. In this work, we study linear compartment models, which are a class of biological models commonly used in pharmacokinetics, physiology, and ecology. In past work, we used commutative algebra and graph theory to identify a class of linear compartment models that we call identifiable cycle models, which are unidentifiable but have the simplest possible identifiable functions (so-called monomial cycles). Here we show how to modify identifiable cycle models by adding inputs, adding outputs, or removing leaks, in such a way that we obtain an identifiable model. We also prove a constructive result on how to combine identifiable models, each corresponding to strongly connected graphs, into a larger identifiable model. We apply these theoretical results to several real-world biological models from physiology, cell biology, and ecology.

Keywords

Identifiability Linear compartment models Identifiable functions Differential algebra 

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Copyright information

© Society for Mathematical Biology 2015

Authors and Affiliations

  • Nicolette Meshkat
    • 1
  • Seth Sullivant
    • 1
  • Marisa Eisenberg
    • 2
  1. 1.Department of MathematicsNorth Carolina State UniversityRaleighUSA
  2. 2.Departments of Epidemiology and MathematicsUniversity of MichiganAnn ArborUSA

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