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


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.


Identifiability Linear compartment models Identifiable functions Differential algebra 



Nicolette Meshkat was partially supported by the David and Lucille Packard Foundation. Seth Sullivant was partially supported by the David and Lucille Packard Foundation and the US National Science Foundation (DMS 0954865).


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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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