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We introduce a class of linear compartmental models called identifiablepath/cycle models which have the property that all of the monomial functions ofparameters associated to the directed cycles and paths from input compartmentsto output compartments are identifiable and give sufficient conditions toobtain one. Removing leaks, we then show how one can obtain a locallyidentifiable model from an identifiable path/cycle model. These identifiablepath/cycle models yield the only identifiable models with certain conditions ontheir graph structure and thus we provide necessary and sufficient conditionsfor identifiable models with certain graph properties. A sufficient conditionbased on the graph structure of the model is also provided so that one can testif a model is an identifiable path/cycle model by examining the graph itself.We also provide some necessary conditions for identifiability based on graphstructure. Our proofs use algebraic and combinatorial techniques.

Identifiable paths and cycles in linear compartmental models