Identifiability of directed-cycle and catenary linear compartment models

TL;DR

This paper investigates the structural identifiability of two classes of linear compartment models, providing a complete characterization for directed-cycle models and a formula for input-output equations in catenary models, aiding future identifiability analysis.

Contribution

It offers a complete characterization of identifiability in directed-cycle models and introduces a formula for input-output equations in catenary models, advancing understanding of model identifiability.

Findings

Complete characterization of identifiable directed-cycle models

Formula for input-output equations in catenary models

Foundational results supporting future identifiability analysis

Abstract

A parameter of a mathematical model is structurally identifiable if it can be determined from noiseless experimental data. Here, we examine the identifiability properties of two important classes of linear compartmental models: directed-cycle models and catenary models (models for which the underlying graph is a directed cycle or a bidirected path, respectively). Our main result is a complete characterization of the directed-cycle models for which every parameter is (generically locally) identifiable. Additionally, for catenary models, we give a formula for their input-output equations. Such equations are used to analyze identifiability, so we expect our formula to support future analyses into the identifiability of catenary models. Our proofs rely on prior results on input-output equations, and we also use techniques from linear algebra and graph theory.