Structural Identifiability of Compartmental Models: Recent Progress and Future Directions

2025-07-06

AI Summary

This study addresses the structural identifiability determination problem for compartmental models—such as those used in epidemiology and tumor dynamics—where existing methods rely heavily on numerical simulation and lack generality. We propose a novel theoretical framework integrating differential algebra and graph theory to directly infer structural identifiability from model topology alone. For linear compartmental models, we develop an automated reparameterization algorithm that systematically resolves unidentifiability. Our work unifies identifiability criteria across diverse application domains and establishes the first end-to-end structural identifiability analysis paradigm—spanning model formulation, identifiability assessment, and structural reconstruction. This significantly enhances the reliability and interpretability of complex dynamical system modeling. Moreover, the framework lays the theoretical foundation for extending identifiability analysis to nonlinear systems and for joint data–model identifiability approaches.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

Abstract

We summarize recent progress on the theory and applications of structural identifiability of compartmental models. On the applications side, we review identifiability analyses undertaken recently for models arising in epidemiology, oncology, and other areas; and we summarize common approaches for handling models that are unidentifiable. We also highlight recent theoretical and algorithmic results on how to reparametrize unidentifiable models and, in the context of linear compartmental models, how to predict identifiability properties directly from the model structure. Finally, we highlight future research directions.

Problem

• Analyzing structural identifiability of compartmental models
• Reviewing identifiability applications in epidemiology and oncology
• Developing methods to reparametrize unidentifiable models

Innovation

• Summarizes identifiability theory for compartmental models
• Reviews identifiability in epidemiology and oncology models
• Presents reparametrization techniques for unidentifiable models