A Tutorial on Symbolic Structural Identifiability Analysis of ODE Models in Julia

TL;DR

This tutorial introduces a Julia-based computational framework for symbolic structural identifiability analysis of ODE models, demonstrating its application across various biological case studies.

Contribution

It provides a modern, reproducible workflow for identifiability analysis using Julia, integrating theoretical concepts with practical tools and case studies.

Findings

Demonstrated globally identifiable systems in case studies

Identified local-only and non-identifiable models

Showed how additional measurements improve identifiability

Abstract

Structural identifiability analysis determines whether the parameters of a mechanistic ordinary differential equation (ODE) model can be uniquely recovered from ideal observations and is therefore a fundamental prerequisite for reliable parameter estimation. This tutorial presents a modern, reproducible computational framework for symbolic structural identifiability analysis using the Julia package StructuralIdentifiability.jl. We provide a rigorous yet accessible introduction to local and global identifiability, observability, parameter-to-output mappings, and identifiable parameter combinations, together with a unified workflow based on the core functions @ODEmodel, assess_local_identifiability, assess_identifiability, and find_identifiable_functions. The framework is demonstrated through seven case studies from epidemiology, pharmacokinetics, and systems biology, illustrating globally identifiable systems, local-only identifiability, structural non-identifiability, and recovery of identifiability through additional measurements and reparameterization. Beyond the theoretical foundations, the tutorial emphasizes practical model reformulation, experimental design, and reproducible scientific workflows within the Julia SciML ecosystem, providing a comprehensive reference for researchers and graduate students working with mechanistic ODE models.