A Tutorial on Structural Identifiability of Epidemic Models Using StructuralIdentifiability.jl

TL;DR

This paper provides a reproducible framework for conducting structural identifiability analysis of ordinary differential equation models using the Julia package StructuralIdentifiability.jl and introduces a visual communication strategy that embeds identifiability results directly into compartmental diagrams, facilitating interpretation and interdisciplinary communication.

Abstract

Structural identifiability is the theoretical ability to uniquely recover model parameters from ideal, noise-free data and is a prerequisite for reliable parameter estimation in epidemic modeling. Despite its importance for calibration and inference, structural identifiability analysis remains underused and inconsistently applied in infectious disease modeling. This paper presents a user-oriented methodological tutorial demonstrating how global structural identifiability analysis can be systematically integrated into epidemic modeling workflows. We provide a reproducible framework for conducting structural identifiability analysis of ordinary differential equation models using the Julia package StructuralIdentifiability.jl. The workflow is illustrated across commonly used epidemic models, including SEIR variants with asymptomatic and presymptomatic transmission, vector-borne disease models, and systems incorporating hospitalization and disease-induced mortality. We also introduce a visual communication strategy that embeds identifiability results directly into compartmental diagrams, facilitating interpretation and interdisciplinary communication. Our results show that identifiability depends critically on model structure, the choice of observed variables, and assumptions about initial conditions, and that identifiable parameter combinations may exist even when individual parameters are not globally identifiable. Emphasizing transparent implementation, interpretation, and communication, this work provides practical guidance and comparative insights across model classes. The tutorial is designed as both a reference and a teaching resource for researchers and educators seeking to incorporate structural identifiability analysis into epidemic model development. All code and annotated diagrams are publicly available to ensure reproducibility and reuse.

Figures (13)

• Figure 1: As illustrated in this figure, the number of publications that include structural identifiability, practical identifiability, or both in their titles has increased markedly between 1990 and 2024. This trend reflects the growing recognition within the modeling community of the importance of rigorous identifiability analyses to support reliable parameter inference. Notably, practical identifiability has received the most attention in recent years, while interest in studies that integrate both structural and practical perspectives continues to rise. Data retrieved from the Web of Science core collection.
• Figure 2: SEIR model flow diagram and structural identifiability results. The top panel shows the compartmental structure of the SEIR model. The bottom panel presents identifiability results from StructuralIdentifiability.jl: with unknown and with known initial conditions. Diagram reproduced with permission from Chowell et al. (2023).
• Figure 3: Flow diagram of the SEIR model extended to account for symptomatic and asymptomatic transmission dynamics. The model captures distinct progression pathways from exposed individuals to symptomatic ($I$) and asymptomatic ($A$) infectious compartments, both of which contribute to onward transmission and recovery. This enhanced structure allows for more realistic modeling of partially observed epidemics, particularly those involving subclinical spread. The bottom panel presents the structural identifiability results obtained using StructuralIdentifiability.jl, under both unknown and known initial condition scenarios. Diagram reproduced with permission from Chowell et al. (2023).
• Figure 4: Flow diagram of the SEIR model with infectious asymptomatic individuals. The diagram illustrates the transitions between the susceptible, exposed, symptomatic, asymptomatic, and recovered states in the population. The bottom panel presents identifiability results from StructuralIdentifiability.jl: with unknown and with known initial conditions. Diagram reproduced with permission from Chowell et al. (2023).
• Figure 5: Flow diagram of the SEIR model extended to include disease-induced mortality. In this formulation, infected individuals may either recover or die as a direct consequence of infection, leading to a decline in total population size over time. This feature enhances the model's realism for high-severity pathogens. The bottom panel displays the structural identifiability results obtained using StructuralIdentifiability.jl under scenarios with both unknown and known initial conditions. Diagram reproduced with permission from Chowell et al. (2023).

Theorems & Definitions (17)

• Definition 1.1
• Proposition 3.1
• Proposition 3.2
• Proposition 3.3
• Proposition 3.4
• Proposition 3.5
• Proposition 3.6
• Proposition 3.7
• Proposition 3.8
• Proposition 3.9