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

Abstract: Structural identifiability -- the theoretical ability to uniquely recover model parameters from ideal, noise-free data -- is a prerequisite for reliable parameter estimation in epidemic modeling. Despite its importance, structural identifiability analysis remains underutilized in the infectious disease modeling literature. In this tutorial, we present a practical and reproducible workflow for conducting structural identifiability analysis of ordinary differential equation models using the Julia package StructuralIdentifiability.jl. We apply the tool to a range of epidemic models, including SEIR variants with asymptomatic and pre-symptomatic transmission, vector-borne systems, and models incorporating hospitalization and disease-induced mortality. We compare results from StructuralIdentifiability.jl with those obtained using DAISY, a widely used differential algebra tool, and highlight cases where the Julia package succeeds in analyzing models that DAISY cannot handle. In particular, StructuralIdentifiability.jl efficiently handles high-dimensional systems and provides symbolic checks for assumptions often overlooked in other methods. Our findings underscore how identifiability depends on model structure, the availability of initial conditions, and the choice of observed states. All code and diagrams are publicly available, making this tutorial a valuable reference for researchers and educators working with dynamic disease models.