Structural identifiability analysis of PDEs: A case study in continuous age-structured epidemic models

TL;DR

This paper develops a framework for structural identifiability analysis of age-structured PDE epidemic models, extending existing methods from ODEs to handle the complexities of PDEs, and demonstrates its application through a case study.

Contribution

It introduces a differential algebra-based pipeline for identifiability analysis of PDE models, filling a gap in existing methods primarily focused on ODEs.

Findings

Identifiability results for specific age-structured PDE models

Comparison of PDE and ODE model identifiability

Insights into age-dependent parameter effects

Abstract

Computational and mathematical models rely heavily on estimated parameter values for model development. Identifiability analysis determines how well the parameters of a model can be estimated from experimental data. Identifiability analysis is crucial for interpreting and determining confidence in model parameter values and to provide biologically relevant predictions. Structural identifiability analysis, in which one assumes data to be noiseless and arbitrarily fine-grained, has been extensively studied in the context of ordinary differential equation (ODE) models, but has not yet been widely explored for age-structured partial differential equation (PDE) models. These models present additional difficulties due to increased number of variables and partial derivatives as well as the presence of boundary conditions. In this work, we establish a pipeline for structural identifiability analysis of age-structured PDE models using a differential algebra framework and derive identifiability results for specific age-structured models. We use epidemic models to demonstrate this framework because of their wide-spread use in many different diseases and for the corresponding parallel work previously done for ODEs. In our application of the identifiability analysis pipeline, we focus on a Susceptible-Exposed-Infected model for which we compare identifiability results for a PDE and corresponding ODE system and explore effects of age-dependent parameters on identifiability. We also show how practical identifiability analysis can be applied in this example.