  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.
