  Identifiability of a mathematical model plays a crucial role in
parameterization of the model. In this study, we establish the structural
identifiability of a Susceptible-Exposed-Infected-Recovered (SEIR) model given
different combinations of input data and investigate practical identifiability
with respect to different observable data, data frequency, and noise
distributions. The practical identifiability is explored by both Monte Carlo
simulations and a Correlation Matrix approach. Our results show that practical
identifiability benefits from higher data frequency and data from the peak of
an outbreak. The incidence data gives the best practical identifiability
results compared to prevalence and cumulative data. In addition, we compare and
distinguish the practical identifiability by Monte Carlo simulations and a
Correlation Matrix approach, providing insights for when to use which method
for other applications.
