  Practical parameter identifiability in ODE-based epidemiological models is a
known issue, yet one that merits further study. It is essentially ubiquitous
due to noise and errors in real data. In this study, to avoid uncertainty
stemming from data of unknown quality, simulated data with added noise are used
to investigate practical identifiability in two distinct epidemiological
models. Particular emphasis is placed on the role of initial conditions, which
are assumed unknown, except those that are directly measured. Instead of just
focusing on one method of estimation, we use and compare results from various
broadly used methods, including maximum likelihood and Markov Chain Monte Carlo
(MCMC) estimation.
  Among other findings, our analysis revealed that the MCMC estimator is
overall more robust than the point estimators considered. Its estimates and
predictions are improved when the initial conditions of certain compartments
are fixed so that the model becomes globally identifiable. For the point
estimators, whether fixing or fitting the that are not directly measured
improves parameter estimates is model-dependent. Specifically, in the standard
SEIR model, fixing the initial condition for the susceptible population S(0)
improved parameter estimates, while this was not true when fixing the initial
condition of the asymptomatic population in a more involved model. Our study
corroborates the change in quality of parameter estimates upon usage of
pre-peak or post-peak time-series under consideration. Finally, our examples
suggest that in the presence of significantly noisy data, the value of
structural identifiability is moot.
