Practical identifiability and parameter estimation of compartmental epidemiological models

Abstract Practical parameter identifiability in ODE-based epidemiological models is a known issue, yet one that merits further study. It is essentially ubiquitous owing 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 and as concerns the question of whether fixing or fitting the initial conditions that are not directly measured improves parameter estimates, we find that the answer is model-dependent. Specifically, in the standard susceptible-exposed-infected-recovered (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. Finally, our examples suggest that in the presence of significantly noisy data, the value of structural identifiability is moot.