Model selection and parameter identification analysis in epidemiological models

Infectious disease modeling can provide critical information for public health. However, simple models can be distorted and complex models are susceptible to overfitting, especially when limited data are available, and there is a trade-off between model complexity and the uncertainty caused by overfitting. In this paper, we apply the Affine Invariant Ensemble Markov Chain Monte Carlo (GWMCMC) algorithm to model selection and parameter identifiability analysis of the spread of COVID-19 in the UK, focusing on how to select the best model and how to assess the parameter identifiability and reliability of the prediction results using limited observational data. We investigate a set of nested two-variant and single-variant models of COVID-19 dynamics for the UK population. Using the public health data from the UK during September 19 – October 9, 2020, we first carry out model selection process to determine the parsimonious model that best represents the data, then we carry out both structural and practical parameter identifiability analysis on the parsimonious model to show that the best-fit parameter values obtained from model calibration are robust from noise perturbations in the data. Public health responses are then incorporated into the baseline transmission model to provide a long-term and short-term forecast of the UK outbreak. This study confirms that model selection and identifiability analysis are very important in mathematical modeling of infectious diseases, and the best model obtained from model selection can better explain the trend of epidemic; the results of identifiability analysis show that a good algorithm can reduce the occurrence of parameter unidentifiability, improve the robustness of parameter estimation, and increase the reliability of prediction results.