Epidemiological model calibration via graybox Bayesian optimization

In this study, we focus on developing efficient calibration methods via Bayesian decision-making for the family of compartmental epidemiological models. The existing calibration methods usually assume that the compartmental model is cheap in terms of its output and gradient evaluation, which may not hold in practice when extending them to more general settings. Therefore, we introduce model calibration methods based on a "graybox" Bayesian optimization (BO) scheme, to enable more efficient calibration for general epidemiological models. This approach uses Gaussian processes as a surrogate to the expensive model, and leverages the functional structure of the compartmental model to enhance calibration performance. Additionally, we develop model calibration methods via a decoupled decision-making strategy for BO, which further exploits the decomposable nature of the functional structure. The calibration efficiencies of the multiple proposed schemes are evaluated based on various data generated by a compartmental model mimicking real-world epidemic processes and COVID-19 datasets. Experimental results demonstrate that our proposed graybox variants of BO schemes can efficiently calibrate computationally expensive models and further improve the calibration performance measured by the logarithm of mean squared errors and achieve faster performance convergence in terms of BO iterations. We anticipate that the proposed calibration methods can be extended to enable fast calibration of more complex epidemiological models, such as the agent-based models.