Automated model discovery based on COVID-19 epidemiological data from Thuringia, Germany

The COVID-19 pandemic presented severe challenges in understanding and predicting the spread of infectious diseases, necessitating innovative approaches beyond traditional epidemiological models. This study introduces an advanced method for automated model discovery using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, leveraging a dataset from the COVID-19 outbreak in Thuringia, Germany, encompassing more than 400,000 patient records and vaccination data. We develop a flexible, data-driven model capturing pandemic dynamics, incorporating external factors and interventions into the mathematical framework. The fixed coefficient values globally determined by SINDy were not accurate for local modelling of the data, a limitation of prior SINDy-based epidemiological applications that our framework directly addresses. We therefore refined our technique based on the differential equations as found by SINDy, by investigating three modifications that account for recent local data, each offering different strengths for short-term prediction, scenario analysis, and capturing nonlinear effects, achieving an R² of 0.87 at a one-week horizon. In a first approach, we re-optimized the coefficient values using seven days of past data, without changing the globally determined differential equation. In a second approach, we allowed a temporal dependence of the coefficient values, fitted using all previous data, in combination with regularization. As a last method, we kept the coefficients fixed to the original values but augmented the differential equation with a small neural network, locally optimized to the data of the past week. Our results link vaccination and public health measures to the pandemic's trajectory. The proposed model allows simulation of intervention scenarios, such as vaccination strategies and public health interventions. While the current study is based on retrospective data from a single region, the framework could serve as a basis for exploring responses to future outbreaks, subject to further validation.