<p>The parameters of the SINDy.</p>

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.