Stochastic Universal Differential Equations for Epidemiological Modeling: Uncertainty Quantification in Disease Transmission Dynamics

Epidemic forecasting requires not only predictions of expected case counts, but also quantification of uncertainty, although existing surrogate modeling frameworks for agent-based models remain fundamentally deterministic. In this thesis a Stochastic Universal Differential Equation framework is presented that extends the deterministic Universal Differential Equation approach by incorporating a learnable stochastic diffusion term, enabling calibrated probabilistic forecasts while preserving the mechanistic interpretability and computational efficiency of the deterministic baseline. In doing so, a two-phase training algorithm is introduced to ensure stable convergence and the framework is validated against the ensemble output from ExaEpi, an exascale agent-based model of a COVID-19 outbreak in the San Francisco Bay Area. The outcome demonstrates that the stochastic extension maintains accuracy of the mean trajectory comparable to the deterministic baseline while producing well-calibrated uncertainty intervals, with the learned diffusion structure autonomously recovering the timing of the shelter-in-place intervention as the primary driver of epidemic uncertainty.