Degree Name
MS (Master of Science)
Program
Mathematical Sciences
Date of Award
5-2026
Committee Chair or Co-Chairs
Jeff Knisley
Committee Members
Michele Joyner, Robert Price
Abstract
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.
Document Type
Thesis - unrestricted
Recommended Citation
Armah-Bonney, Alice Menaya, "Stochastic Universal Differential Equations for Epidemiological Modeling: Uncertainty Quantification in Disease Transmission Dynamics" (2026). Electronic Theses and Dissertations. Paper 4655. https://dc.etsu.edu/etd/4655
Copyright
Copyright by the authors.
Included in
Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons, Population Health Commons
