Gaussian process modelling of infectious diseases using the Greta software package and GPUs

Comprehensive Summary

This retrospective, single-region modeling study asked whether Gaussian process (GP) regression can accurately model and forecast spatio-temporal variation in tuberculosis (TB) incidence, using Bayesian Gaussian process models to perform disease risk estimation and short- to medium-term prediction. Researchers analyzed n = 6,760 weekly TB case counts from local and unitary authorities in the East and West Midlands of England between 2022 and early 2024, using publicly available UK notifiable disease surveillance data. Case counts were preprocessed by incorporating population offsets and spatial coordinates, and were modeled using negative binomial and zero-inflated negative binomial likelihoods to address overdispersion and excess zeros. The models tested included spatio-temporal Gaussian processes with Matérn, exponential, radial basis function, and periodic kernels, fitted using Bayesian Hamiltonian Monte Carlo and sparse approximations, and compared across kernel structures and likelihood choices using leave-one-out cross-validation (LOOIC), continuous ranked probability score (CRPS), Bayesian p-values, and RMSE. GPU-accelerated implementations using TensorFlow substantially reduced computational time relative to CPU-based fitting. The analysis showed that a Matérn(3/2) temporal kernel combined with a periodic component and a mid-smoothness spatial Matérn kernel provided the best trade-off between model fit and complexity, with accurate and stable predictions up to 26 weeks ahead and only modest increases in prediction error as the forecast horizon extended. GPU implementation yielded a 60–70% reduction in total model fitting time, enabling practical Bayesian inference at this scale. Secondary analyses included posterior predictive checks using the Freeman–Tukey statistic, kernel sensitivity testing, and extended-horizon forecasting. Predictive performance remained consistent across regions, and posterior uncertainty appropriately widened in data-sparse settings, supporting the model’s ability to quantify epidemiologic uncertainty. Limitations include reliance on a single geographic region, absence of external validation, and limited incorporation of demographic or environmental covariates, as well as the fact that outcomes reflect surveillance-level incidence patterns rather than patient-level clinical outcomes, precluding direct claims of clinical efficacy.

Outcomes and Implications

This study suggests that GPU-accelerated Gaussian process models can provide timely, uncertainty-aware forecasts of infectious disease incidence that are well-suited for public health surveillance and planning. While not a diagnostic or patient-facing tool, this approach could be applied in practice to support health system preparedness, such as anticipating regional TB burden, informing allocation of public health resources, and identifying areas at elevated short-term risk. With further validation and integration of demographic, environmental, or healthcare access data, similar GP-based frameworks could be extended to other infectious diseases or geographic settings, helping translate advanced statistical learning methods into actionable population-level decision support rather than direct bedside care.