  Modeling and prediction of epidemic spread are critical to assist in
policy-making for mitigation. Therefore, we present a new method based on
Gaussian Process Regression to model and predict epidemics, and it quantifies
prediction confidence through variance and high probability error bounds.
Gaussian Process Regression excels in using small datasets and providing
uncertainty bounds, and both of these properties are critical in modeling and
predicting epidemic spreading processes with limited data. However, the
derivation of formal uncertainty bounds remains lacking when using Gaussian
Process Regression in the setting of epidemics, which limits its usefulness in
guiding mitigation efforts. Therefore, in this work, we develop a novel bound
on the variance of the prediction that quantifies the impact of the epidemic
data on the predictions we make. Further, we develop a high probability error
bound on the prediction, and we quantify how the epidemic spread, the infection
data, and the length of the prediction horizon all affect this error bound. We
also show that the error stays below a certain threshold based on the length of
the prediction horizon. To illustrate this framework, we leverage Gaussian
Process Regression to model and predict COVID-19 using real-world infection
data from the United Kingdom.
