This dissertation develops statistical methods for estimating the reproduction rate and for forecasting infectious disease. We present: (1) direct, stable estimators for the productivity in Hawkes processes, with a comparison of their relative performance; (2) an application to COVID-19 case data demonstrating the utility of the estimated reproduction rate, which corresponds to the Hawkes productivity, as an early warning signal for surges; and (3) a framework for sharing information across outbreaks by fitting each wave separately with simple curves, borrowing strength from prior outbreaks to stabilize estimation and improve forecasts.