The reproduction rate from Hawkes models accurately forecasts surges in cases.

Rt-based forecasts achieve up to 88% accuracy with Covid-19 case data.

Transmission parameters and reproduction rate can be jointly estimated.

Hawkes point process models have been shown to forecast the number of daily new cases of epidemic diseases, including SARS-CoV-2 (Covid-19), with high accuracy. Here, we explore how accurately Hawkes models forecast surges of Covid-19 in the United States. We use Hawkes models to estimate the effective reproduction rate Rt and transmission density parameters for Covid-19 case counts in each of the 50 United States, then forecast Rt in future weeks with simple exponential smoothing. A classifier based on Rt>x is applied to predict upcoming surges in cases each week from August 2020 to December 2021, using only data available up to that week. At false alarm rates below 5%, the forecasts based on Rt are correct more often than forecasts based on smoothing the raw case count data, achieving a maximum accuracy of 90% with Rt>1.39. The optimal decision boundary uses a combination of Rt and observed data.

Covid-19

Effective reproduction rate

Epidemiological forecasting

Forecasting

Hawkes model

Point process

© 2025 The Authors. Published by Elsevier B.V.