Detection of surges of SARS-Cov-2 using nonparametric Hawkes models

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 $R_t$ and transmission density parameters for Covid-19 case counts in each of the 50 United States, then forecast $R_t$ in future weeks with simple exponential smoothing. A classifier based on $R_t>x$ 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 $R_t$ are correct more often than forecasts based on smoothing the raw case count data, achieving a maximum accuracy of 90% with $R_t>1.39$. The optimal decision boundary uses a combination of $R_t$ and observed data.