Bayesian estimation of real-time epidemic growth rates using Gaussian processes: local dynamics of SARS-CoV-2 in England

Quantitative assessments of the recent state of an epidemic and short-term projections for the near future are key public-health tools that have substantial policy impacts, helping to determine if existing control measures are sufficient or need to be strengthened. Key to these quantitative assessments is the ability to rapidly and robustly measure the speed with which an epidemic is growing or decaying. Frequently, epidemiological trends are addressed in terms of the (time-varying) reproductive number R. Here, we take a more parsimonious approach and calculate the exponential growth rate, r, using a Bayesian hierarchical model to fit a Gaussian process to the epidemiological data. We show how the method can be employed when only case data from positive tests are available, and the improvement gained by including the total number of tests as a measure of the heterogeneous testing effort. Although the methods are generic, we apply them to SARS-CoV-2 cases and testing in England, making use of the available high-resolution spatio-temporal data to determine long-term patterns of national growth, highlight regional growth, and spatial heterogeneity.