Time-varying reproduction number estimation: fusing compartmental models with generalized additive models

The reproduction number, the mean number of secondary cases infected by each primary case, gives an indication of the effort required to control the disease. Beyond the well-known basic reproduction number, there are two natural extensions, namely the control and effective reproduction numbers. As behaviour, population immunity and viral characteristics can change with time, these reproduction numbers can vary over time. Real-world data can be complex, so in this work we consider a generalized additive model to smooth surveillance data through the explicit incorporation of day-of-the-week effects, to provide a simple measure of the time-varying growth rate associated with the data. Converting the resulting spline into an estimator for both the control and effective reproduction numbers requires assumptions on a model structure, which we here assume to be a compartmental model. The reproduction numbers calculated are based on both simulated and real-world data, and are compared with estimates from an already existing tool. The derived method for estimating the time-varying reproduction number is effective, efficient and comparable with other methods. It provides a useful alternative approach, which can be included as part of a toolbox of models, that is particularly apt at smoothing out day-of-the-week effects in surveillance.