Time-varying reproduction number estimation: Fusing compartmental models with generalised additive models

The reproduction number, the mean number of secondary cases infected by each primary case, is a central metric in infectious disease epidemiology, and played a key role in the COVID-19 pandemic response. This is because it gives an indication of the effort required to control the disease. Beyond the well-known basic reproduction number, there are two natural versions, 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 and in different regions.

Real world data can be complex, for example with daily variation in numbers due to weekend surveillance biases as well as natural stochastic noise. As such, in this work we consider a Generalised Additive Model to smooth real 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 to 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.