Reproduction number estimation using smoothing methods Reproduction number and smoothing methods

The reproduction number for an epidemic is crucial as it helps to understand the potential spread of an infectious disease within a population. It is often estimated through case counting and contact tracing methods. Here, we propose an alternative approach based on real-time smoothing techniques. A generalized additive model (GAM) is proposed to model the number of new infectious cases. The characteristics of the smoothing functions are used to estimate the basic reproduction number, R0, and the effective reproduction number, Rt. The proposed method is assessed on simulated data. We simulated three epidemic scenarios with different transmissibility levels, corresponding to different R0 values (11.52, 2.88, and 1.06), using a stochastic SEIR model. The method was then compared with validated methods already implemented in R software: the exponential growth method developed by Obadia et al. and the renewal process method developed by Cori et al. Our splines smoothing method estimated credible tolerance intervals and provided a better fit to data variations while maintaining an appropriate balance between bias, precision and coverage. This reflects the methods flexibility and ability to capture the epidemic dynamics. In the three scenarios, the splines smoothing method produced median R0 estimates of 12.33 [8.34-18.03], 2.33 [1.56-3.56], and 1.31 [0.77-3.45]. The renewal process method led to credible median R0 estimates of 12.78 [10.48-17.48], 2.51 [2.02-5.29] and 1.91 [1.23-3.98], respectively. Neither method exhibits a distinct superiority across all contexts. Their efficacy varies depending on performance priorities. In contrast, the exponential method showed inferior performance relative to the other two approaches, exhibiting moderate bias and potentially lower coverage rates with median R0 estimates of 13.90 [10.39-33.47], 2.29 [1.08-7.6] and 1.07 [0.39-5.56]. Real-time smoothing provides results comparable to established classical methods while retaining the full flexibility of generalized additive models. Author summaryIn the context of infectious disease outbreaks, understanding the spread rate is crucial. The reproduction number, which represents the average number of secondary infections generated by an infected individual is a widely used metric. This number can be estimated at the onset of the epidemic (basic reproduction number, R0) or at a specific point in time (effective reproduction number, Rt). The objective of this work is to propose an estimate based on statistical smoothing methods, specifically the Generalized Additive Model (GAM) smoothing method. This method provides a more accurate estimate of the epidemics initial phase and estimates R0 as effectively. The strength of the splines smoothing method lies in its adaptability across different, scenarios, allowing it to track changes in the data. We compared this approach to two commonly used methods for estimating the reproduction number. While the exponential growth method is simple but less efficient, the spline smoothing method demonstrated comparable efficacy to the renewal process method. Furthermore, it identifies the initial phase of the epidemic with rigor and simplicity and y and offers flexibility by allowing various smoothing techniques.