Estimate of the development of the epidemic reproduction number Rt from Coronavirus SARS-CoV-2 case data and implications for political measures based on prognostics

Sahamoddin Khailaie; Tanmay Mitra; Arnab Bandyopadhyay; Marta Schips; Pietro Mascheroni; Patrizio Vanella; Berit Lange; Sebastian Binder; Michael Meyer-Hermann

The basic reproduction number is a good measure for the long-term evolution of an epidemic that can be derived from such models (see Methods, Eq. (9)). However, it assumes constant conditions over the whole period analysed. In particular, the effect of NPIs on viral spreading enters the reproduction number only in a way mixed with the time before NPIs. For the evaluation of NPI effects on viral spreading, a time-varying reproduction number Rt has to be determined (Cori et al. 2013) . We opted for a shifting time window in each of which Rt is determined. We developed an automatized algorithm for the fast analysis of the current Rt (see Methods). Importantly, each time window is not analysed independently but includes the history of the epidemic by starting from the saved state of the simulation at the beginning of each time window. This analysis was developed for the sake of providing a daily updated evaluation of the reproduction number suitable to support political decisions on NPIs in the course of the CoV-outbreak and applied to German data ( Figure 2 ). Table 1 were used and the transmission rate R1 was varied (see Methods). (B) Time-varying reproduction number Rt as resulting from the fit in each time window in (A). The parameter sets were randomly sampled within the ranges in Table 1 and, upon refitting, this induced a variability of reported Rt values. The box plot shows the 25 and 75 percentiles as well as the min and the max values. Both used parameters sets (literature-based and derived from Italy-fit) are compared. (C-D) Same analysis for each federal state in Germany separately. Only the median value from an analysis as in (B) is reported for better visibility. The complete information can be found in the supplement. (E) The last reported Rt value in each federal state of Germany sorted by median values. Same box plot as in (B). The horizontal line shows Rt=1. (B-E): Each data point is a result of 100 randomly sampled parameter sets. The data for analysis were taken from (Nationale Plattform für geographische Daten 2020; GENESIS-Online 2020a, 2020b; own calculation and design).