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

In order to assess the impact of political measures onto the development of the reproduction number Rt, the cumulative numbers of registered cases in the respective federal state are used. The cumulative case number is compared to the sum of infected individuals and all subsequent states in the model, i.e. with I+H+U+D+R-RC. A time window of a width of one week is defined starting at the day of the first reported case (Cori et al. 2013) . This allows to determine Rt in the first week and to define proper initial conditions for the first sliding time window. Then, in repeating cycles, the best Rt for the first time window is determined, a new set of initial conditions is defined a day later, including the reduced fraction of susceptible individuals S(tk)/N(tk), where S(tk) is the value of S at the starting time tk of the k-th time window and N(tk) is the total population at the same time --note that fatal cases reduce the total population --, and the time window is shifted one day later. The series of Rt-values for each of the sliding time windows is reported.