A new Reproduction Index Ri and its Usefulness for Germany's Covid19-Data

Conradt, R. N. J.

In the course of a large-scale infectious disease a time-dependent Reproduction rate is an important parameter for political, economic and social decisions. In this paper we focus on that parameter and introduce a mathematical implementation in addition to the mostly used definition of Robert-Koch-Institute (RKI) in Germany. Such value is of particular interest in order to serve as a criterion for possible Lock-Downs and "LockUps" in society and can provide deep insights into a pandemic event. Both the definition of the new Reproduction index and the RKI's Reproduction number are compared analytically, applied to simple model calculations and finally on real Covid19 data. Clear advantages of the new Reproduction index become apparent and some weaknesses of the RKI's Reproduction number become clearly visible. In addition we propose two additional ways of displaying pandemic data to have the pandemic behaviour at a glance. We find that some signatures of the pandemic appear now very well expressed - especially in conjunction with the new Reproduction index R_i. This all could be very helpful for future political, social and economic decisions.