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COVID-19 Infections in Germany


Key words: COVID-19, pandemic, Germany, coronavirus, simulation
Date of last update: 3 April 2020
This page provides illustrations on the observed evolution of the COVID-19 pandemic in Germany and the expected developments during the next few weeks.
The underlying data sets (statistics-rki-covid-19.csv) are collected from Robert Koch Institut and Johns Hopkins University for Systems Science and Engineering (JHU CCSE).

number of infections

Fig. 1: Cumulative number of COVID-19 infections in the sixteen Federal States of Germany as a function of time. Note that the curves by Robert Koch Institut (RKI) and Johns Hopkins University (JHU) indicating the total number of infections, marked in black and grey, respectively, are offset by a few days. As of 17 March 2020 (marked by a vertical dashed line) Robert Koch Institut only publishes data sets it receives in digital form; these numbers are somewhat smaller than those reported manually to RKI until 17 March 2020. Dashed lines connecting the individual data points serve as a guide to the eye.


transmission rates

Fig. 2: COVID-19 infection transmission rates in the sixteen Federal States of Germany as a function of time. Rates are calculated using a Savitzky-Golay derivative filter of polynomial degree 2 and order 9 (corresponding to a filter window of about four days). Values below 50 are disregarded.


A corresponding analysis of the transmission rates observed in the Hubei region, China (see Fig. 3 below) indicate that the policies enforced by the Chinese authorities were successful in significantly reducing the transmission rate below 0.1 day-1 already in early February.

transmission rate Hubei

Fig. 3: Temporal evolution of COVID-19 transmission rates for the Hubei region, China. An exponential rate decrease with a time constant of −0.2 day-1 (red line) is plotted for comparison.


The next three plots show results from simple-minded simulations estimating of the number of infections during the next few weeks. The only free parameter of the simulation (MATLAB script) is the transmission rate which controls the temporal evolution of the number of infections.
The simulations are based on these assumptions:
  • Initially, 50% of the entire population in Germany, i.e. 40 Mill. people are susceptible to an infection.
  • Once infected, patients are contagious for a fixed number of days.
  • After this time period people no longer spread the virus; they are immune and cannot be infected again.
Three scenarios are simulated:
  • Scenario >WorstCase< : the transmission rate remains at the current value.
  • Scenario >BestCase< : the transmission rate decreases from the current value to zero with a time constant of −0.1 day-1.
  • Scenario >MiddleGround< : the transmission rate decreases slower from the current value to zero with a time constant of −0.02 day-1.
The next three figure shows the results.

simulation

Fig. 4: Expected number of instantaneous infections (number of infected patients at a given time) as a function time if the transmission rate remains at the current value (dashed blue line), the expected number of recoveries are plotted in green. The solid blue line indicates the cumulative number of infections, i.e. the sum of instantaneous infections and recoveries. The number of recoveries in the immediate future (next few weeks) are given by the already known number of infections causing some stagger. Values of cumulative number of infections and recoveries as reported by Johns Hopkins University for Systems Science and Engineering (JHU CCSE) are marked by stars and circles, respectively.


simulation

Fig. 5: Same as Fig. 4, however with a transmission rate exponentially decreasing from the current value to zero with a time constant of −0.1 day-1 (see Fig. 3)


simulation

Fig. 6: Same as Fig. 4, however with a transmission rate exponentially decreasing from the current value to zero with a time constant of only −0.02 day-1 (see Fig. 3)


A mean infection time period of 20 days is assumed. In scenario >WorstCase< the maximum of 1.7 Mill. infections is reached on 4 October, whereas scenario >BestCase< succeeds in reducing the maximum number of infections to 94,100 on 8 April. Scenario >MiddleGround< predicts a maximum number of 110,500 infections on 14 April.
It is noteworthy that no scenario predicts the infection of all 40 Mill. susceptible individuals; that is, one or more additional infection waves may occur.

doubling time versus transmission rate

Fig. 7: Relationship between transmission rate and infection doubling time.