Jonas Dehning, Johannes Zierenberg, F. Paul Spitzner, Michael Wibral, Joao Pinheiro Neto, Michael Wilczek, Viola Priesemann
Published Online 15 May 2020
As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A major challenge for short-term forecasts is the assessment of key epidemiological parameters and how they change when first interventions show an effect. By combining an established epidemiological model with Bayesian inference, we analyze the time dependence of the effective growth rate of new infections. Focusing on COVID-19 spread in Germany, we detect change points in the effective growth rate that correlate well with the times of publicly announced interventions. Thereby, we can quantify the effect of interventions, and we can incorporate the corresponding change points into forecasts of future scenarios and case numbers. Our code is freely available and can be readily adapted to any country or region.
We presented a Bayesian approach for monitoring of the effect of non-pharmaceutical governmental interventions on the epidemic spread of an infectious respiratory disease. Using the example of the COVID-19 outbreak in Germany, we applied this approach to infer the central epidemiological parameters and three change points in the spreading rate from the number of reported cases. We showed that change points in the spreading rate affect the confirmed case numbers with a delay of about two weeks (median reporting delay of D=11.4 days plus a median change-point duration of 3 days). Thereby, we were able to relate the inferred change points to the three major governmental interventions in Germany: We found a clear reduction of the spreading rate related to each governmental intervention and the concurring adaptation of individual behavior, (i) the cancellation of large events with more than 1000 participants (around March 9), (ii) the closing of schools, childcare centers and the majority of stores (in effect March 16), and (iii) the contact ban and closing of all non-essential stores (in effect March 23).
Our results indicate that the full extent of interventions was necessary to stop exponential growth. The first two interventions brought a reduction of the growth rate from 30% to 12% and down to 2%, respectively. However, these numbers still implied exponential growth. Only with the third intervention, the contact ban, we found that the epidemic changed from growth to decay. However, the decay rate of about −3% (CI [−5%,−2%]) remains close to zero. Hence, even a minor increase in the spreading rate may again switch the dynamics to the unstable regime with exponential growth.