Inferring COVID-19 spreading rates and potential change points for case number forecasts

Jonas Dehning; Johannes Zierenberg; Frank Paul Spitzner; Michael Wibral; Joao Pinheiro Neto; Michael Wilczek; Viola Priesemann

Conclusions. We developed a Bayesian framework to infer the spreading rate λ and the timing and magnitude of change points. Thereby, the efficiency of political and individual measures for social distancing and containment can be assessed in a timely manner. We find first evidence for a successive decrease of the spreading rate in Germany around March 9 and around March 16, which significantly reduced the magnitude of exponential growth, but was not sufficient to turn growth into decay. The development in the coming week will reveal the efficiency of the contact ban initiated on March 23. In general, our analysis code may help to infer the efficiency of measures taken in other countries and inform policy makers about tightening, loosening and selecting appropriate rules for containment. Inference of change points in the spreading rate λ from confirmed COVID-19 cases in Germany. A: Prior (blue) and posterior (orange) distributions for five of the central parameters of an SIR model with two change points (at time t1 and t2), where the spreading rate changes from λ0 → λ1 → λ2. B: The inferred growth rate λ * , i.e. the difference between spreading and recovery rate (λ * = λ − µ) for an SIR model that assumes scenarios with one, two or three change points (red, orange, green; fitted to case reports until March 25, April 1 and April 9, respectively). The timing of the inferred change points corresponds well to the timing of the governmental interventions in Germany (depicted as * ). C,D: The model-fit of the new confirmed cases and (cumulative) total confirmed cases is depicted for the models with one, two or three change points. The three scenarios depend strongly on whether one includes the third change point or not: the number of new confirmed cases grow exponentially (red, orange) or are approximately constant (green). This illustrates that the future development depends strongly on our distancing behavior. B,C: Note the delay D between change point (i.e. change in spreading behavior) and observation of confirmed cases of almost two weeks.