Estimating the Course of the COVID-19 Pandemic in Germany via Spline-based Hierarchical Modelling of Death Counts

Abstract

The effective reproduction number is a key figure in context of the COVID-19 pandemic, which is typically estimated based on daily confirmed cases. Here, we consider a retrospective modelling approach for estimating effective reproduction numbers based on death counts during the first year of the pandemic in Germany. The proposed Bayesian hierarchical model incorporates splines to estimate reproduction numbers flexibly over time while adjusting for varying effective infection fatality rates. The approach also provides estimates of dark figures regarding undetected infections over time. Results for Germany illustrate that estimates based on death counts are often similar to classical estimates based on confirmed cases. However, considering death counts is more robust against shifts in testing policies: in particular, confirmed cases indicate a spike in the effective reproduction number linked to a local super-spreading event in June 2020, whereas our model does not estimate a spike but reduced dark figures of infections. During the second wave of infections, classical estimates suggest a flattening trend of infections following the "lockdown light" in November 2020, while our results indicate that infections continued to rise until the "second lockdown" in December 2020. This observation is associated with more stringent testing criteria introduced concurrently with the "lockdown light", which is reflected in subsequently increasing dark figures of infections estimated by our model. In light of progressive vaccinations, shifting the focus from modelling confirmed cases to reported deaths with the possibility to incorporate effective infection fatality rates might be of increasing relevance for the future surveillance of the pandemic.