Development of the reproduction number from coronavirus SARS-CoV-2 case data in Germany and implications for political measures

Abstract

Background SARS-CoV-2 has induced a worldwide pandemic and subsequent non-pharmaceutical interventions (NPIs) to control the spread of the virus. As in many countries, the SARS-CoV-2 pandemic in Germany has led to a consecutive roll-out of different NPIs. As these NPIs have (largely unknown) adverse effects, targeting them precisely and monitoring their effectiveness are essential. We developed a compartmental infection dynamics model with specific features of SARS-CoV-2 that allows daily estimation of a time-varying reproduction number and published this information openly since the beginning of April 2020. Here, we present the transmission dynamics in Germany over time to understand the effect of NPIs and allow adaptive forecasts of the epidemic progression. Methods We used a data-driven estimation of the evolution of the reproduction number for viral spreading in Germany as well as in all its federal states using our model. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread in different regions of Italy, the model was optimized to fit data from the Robert Koch Institute. Results The time-varying reproduction number (Rt) in Germany decreased to <1 in early April 2020, 2–3 weeks after the implementation of NPIs. Partial release of NPIs both nationally and on federal state level correlated with moderate increases in Rt until August 2020. Implications of state-specific Rt on other states and on national level are characterized. Retrospective evaluation of the model shows excellent agreement with the data and usage of inpatient facilities well within the healthcare limit. While short-term predictions may work for a few weeks, long-term projections are complicated by unpredictable structural changes. Conclusions The estimated fraction of immunized population by August 2020 warns of a renewed outbreak upon release of measures. A low detection rate prolongs the delay reaching a low case incidence number upon release, showing the importance of an effective testing-quarantine strategy. We show that real-time monitoring of transmission dynamics is important to evaluate the extent of the outbreak, short-term projections for the burden on the healthcare system, and their response to policy changes.

Data-Driven Prediction of COVID-19 Cases in Germany for Decision Making

“…The estimated reproduction number R(t) oscillates around a value of 1 and illustrates the effect of describing the politics' countermeasures and the population's (e) 7-day incidence compliance to them (Figure 2, Panel (d)). This is in line with several publications [9], [19], [20] reporting similar behavior of the reproduction number. In general, oscillations in dynamical systems often are attributed to a feedback with delay, which is also the case here for the reproduction number R(t).…”

Regional opening strategies with commuter testing and containment of new SARS-CoV-2 variants in Germany

“…For each county, we use an age-resolved SIR-type model based on [8,11], with particular new focus on commuter testing. The model uses the compartments Susceptible (S i ); Exposed (E i ), who carry the virus but are not yet infectious to others; Carriers (C i ), who carry the virus and are infectious to others but do not yet show symptoms (they may be preor asymptomatic); Infected (I i ), who carry the virus, are infectious and show symptoms; Hospitalized (H i ), who experience a severe development of the disease; In Intensive Care Unit (U i ); Dead (D i ); and Recovered (R i ), who cannot be infected again.…”

“…The prediction of SARS-CoV-2 infections by mathematical models is an active area of research of many groups from all over the world. In particular for Germany, e.g., the authors of [5,6,7,8,9,10,11,12] have studied the effects of political interventions and provided predictions for the development of new cases. Spatial resolutions with a particular focus on networks and mobility was, among others, presented by the authors of [5,9,12,11].…”

Heterogeneity matters: Contact structure and individual variation shape epidemic dynamics

“…José Lourenço et al infer epidemiological parameters [40]. Khailaie et al analyze how changes in the reproduction number affect the epidemic dynamics [41]. Stutt et al evaluate the effectiveness of NPIs [42].…”