Estimation of R0 for the spread of SARS-CoV-2 in Germany from excess mortality.

For SARS-CoV-2, R0 calculations in the range of 2-3 dominate the literature, but much higher estimates have also been published. Because capacity for RT-PCR testing increased greatly in the early phase of the Covid-19 pandemic, R0 determinations based on these incidence values are subject to strong bias. We propose to use Covid-19-induced excess mortality to determine R0 regardless of RT-PCR testing capacity. We used data from the Robert Koch Institute (RKI) on the incidence of Covid cases, Covid-related deaths, number of RT-PCR tests performed, and excess mortality calculated from data from the Federal Statistical Office in Germany. We determined R0 using exponential growth estimates with a serial interval of 4.7 days. We used only datasets that were not yet under the influence of policy measures (e.g., lockdowns or school closures). The uncorrected R0 value for the spread of SARS-CoV-2 based on RT-PCR incidence data was 2.56 (95% CI 2.52-2.60) for Covid-19 cases and 2.03 (95% CI 1.96-2.10) for Covid-19-related deaths. However, because the number of RT-PCR tests increased by a growth factor of 1.381 during the same period, these R0 values must be corrected accordingly (R0corrected = R0uncorrected/1.381), yielding 1.86 for Covid-19 cases and 1.47 for Covid-19 deaths. The R0 value based on excess deaths was calculated to be 1.34 (95% CI 1.32-1.37). A sine-function-based adjustment for seasonal effects of 40% corresponds to a maximum value of R0January = 1.68 and a minimum value of R0July = 1.01. Our calculations show an R0 that is much lower than previously thought. This relatively low range of R0 fits very well with the observed seasonal pattern of infection across Europe in 2020 and 2021, including the emergence of more contagious escape variants such as delta or omicron. In general, our study shows that excess mortality can be used as a reliable surrogate to determine the R0 in pandemic situations.

A systems-biology model of the tumor necrosis factor (TNF) interactions with TNF receptor 1 and 2.

MOTIVATION: Clustering enables TNF receptors to stimulate intracellular signaling. The differential soluble ligand-induced clustering behavior of TNF receptor 1 (TNFR1) and TNFR2 was modeled. A structured, rule-based model implemented ligand-independent pre-ligand binding assembly domain (PLAD)-mediated homotypic low affinity interactions of unliganded and liganded TNF receptors. RESULTS: Soluble TNF initiates TNFR1 signaling but not TNFR2 signaling despite receptor binding unless it is secondarily oligomerized. We consider high affinity binding of TNF to signaling-incompetent pre-assembled dimeric TNFR1 and TNFR2 molecules and secondary clustering of liganded dimers to signaling competent ligand-receptor clusters. Published receptor numbers, affinities and measured different activities of clustered receptors validated model simulations for a large range of receptor and ligand concentrations. Different PLAD-PLAD affinities and different activities of receptor clusters explain the observed differences in the TNF receptor stimulating activities of soluble TNF. AVAILABILITY AND IMPLEMENTATION: All scripts and data are in manuscript and supplement at Bioinformatics online. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.