Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany.

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.

Suppressive might of a few: T follicular regulatory cells impede auto-reactivity despite being outnumbered in the germinal centres.

The selection of high-affinity B cells and the production of high-affinity antibodies are mediated by T follicular helper cells (Tfhs) within germinal centres (GCs). Therein, somatic hypermutation and selection enhance B cell affinity but risk the emergence of self-reactive B cell clones. Despite being outnumbered compared to their helper counterpart, the ablation of T follicular regulatory cells (Tfrs) results in enhanced dissemination of self-reactive antibody-secreting cells (ASCs). The specific mechanisms by which Tfrs exert their regulatory action on self-reactive B cells are largely unknown. We developed computer simulations to investigate how Tfrs regulate either selection or differentiation of B cells to prevent auto-reactivity. We observed that Tfr-induced apoptosis of self-reactive B cells during the selection phase impedes self-reactivity with physiological Tfr numbers, especially when Tfrs can access centrocyte-enriched GC areas. While this aided in selecting non-self-reactive B cells by restraining competition, higher Tfr numbers distracted non-self-reactive B cells from receiving survival signals from Tfhs. Thus, the location and number of Tfrs must be regulated to circumvent such Tfr distraction and avoid disrupting GC evolution. In contrast, when Tfrs regulate differentiation of selected centrocytes by promoting recycling to the dark zone phenotype of self-reactive GC resident pre-plasma cells (GCPCs), higher Tfr numbers were required to impede the circulation of self-reactive ASCs (s-ASCs). On the other hand, Tfr-engagement with GCPCs and subsequent apoptosis of s-ASCs can control self-reactivity with low Tfr numbers, but does not confer selection advantage to non-self-reactive B cells. The simulations predict that to restrict auto-reactivity, natural redemption of self-reactive B cells is insufficient and that Tfrs should increase the mutation probability of self-reactive B cells.

Apoptotic cell fragments locally activate tingible body macrophages in the germinal center.

Germinal centers (GCs) that form within lymphoid follicles during antibody responses are sites of massive cell death. Tingible body macrophages (TBMs) are tasked with apoptotic cell clearance to prevent secondary necrosis and autoimmune activation by intracellular self antigens. We show by multiple redundant and complementary methods that TBMs derive from a lymph node-resident, CD169-lineage, CSF1R-blockade-resistant precursor that is prepositioned in the follicle. Non-migratory TBMs use cytoplasmic processes to chase and capture migrating dead cell fragments using a "lazy" search strategy. Follicular macrophages activated by the presence of nearby apoptotic cells can mature into TBMs in the absence of GCs. Single-cell transcriptomics identified a TBM cell cluster in immunized lymph nodes which upregulated genes involved in apoptotic cell clearance. Thus, apoptotic B cells in early GCs trigger activation and maturation of follicular macrophages into classical TBMs to clear apoptotic debris and prevent antibody-mediated autoimmune diseases.

Amount of antigen, T follicular helper cells and affinity of founder cells shape the diversity of germinal center B cells: A computational study.

A variety of B cell clones seed the germinal centers, where a selection stringency expands the fitter clones to generate higher affinity antibodies. However, recent experiments suggest that germinal centers often retain a diverse set of B cell clones with a range of affinities and concurrently carry out affinity maturation. Amid a tendency to flourish germinal centers with fitter clones, how several B cell clones with differing affinities can be concurrently selected remains poorly understood. Such a permissive selection may allow non-immunodominant clones, which are often rare and of low-affinity, to somatically hypermutate and result in a broad and diverse B cell response. How the constituent elements of germinal centers, their quantity and kinetics may modulate diversity of B cells, has not been addressed well. By implementing a state-of-the-art agent-based model of germinal center, here, we study how these factors impact temporal evolution of B cell clonal diversity and its underlying balance with affinity maturation. While we find that the extent of selection stringency dictates clonal dominance, limited antigen availability on follicular dendritic cells is shown to expedite the loss of diversity of B cells as germinal centers mature. Intriguingly, the emergence of a diverse set of germinal center B cells depends on high affinity founder cells. Our analysis also reveals a substantial number of T follicular helper cells to be essential in balancing affinity maturation with clonal diversity, as a low number of T follicular helper cells impedes affinity maturation and also contracts the scope for a diverse B cell response. Our results have implications for eliciting antibody responses to non-immunodominant specificities of the pathogens by controlling the regulators of the germinal center reaction, thereby pivoting a way for vaccine development to generate broadly protective antibodies.

The common interests of health protection and the economy: evidence from scenario calculations of COVID-19 containment policies.

We develop a novel approach integrating epidemiological and economic models that allows data-based simulations during a pandemic. We examine the economically optimal opening strategy that can be reconciled with the containment of a pandemic. The empirical evidence is based on data from Germany during the SARS-CoV-2 pandemic. Our empirical findings reject the view that there is necessarily a conflict between health protection and economic interests and suggest a non-linear U-shape relationship: it is in the interest of public health and the economy to balance non-pharmaceutical interventions in a manner that further reduces the incidence of infections. Our simulations suggest that a prudent strategy that leads to a reproduction number of around 0.75 is economically optimal. Too restrictive policies cause massive economic costs. Conversely, policies that are too loose lead to higher death tolls and higher economic costs in the long run. We suggest this finding as a guide for policy-makers in balancing interests of public health and the economy during a pandemic.

Testing and isolation to prevent overloaded healthcare facilities and reduce death rates in the SARS-CoV-2 pandemic in Italy.

Background: During the first wave of COVID-19, hospital and intensive care unit beds got overwhelmed in Italy leading to an increased death burden. Based on data from Italian regions, we disentangled the impact of various factors contributing to the bottleneck situation of healthcare facilities, not well addressed in classical SEIR-like models. A particular emphasis was set on the undetected fraction (dark figure), on the dynamically changing hospital capacity, and on different testing, contact tracing, quarantine strategies. Methods: We first estimated the dark figure for different Italian regions. Using parameter estimates from literature and, alternatively, with parameters derived from a fit to the initial phase of COVID-19 spread, the model was optimized to fit data (infected, hospitalized, ICU, dead) published by the Italian Civil Protection. Results: We show that testing influenced the infection dynamics by isolation of newly detected cases and subsequent interruption of infection chains. The time-varying reproduction number (R t) in high testing regions decreased to <1 earlier compared to the low testing regions. While an early test and isolate (TI) scenario resulted in up to ~31% peak reduction of hospital occupancy, the late TI scenario resulted in an overwhelmed healthcare system. Conclusions: An early TI strategy would have decreased the overall hospital usage drastically and, hence, death toll (∼34% reduction in Lombardia) and could have mitigated the lack of healthcare facilities in the course of the pandemic, but it would not have kept the hospitalization amount within the pre-pandemic hospital limit.

High SARS-CoV-2 seroprevalence in children and adults in the Austrian ski resort of Ischgl.

BACKGROUND: In early March 2020, a SARS-CoV-2 outbreak in the ski resort Ischgl in Austria initiated the spread of SARS-CoV-2 throughout Austria and Northern Europe. METHODS: Between April 21st and 27th 2020, a cross-sectional epidemiologic study targeting the full population of Ischgl (n = 1867), of which 79% could be included (n = 1473, incl. 214 children), was performed. For each individual, the study involved a SARS-CoV-2 PCR, antibody testing and structured questionnaires. A mathematical model was used to help understand the influence of the determined seroprevalence on virus transmission. RESULTS: The seroprevalence was 42.4% (95% confidence interval (CI) 39.8-44.7). Individuals under 18 showed a significantly lower seroprevalence of 27.1% (95% CI 21.3-33.6) than adults (45%; 95% CI 42.2-47.7; OR of 0.455, 95% CI 0.356-0.682, p < 0.001). Of the seropositive individuals, 83.7% had not been diagnosed to have had SARS-CoV-2 infection previously. The clinical course was generally mild. Over the previous two months, two COVID-19-related deaths had been recorded, corresponding to an infection fatality rate of 0.25% (95% CI 0.03-0.91). Only 8 (0.5 %) individuals were newly diagnosed to be infected with SARS-CoV-2 during this study. CONCLUSIONS: Ischgl was hit early and hard by SARS-CoV-2 leading to a high local seroprevalence of 42.4%, which was lower in individuals below the age of 18 than in adults. Mathematical modeling suggests that a drastic decline of newly infected individuals in Ischgl by the end of April occurred due to the dual impact from the non-pharmacological interventions and a high immunization of the Ischgl population.

Assessment of effective mitigation and prediction of the spread of SARS-CoV-2 in Germany using demographic information and spatial resolution.

Non-pharmaceutical interventions (NPIs) are important to mitigate the spread of infectious diseases as long as no vaccination or outstanding medical treatments are available. We assess the effectiveness of the sets of non-pharmaceutical interventions that were in place during the course of the Coronavirus disease 2019 (Covid-19) pandemic in Germany. Our results are based on hybrid models, combining SIR-type models on local scales with spatial resolution. In order to account for the age-dependence of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), we include realistic prepandemic and recently recorded contact patterns between age groups. The implementation of non-pharmaceutical interventions will occur on changed contact patterns, improved isolation, or reduced infectiousness when, e.g., wearing masks. In order to account for spatial heterogeneity, we use a graph approach and we include high-quality information on commuting activities combined with traveling information from social networks. The remaining uncertainty will be accounted for by a large number of randomized simulation runs. Based on the derived factors for the effectiveness of different non-pharmaceutical interventions over the past months, we provide different forecast scenarios for the upcoming time.

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

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.

Mathematical Model Shows How Sleep May Affect Amyloid-ß Fibrillization.

Deposition of amyloid-ß (Aß) fibers in the extracellular matrix of the brain is a ubiquitous feature associated with several neurodegenerative disorders, especially Alzheimer's disease (AD). Although many of the biological aspects that contribute to the formation of Aß plaques are well addressed at the intra- and intercellular levels in short timescales, an understanding of how Aß fibrillization usually starts to dominate at a longer timescale despite the presence of mechanisms dedicated to Aß clearance is still lacking. Furthermore, no existing mathematical model integrates the impact of diurnal neural activity as emanated from circadian regulation to predict disease progression due to a disruption in the sleep-wake cycle. In this study, we develop a minimal model of Aß fibrillization to investigate the onset of AD over a long timescale. Our results suggest that the diseased state is a manifestation of a phase change of the system from soluble Aß (sAß) to fibrillar Aß (fAß) domination upon surpassing a threshold in the production rate of sAß. By incorporating the circadian rhythm into our model, we reveal that fAß accumulation is crucially dependent on the regulation of the sleep-wake cycle, thereby indicating the importance of good sleep hygiene in averting AD onset. We also discuss potential intervention schemes to reduce fAß accumulation in the brain by modification of the critical sAß production rate.

Emergent memory in cell signaling: Persistent adaptive dynamics in cascades can arise from the diversity of relaxation time-scales.

The mitogen-activated protein kinase (MAPK) signaling cascade, an evolutionarily conserved motif present in all eukaryotic cells, is involved in coordinating crucial cellular functions. While the asymptotic dynamical behavior of the pathway stimulated by a time-invariant signal is relatively well-understood, we show using a computational model that it exhibits a rich repertoire of transient adaptive responses to changes in stimuli. When the signal is switched on, the response is characterized by long-lived modulations in frequency as well as amplitude. On withdrawing the stimulus, the activity decays over long timescales, exhibiting reverberations characterized by repeated spiking in the activated MAPK concentration. The long-term persistence of such post-stimulus activity suggests that the cascade retains memory of the signal for a significant duration following its removal. The molecular mechanism underlying the reverberatory activity is related to the existence of distinct relaxation rates for the different cascade components. This results in the imbalance of fluxes between different layers of the cascade, with the reuse of activated kinases as enzymes when they are released from sequestration in complexes. The persistent adaptive response, indicative of a cellular "short-term" memory, suggests that this ubiquitous signaling pathway plays an even more central role in information processing by eukaryotic cells.