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.

Antibody Mediated Intercommunication of Germinal Centers.

Antibody diversification and selection of B cells occur in dynamic structures called germinal centers (GCs). Passively administered soluble antibodies regulate the GC response by masking the antigen displayed on follicular dendritic cells (FDCs). This suggests that GCs might intercommunicate via naturally produced soluble antibodies, but the role of such GC-GC interactions is unknown. In this study, we performed in silico simulations of interacting GCs and predicted that intense interactions by soluble antibodies limit the magnitude and lifetime of GC responses. With asynchronous GC onset, we observed a higher inhibition of late formed GCs compared to early ones. We also predicted that GC-GC interactions can lead to a bias in the epitope recognition even in the presence of equally dominant epitopes due to differences in founder cell composition or initiation timing of GCs. We show that there exists an optimal range for GC-GC interaction strength that facilitates the affinity maturation towards an incoming antigenic variant during an ongoing GC reaction. These findings suggest that GC-GC interactions might be a contributing factor to the unexplained variability seen among individual GCs and a critical factor in the modulation of GC response to antigenic variants during viral infections.

Investigating the Mechanism of Germinal Center Shutdown.

Germinal centers (GCs) are transient structures where affinity maturation of B cells gives rise to high affinity plasma and memory cells. The mechanism of GC shutdown is unclear, despite being an important phenomenon maintaining immune homeostasis. In this study, we used a mathematical model to identify mechanisms that can independently promote contraction of GCs leading to shutdown. We show that GC shutdown can be promoted by antigen consumption by B cells, antigen masking by soluble antibodies, alterations in follicular dendritic cell (FDC) network area, modulation of immune complex cycling rate constants, alterations in T follicular helper signaling, increased terminal differentiation and reduced B cell division capacity. Proposed mechanisms promoted GC contraction by ultimately decreasing the number of B cell divisions and recycling cells. Based on the in-silico predictions, we suggest a combination of experiments that can be potentially employed by future studies to unravel the mechanistic basis of GC shutdown such as measurements of the density of pMHC presentation of B cells, FDC network size per B cell, fraction of cells expressing differentiation markers. We also show that the identified mechanisms differentially affect the efficiency of GC reaction estimated based on the quantity and quality of resulting antibodies.

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.

In Silico Analysis of the Longevity and Timeline of Individual Germinal Center Reactions in a Primary Immune Response.

Germinal centers (GCs) are transient structures in the secondary lymphoid organs, where B cells undergo affinity maturation to produce high affinity memory and plasma cells. The lifetime of GC responses is a critical factor limiting the extent of affinity maturation and efficiency of antibody responses. While the average lifetime of overall GC reactions in a lymphoid organ is determined experimentally, the lifetime of individual GCs has not been monitored due to technical difficulties in longitudinal analysis. In silico analysis of the contraction phase of GC responses towards primary immunization with sheep red blood cells suggested that if individual GCs had similar lifetimes, the data would be consistent only when new GCs were formed until a very late phase after immunization. Alternatively, there could be a large variation in the lifetime of individual GCs suggesting that both long and short-lived GCs might exist in the same lymphoid organ. Simulations predicted that such differences in the lifetime of GCs could arise due to variations in antigen availability and founder cell composition. These findings identify the potential factors limiting GC lifetime and contribute to an understanding of overall GC responses from the perspective of individual GCs in a primary immune response.

Germinal Centre Shutdown.

Germinal Centres (GCs) are transient structures in secondary lymphoid organs, where affinity maturation of B cells takes place following an infection. While GCs are responsible for protective antibody responses, dysregulated GC reactions are associated with autoimmune disease and B cell lymphoma. Typically, 'normal' GCs persist for a limited period of time and eventually undergo shutdown. In this review, we focus on an important but unanswered question - what causes the natural termination of the GC reaction? In murine experiments, lack of antigen, absence or constitutive T cell help leads to premature termination of the GC reaction. Consequently, our present understanding is limited to the idea that GCs are terminated due to a decrease in antigen access or changes in the nature of T cell help. However, there is no direct evidence on which biological signals are primarily responsible for natural termination of GCs and a mechanistic understanding is clearly lacking. We discuss the present understanding of the GC shutdown, from factors impacting GC dynamics to changes in cellular interactions/dynamics during the GC lifetime. We also address potential missing links and remaining questions in GC biology, to facilitate further studies to promote a better understanding of GC shutdown in infection and immune dysregulation.

Rate of Immune Complex Cycling in Follicular Dendritic Cells Determines the Extent of Protecting Antigen Integrity and Availability to Germinal Center B Cells.

Follicular dendritic cells (FDCs) retain immune complexes (ICs) for prolonged time periods and are important for germinal center (GC) reactions. ICs undergo periodic cycling in FDCs, a mechanism supporting an extended half-life of Ag. Based on experimental data, we estimated that the average residence time of PE-ICs on FDC surface and interior were 21 and 36 min, respectively. GC simulations show that Ag cycling might impact GC dynamics because of redistribution of Ag on the FDC surface and by protecting Ag from degradation. Ag protection and influence on GC dynamics varied with Ag cycling time and total Ag concentration. Simulations predict that blocking Ag cycling terminates the GC reaction and decreases plasma cell production. Considering that cycling of Ag could be a target for the modulation of GC reactions, our findings highlight the importance of understanding the mechanism and regulation of IC cycling in FDCs.

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.

Naive- and Memory-like CD21low B Cell Subsets Share Core Phenotypic and Signaling Characteristics in Systemic Autoimmune Disorders.

An expansion of CD21low B cells has been described in a variety of diseases associated with persistent immune stimulation as in chronic infection, immunodeficiency, or autoimmunity. Different developmental stages of CD21low B cells have been highlighted in specific diseases; however, a systematic comparison of distribution, phenotype, and signaling capacity of these populations has not yet been performed to delineate the pivotal character of this unusual B cell population. Screening of more than 200 patients with autoimmune disease demonstrated that the prevalence of patients with expanded CD21low B cells varies between diseases. The expansion was frequent in patients with systemic lupus erythematosus, in which it correlated to relative B cell lymphopenia and duration of disease. Different proportions of distinct developmental stages of CD21low B cells co-occur in nearly all patients with autoimmune disease. Although in most patients, naive-like and CD27- switched memory B cells were the most prominent CD21low subpopulations, there was no detectable association of the pattern with the underlying disease. Despite their distinct developmental stage, all CD21low B cells share a common core phenotype including the increased expression of inhibitory receptors, associated with an elevated constitutive phosphorylation of proximal signaling molecules downstream of the BCR but impaired Ca2+ mobilization and NF-κB activation after BCR stimulation. Further, this was accompanied by impaired upregulation of CD69, although CD86 upregulation was preserved. Beyond maturation-associated differences, the common core characteristics of all CD21low B cell populations suggests either a common ancestry or a shared sustained imprint by the environment they originated in.

Synchronous Germinal Center Onset Impacts the Efficiency of Antibody Responses.

The germinal center reaction is an important target for modulating antibody responses. Antibody production from germinal centers is regulated by a negative feedback mechanism termed antibody feedback. By imposing antibody feedback, germinal centers can interact and regulate the output of other germinal centers. Using an agent-based model of the germinal center reaction, we studied the impact of antibody feedback on kinetics and efficiency of a germinal center. Our simulations predict that high feedback of antibodies from germinal centers reduces the production of plasma cells and subsequently the efficiency of the germinal center reaction by promoting earlier termination. Affinity maturation is only weakly improved by increased antibody feedback and ultimately interrupted because of premature termination of the reaction. The model predicts that the asynchronous onset and changes in number of germinal centers could alter the efficiency of antibody response due to changes in feedback by soluble antibodies. Consequently, late initialized germinal centers have a compromised output due to higher antibody feedback from the germinal centers formed earlier. The results demonstrate potential effects of germinal center intercommunication and highlight the importance of understanding germinal center interactions for optimizing the antibody response, in particular, in the elderly and in the context of vaccination.

Class-Switch Recombination Occurs Infrequently in Germinal Centers.

Class-switch recombination (CSR) is a DNA recombination process that replaces the immunoglobulin (Ig) constant region for the isotype that can best protect against the pathogen. Dysregulation of CSR can cause self-reactive BCRs and B cell lymphomas; understanding the timing and location of CSR is therefore important. Although CSR commences upon T cell priming, it is generally considered a hallmark of germinal centers (GCs). Here, we have used multiple approaches to show that CSR is triggered prior to differentiation into GC B cells or plasmablasts and is greatly diminished in GCs. Despite finding a small percentage of GC B cells expressing germline transcripts, phylogenetic trees of GC BCRs from secondary lymphoid organs revealed that the vast majority of CSR events occurred prior to the onset of somatic hypermutation. As such, we have demonstrated the existence of IgM-dominated GCs, which are unlikely to occur under the assumption of ongoing switching.

Computer Simulation of Multi-Color Brainbow Staining and Clonal Evolution of B Cells in Germinal Centers.

Clonal evolution of B cells in germinal centers (GCs) is central to affinity maturation of antibodies in response to pathogens. Permanent or tamoxifen-induced multi-color recombination of B cells based on the brainbow allele allows monitoring the degree of color dominance in the course of the GC reaction. Here, we use computer simulations of GC reactions in order to replicate the evolution of color dominance in silico and to define rules for the interpretation of these data in terms of clonal dominance. We find that a large diversity of clonal dominance is generated in simulated GCs in agreement with experimental results. In the extremes, a GC can be dominated by a single clone or can harbor many co-existing clones. These properties can be directly derived from the measurement of color dominance when all B cells are stained before the GC onset. Upon tamoxifen-induced staining, the correlation between clonal structure and color dominance depends on the timing and duration of the staining procedure as well as on the total number of stained B cells. B cells can be stained with 4 colors if a single brainbow allele is used, using both alleles leads to 10 different colors. The advantage of staining with 10 instead of 4 colors becomes relevant only when the 10 colors are attributed with rather similar probability. Otherwise, 4 colors exhibit a comparable predictive power. These results can serve as a guideline for future experiments based on multi-color staining of evolving systems.

How to Simulate a Germinal Center.

Germinal centers host a mini-evolutionary environment where B cells can mutate their receptor and be selected depending on its affinity to target antigens in a process called affinity maturation. Starting from founder cells with a weak B cell receptor affinity, germinal centers release output cells as antibody-secreting cells or memory cells with a very high affinity, a property which is essential for pathogen clearance and immune memory. Therapeutic interventions on the germinal centers are tantalizing approaches to improve vaccines or to support rejection of chronic pathogens such as HIV. However, the complexity of the selection processes makes it very hard to make reliable predictions. Here, we present in detail how to build an agent-based model (hyphasma), accounting for the dynamics of the germinal center. It encompasses the core quantitative traits of affinity maturation, and allowed to make reliable predictions in previous studies.

Functional modules of sigma factor regulons guarantee adaptability and evolvability.

The focus of modern molecular biology turns from assigning functions to individual genes towards understanding the expression and regulation of complex sets of molecules. Here, we provide evidence that alternative sigma factor regulons in the pathogen Pseudomonas aeruginosa largely represent insulated functional modules which provide a critical level of biological organization involved in general adaptation and survival processes. Analysis of the operational state of the sigma factor network revealed that transcription factors functionally couple the sigma factor regulons and significantly modulate the transcription levels in the face of challenging environments. The threshold quality of newly evolved transcription factors was reached faster and more robustly in in silico testing when the structural organization of sigma factor networks was taken into account. These results indicate that the modular structures of alternative sigma factor regulons provide P. aeruginosa with a robust framework to function adequately in its environment and at the same time facilitate evolutionary change. Our data support the view that widespread modularity guarantees robustness of biological networks and is a key driver of evolvability.

Implications of Intravital Imaging of Murine Germinal Centers on the Control of B Cell Selection and Division.

Intravital imaging of antibody optimization in germinal center (GC) reactions has set a new dimension in the understanding of the humoral immune response during the last decade. The inclusion of spatio-temporal cellular dynamics in the research on GCs required analysis using the agent-based mathematical models. In this study, we integrate the available intravital imaging data from various research groups and incorporate these into a quantitative mathematical model of GC reactions and antibody affinity maturation. Interestingly, the integration of data concerning the spatial organization of GCs and B cell motility allows to draw conclusions on the strength of the selection pressure and the control of B cell division by T follicular helper cells.

Ebola virus infection modeling and identifiability problems.

The recent outbreaks of Ebola virus (EBOV) infections have underlined the impact of the virus as a major threat for human health. Due to the high biosafety classification of EBOV (level 4), basic research is very limited. Therefore, the development of new avenues of thinking to advance quantitative comprehension of the virus and its interaction with the host cells is urgently needed to tackle this lethal disease. Mathematical modeling of the EBOV dynamics can be instrumental to interpret Ebola infection kinetics on quantitative grounds. To the best of our knowledge, a mathematical modeling approach to unravel the interaction between EBOV and the host cells is still missing. In this paper, a mathematical model based on differential equations is used to represent the basic interactions between EBOV and wild-type Vero cells in vitro. Parameter sets that represent infectivity of pathogens are estimated for EBOV infection and compared with influenza virus infection kinetics. The average infecting time of wild-type Vero cells by EBOV is slower than in influenza infection. Simulation results suggest that the slow infecting time of EBOV could be compensated by its efficient replication. This study reveals several identifiability problems and what kind of experiments are necessary to advance the quantification of EBOV infection. A first mathematical approach of EBOV dynamics and the estimation of standard parameters in viral infections kinetics is the key contribution of this work, paving the way for future modeling works on EBOV infection.

Effects of aging on influenza virus infection dynamics.

UNLABELLED: The consequences of influenza virus infection are generally more severe in individuals over 65 years of age (the elderly). Immunosenescence enhances the susceptibility to viral infections and renders vaccination less effective. Understanding age-related changes in the immune system is crucial in order to design prophylactic and immunomodulatory strategies to reduce morbidity and mortality in the elderly. Here, we propose different mathematical models to provide a quantitative understanding of the immune strategies in the course of influenza virus infection using experimental data from young and aged mice. Simulation results suggested a central role of CD8(+) T cells for adequate viral clearance kinetics in young and aged mice. Adding the removal of infected cells by natural killer cells did not improve the model fit in either young or aged animals. We separately examined the infection-resistant state of cells promoted by the cytokines alpha/beta interferon (IFN-α/ß), IFN-γ, and tumor necrosis factor alpha (TNF-α). The combination of activated CD8(+) T cells with any of the cytokines provided the best fits in young and aged animals. During the first 3 days after infection, the basic reproductive number for aged mice was 1.5-fold lower than that for young mice (P < 0.05). IMPORTANCE: The fits of our models to the experimental data suggest that the increased levels of IFN-α/ß, IFN-γ, and TNF-α (the "inflammaging" state) promote slower viral growth in aged mice, which consequently limits the stimulation of immune cells and contributes to the reported impaired responses in the elderly. A quantitative understanding of influenza virus pathogenesis and its shift in the elderly is the key contribution of this work.

Population Dynamics of Borrelia burgdorferi in Lyme Disease.

Many chronic inflammatory diseases are known to be caused by persistent bacterial or viral infections. A well-studied example is the tick-borne infection by the gram-negative spirochaetes of the genus Borrelia in humans and other mammals, causing severe symptoms of chronic inflammation and subsequent tissue damage (Lyme Disease), particularly in large joints and the central nervous system, but also in the heart and other tissues of untreated patients. Although killed efficiently by human phagocytic cells in vitro, Borrelia exhibits a remarkably high infectivity in mice and men. In experimentally infected mice, the first immune response almost clears the infection. However, approximately 1 week post infection, the bacterial population recovers and reaches an even larger size before entering the chronic phase. We developed a mathematical model describing the bacterial growth and the immune response against Borrelia burgdorferi in the C3H mouse strain that has been established as an experimental model for Lyme disease. The peculiar dynamics of the infection exclude two possible mechanistic explanations for the regrowth of the almost cleared bacteria. Neither the hypothesis of bacterial dissemination to different tissues nor a limitation of phagocytic capacity were compatible with experiment. The mathematical model predicts that Borrelia recovers from the strong initial immune response by the regrowth of an immune-resistant sub-population of the bacteria. The chronic phase appears as an equilibration of bacterial growth and adaptive immunity. This result has major implications for the development of the chronic phase of Borrelia infections as well as on potential protective clinical interventions.