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The novel coronavirus (SARS-CoV-2), identified in China at the end of December 2019 and causing the disease COVID-19, has meanwhile led to outbreaks all over the globe with about 2.2 million confirmed cases and more than 150,000 deaths as of April 17, 2020 [37]. In view of most recent information on testing activity [32], we present here an update of our initial work [4]. In this work, mathematical models have been developed to study the spread of COVID-19 among the population in Germany and to asses the impact of non-pharmaceutical interventions. Systems of differential equations of SEIR type are extended here to account for undetected infections, as well as for stages of infections and age groups. The models are calibrated on data until April 5, data from April 6 to 14 are used for model validation. We simulate different possible strategies for the mitigation of the current outbreak, slowing down the spread of the virus and thus reducing the peak in daily diagnosed cases, the demand for hospitalization or intensive care units admissions, and eventually the number of fatalities. Our results suggest that a partial (and gradual) lifting of introduced control measures could soon be possible if accompanied by further increased testing activity, strict isolation of detected cases and reduced contact to risk groups.
Stabilization exercise (SE) is evident for the management of chronic non-specific low back pain (LBP). The optimal dose-response-relationship for the utmost treatment success is, thus, still unknown. The purpose is to systematically review the dose-response-relationship of stabilisation exercises on pain and disability in patients with chronic non-specific LBP. A systematic review with meta-regression was conducted (Pubmed, Web of Knowledge, Cochrane). Eligibility criteria were RCTs on patients with chronic non-specific LBP, written in English/German and adopting a longitudinal core-specific/stabilising/motor control exercise intervention with at least one outcome for pain intensity and/or disability. Meta-regressions (dependent variable = effect sizes (Cohens d) of the interventions (for pain and for disability), independent variable = training characteristics (duration, frequency, time per session)), and controlled for (low) study quality (PEDro) and (low) sample sizes (n) were conducted to reveal the optimal dose required for therapy success. From the 3,415 studies initially selected, 50 studies (n = 2,786 LBP patients) were included. N = 1,239 patients received SE. Training duration was 7.0 ± 3.3 weeks, training frequency was 3.1 ± 1.8 sessions per week with a mean training time of 44.6 ± 18.0 min per session. The meta-regressions’ mean effect size was d = 1.80 (pain) and d = 1.70 (disability). Total R2 was 0.445 and 0.17. Moderate quality evidence (R2 = 0.231) revealed that a training duration of 20 to 30 min elicited the largest effect (both in pain and disability, logarithmic association). Low quality evidence (R2 = 0.125) revealed that training 3 to 5 times per week led to the largest effect of SE in patients with chronic non-specific LBP (inverted U-shaped association). In patients with non-specific chronic LBP, stabilization exercise with a training frequency of 3 to 5 times per week (Grade C) and a training time of 20 to 30 min per session (Grade A) elicited the largest effect on pain and disability.
In this paper we present a new approach to deterministic modelling of COVID-19 epidemic. Our model dynamics is expressed by a single prognostic variable which satisfies an integro-differential equation. All unknown parameters are described with a single, time-dependent variable R(t). We show that our model has similarities to classic compartmental models, such as SIR, and that the variable R(t) can be interpreted as a generalized effective reproduction number. The advantages of our approach are the simplicity of having only one equation, the numerical stability due to an integral formulation and the reliability since the model is formulated in terms of the most trustable statistical data variable: the number of cumulative diagnosed positive cases of COVID-19. Once this dynamic variable is calculated, other non-dynamic variables, such as the number of heavy cases (hospital beds), the number of intensive-care cases (ICUs) and the fatalities, can be derived from it using a similarly stable, integral approach. The formulation with a single equation allows us to calculate from real data the values of the sample effective reproduction number, which can then be fitted. Extrapolated values of R(t) can be used in the model to make reliable forecasts, though under the assumption that measures for reducing infections are maintained. We have applied our model to more than 15 countries and the ongoing results are available on a web-based platform [1]. In this paper, we focus on the data for two exemplary countries, Italy and Germany, and show that the model is capable of reproducing the course of the epidemic in the past and forecasting its course for a period of four to five weeks with a reasonable numerical stability.
Airborne transmission of SARS-CoV-2 through virus-containing aerosol particles has been established as an important pathway for Covid-19 infection. Suitable measures to prevent such infections are imperative, especially in situations when a high number of persons convene in closed rooms. Here we tested the efficiency and practicability of operating four air purifiers equipped with HEPA filters in a high school classroom while regular classes were taking place. We monitored the aerosol number concentration for particles > 3 nm at two locations in the room, the aerosol size distribution in the range from 10 nm to 10 µm, PM10 and CO2 concentration. For comparison, we performed similar measurements in a neighboring classroom without purifiers. In times when classes were conducted with windows and door closed, the aerosol concentration was reduced by more than 90 % within less than 30 minutes when running the purifiers (air exchange rate 5.5 h-1). The reduction was homogeneous throughout the room and for all particle sizes. The measurements are supplemented by a calculation estimating the maximum concentration levels of virus-containing aerosol from a highly contagious person speaking in a closed room with and without air purifiers. Measurements and calculation demonstrate that air purifiers potentially represent a well-suited measure to reduce the risks of airborne transmission of SARS-CoV-2 substantially. Staying for two hours in a closed room with a highly infective person, we estimate that the inhaled dose is reduced by a factor of six when using air purifiers with a total air exchange rate of 5.7 h-1.
The development of binocular vision is an active learning process comprising the development of disparity tuned neurons in visual cortex and the establishment of precise vergence control of the eyes. We present a computational model for the learning and self-calibration of active binocular vision based on the Active Efficient Coding framework, an extension of classic efficient coding ideas to active perception. Under normal rearing conditions, the model develops disparity tuned neurons and precise vergence control, allowing it to correctly interpret random dot stereogramms. Under altered rearing conditions modeled after neurophysiological experiments, the model qualitatively reproduces key experimental findings on changes in binocularity and disparity tuning. Furthermore, the model makes testable predictions regarding how altered rearing conditions impede the learning of precise vergence control. Finally, the model predicts a surprising new effect that impaired vergence control affects the statistics of orientation tuning in visual cortical neurons.
The spike protein (S) of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is required for cell entry and is the primary focus for vaccine development. In this study, we combined cryo–electron tomography, subtomogram averaging, and molecular dynamics simulations to structurally analyze S in situ. Compared with the recombinant S, the viral S was more heavily glycosylated and occurred mostly in the closed prefusion conformation. We show that the stalk domain of S contains three hinges, giving the head unexpected orientational freedom. We propose that the hinges allow S to scan the host cell surface, shielded from antibodies by an extensive glycan coat. The structure of native S contributes to our understanding of SARS-CoV-2 infection and potentially to the development of safe vaccines.
The spike (S) protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is required for cell entry and is the major focus for vaccine development. We combine cryo electron tomography, subtomogram averaging and molecular dynamics simulations to structurally analyze S in situ. Compared to recombinant S, the viral S is more heavily glycosylated and occurs predominantly in a closed pre-fusion conformation. We show that the stalk domain of S contains three hinges that give the globular domain unexpected orientational freedom. We propose that the hinges allow S to scan the host cell surface, shielded from antibodies by an extensive glycan coat. The structure of native S contributes to our understanding of SARS-CoV-2 infection and the development of safe vaccines. The large scale tomography data set of SARS-CoV-2 used for this study is therefore sufficient to resolve structural features to below 5 Ångstrom, and is publicly available at EMPIAR-10453.
The auditory midbrain (inferior colliculus, IC) plays an important role in sound processing, acting as hub for acoustic information extraction and for the implementation of fast audio-motor behaviors. IC neurons are topographically organized according to their sound frequency preference: dorsal IC regions encode low frequencies while ventral areas respond best to high frequencies, a type of sensory map defined as tonotopy. Tonotopic maps have been studied extensively using artificial stimuli (pure tones) but our knowledge of how these maps represent information about sequences of natural, spectro-temporally rich sounds is sparse. We studied this question by conducting simultaneous extracellular recordings across IC depths in awake bats (Carollia perspicillata) that listened to sequences of natural communication and echolocation sounds. The hypothesis was that information about these two types of sound streams is represented at different IC depths since they exhibit large differences in spectral composition, i.e., echolocation covers the high-frequency portion of the bat soundscape (> 45 kHz), while communication sounds are broadband and carry most power at low frequencies (20–25 kHz). Our results showed that mutual information between neuronal responses and acoustic stimuli, as well as response redundancy in pairs of neurons recorded simultaneously, increase exponentially with IC depth. The latter occurs regardless of the sound type presented to the bats (echolocation or communication). Taken together, our results indicate the existence of mutual information and redundancy maps at the midbrain level whose response cannot be predicted based on the frequency composition of natural sounds and classic neuronal tuning curves.
Neural oscillations are at the core of important computations in the mammalian brain. Interactions between oscillatory activities in different frequency bands, such as delta (1-4 Hz), theta (4-8 Hz), or gamma (>30 Hz), are a powerful mechanism for binding fundamentally distinct spatiotemporal scales of neural processing. Phase-amplitude coupling (PAC) is one such plausible and well-described interaction, but much is yet to be uncovered regarding how PAC dynamics contribute to sensory representations. In particular, although PAC appears to have a major role in audition, the characteristics of coupling profiles in sensory and integration (i.e. frontal) cortical areas remain obscure. Here, we address this question by studying PAC dynamics in the frontal-auditory field (FAF; an auditory area in the bat frontal cortex) and the auditory cortex (AC) of the bat Carollia perspicillata. By means of simultaneous electrophysiological recordings in frontal and auditory cortices examining local-field potentials (LFPs), we show that the amplitude of gamma-band activity couples with the phase of low-frequency LFPs in both structures. Our results demonstrate that the coupling in FAF occurs most prominently in delta/high-gamma frequencies (1-4/75-100 Hz), whereas in the AC the coupling is strongest in the theta/low-gamma (2-8/25-55 Hz) range. We argue that distinct PAC profiles may represent different mechanisms for neuronal processing in frontal and auditory cortices, and might complement oscillatory interactions for sensory processing in the frontal-auditory cortex network.
It becomes more and more obvious that deregulation of host metabolism play an important role in SARS-CoV-2 pathogenesis with implication for increased risk of severe course of COVID-19. Furthermore, it is expected that COVID-19 patients recovered from severe disease may experience long-term metabolic disorders. Thereby understanding the consequences of SARS-CoV-2 infection on host metabolism can facilitate efforts for effective treatment option. We have previously shown that SARS-CoV-2-infected cells undergo a shift towards glycolysis and that 2-deoxy-D-glucose (2DG) inhibits SARS-CoV-2 replication. Here, we show that also pentose phosphate pathway (PPP) is remarkably deregulated. Since PPP supplies ribonucleotides for SARS-CoV-2 replication, this could represent an attractive target for an intervention. On that account, we employed the transketolase inhibitor benfooxythiamine and showed dose-dependent inhibition of SARS-CoV-2 in non-toxic concentrations. Importantly, the antiviral efficacy of benfooxythiamine was further increased in combination with 2DG.