Chaos in Opinion-Driven Disease Dynamics.

During the COVID-19 pandemic, it became evident that the effectiveness of applying intervention measures is significantly influenced by societal acceptance, which, in turn, is affected by the processes of opinion formation. This article explores one among the many possibilities of coupled opinion-epidemic systems. The findings reveal either intricate periodic patterns or chaotic dynamics, leading to substantial fluctuations in opinion distribution and, consequently, significant variations in the total number of infections over time. Interestingly, the model exhibits a protective pattern.

The impact of travelling on the COVID-19 infection cases in Germany.

BACKGROUND: COVID-19 continues to disrupt social lives and the economy of many countries and challenges their healthcare capacities. Looking back at the situation in Germany in 2020, the number of cases increased exponentially in early March. Social restrictions were imposed by closing e.g. schools, shops, cafés and restaurants, as well as borders for travellers. This reaped success as the infection rate descended significantly in early April. In mid July, however, the numbers started to rise again. Of particular reasons was that from mid June onwards, the travel ban has widely been cancelled or at least loosened. We aim to measure the impact of travellers on the overall infection dynamics for the case of (relatively) few infectives and no vaccinations available. We also want to analyse under which conditions political travelling measures are relevant, in particular in comparison to local measures. By travel restrictions in our model we mean all possible measures that equally reduce the possibility of infected returnees to further spread the disease in Germany, e.g. travel bans, lockdown, post-arrival tests and quarantines. METHODS: To analyse the impact of travellers, we present three variants of an susceptible-exposed-infected-recovered-deceased model to describe disease dynamics in Germany. Epidemiological parameters such as transmission rate, lethality, and detection rate of infected individuals are incorporated. We compare a model without inclusion of travellers and two models with a rate measuring the impact of travellers incorporating incidence data from the Johns Hopkins University. Parameter estimation was performed with the aid of the Monte-Carlo-based Metropolis algorithm. All models are compared in terms of validity and simplicity. Further, we perform sensitivity analyses of the model to observe on which of the model parameters show the largest influence the results. In particular, we compare local and international travelling measures and identify regions in which one of these shows larger relevance than the other. RESULTS: In the comparison of the three models, both models with the traveller impact rate yield significantly better results than the model without this rate. The model including a piecewise constant travel impact rate yields the best results in the sense of maximal likelihood and minimal Bayesian Information Criterion. We synthesize from model simulations and analyses that travellers had a strong impact on the overall infection cases in the considered time interval. By a comparison of the reproductive ratios of the models under traveller/no-traveller scenarios, we found that higher traveller numbers likely induce higher transmission rates and infection cases even in the further course, which is one possible explanation to the start of the second wave in Germany as of autumn 2020. The sensitivity analyses show that the travelling parameter, among others, shows a larger impact on the results. We also found that the relevance of travel measures depends on the value of the transmission parameter: In domains with a lower transmission parameter, caused either by the current variant or local measures, it is found that handling the travel parameters is more relevant than those with lower value of the transmission. CONCLUSIONS: We conclude that travellers is an important factor in controlling infection cases during pandemics. Depending on the current situation, travel restrictions can be part of a policy to reduce infection numbers, especially when case numbers and transmission rate are low. The results of the sensitivity analyses also show that travel measures are more effective when the local transmission is already reduced, so a combination of those two appears to be optimal. In any case, supervision of the influence of travellers should always be undertaken, as another pandemic or wave can happen in the upcoming years and vaccinations and basic hygiene rules alone might not be able to prevent further infection waves.

Rules of nature's Formula Run: Muscle mechanics during late stance is the key to explaining maximum running speed.

The maximum running speed of legged animals is one evident factor for evolutionary selection-for predators and prey. Therefore, it has been studied across the entire size range of animals, from the smallest mites to the largest elephants, and even beyond to extinct dinosaurs. A recent analysis of the relation between animal mass (size) and maximum running speed showed that there seems to be an optimal range of body masses in which the highest terrestrial running speeds occur. However, the conclusion drawn from that analysis-namely, that maximum speed is limited by the fatigue of white muscle fibres in the acceleration of the body mass to some theoretically possible maximum speed-was based on coarse reasoning on metabolic grounds, which neglected important biomechanical factors and basic muscle-metabolic parameters. Here, we propose a generic biomechanical model to investigate the allometry of the maximum speed of legged running. The model incorporates biomechanically important concepts: the ground reaction force being counteracted by air drag, the leg with its gearing of both a muscle into a leg length change and the muscle into the ground reaction force, as well as the maximum muscle contraction velocity, which includes muscle-tendon dynamics, and the muscle inertia-with all of them scaling with body mass. Put together, these concepts' characteristics and their interactions provide a mechanistic explanation for the allometry of maximum legged running speed. This accompanies the offering of an explanation for the empirically found, overall maximum in speed: In animals bigger than a cheetah or pronghorn, the time that any leg-extending muscle needs to settle, starting from being isometric at about midstance, at the concentric contraction speed required for running at highest speeds becomes too long to be attainable within the time period of a leg moving from midstance to lift-off. Based on our biomechanical model, we, thus, suggest considering the overall speed maximum to indicate muscle inertia being functionally significant in animal locomotion. Furthermore, the model renders possible insights into biological design principles such as differences in the leg concept between cats and spiders, and the relevance of multi-leg (mammals: four, insects: six, spiders: eight) body designs and emerging gaits. Moreover, we expose a completely new consideration regarding the muscles' metabolic energy consumption, both during acceleration to maximum speed and in steady-state locomotion.

The startle reflex in echolocating odontocetes: basic physiology and practical implications.

The acoustic startle reflex is an oligo-synaptic reflex arc elicited by rapid-onset sounds. Odontocetes evolved a range of specific auditory adaptations to aquatic hearing and echolocation, e.g. the ability to downregulate their auditory sensitivity when emitting clicks. However, it remains unclear whether these adaptations also led to changes of the startle reflex. We investigated reactions to startling sounds in two bottlenose dolphins (Tursiops truncatus) and one false killer whale (Pseudorca crassidens). Animals were exposed to 50 ms, 1/3 octave band noise pulses of varying levels at frequencies of 1, 10, 25 and 32 kHz while positioned in a hoop station. Startle responses were quantified by measuring rapid muscle contractions using a three-dimensional accelerometer attached to the dolphin. Startle magnitude increased exponentially with increasing received levels. Startle thresholds were frequency dependent and ranged from 131 dB at 32 kHz to 153 dB at 1 kHz (re. 1 µPa). Startle thresholds only exceeded masked auditory AEP thresholds of the animals by 47 dB but were ∼82 dB above published behavioural audiograms for these species. We also tested the effect of stimulus rise time on startle magnitude using a broadband noise pulse. Startle responses decreased with increasing rise times from 2 to 100 ms. Models suggested that rise times of 141-220 ms were necessary to completely mitigate startle responses. Our data showed that the startle reflex is conserved in odontocetes and follows similar principles as in terrestrial mammals. These principles should be considered when assessing and mitigating the effects of anthropogenic noise on marine mammals.

Effects of impulsive noise on marine mammals: investigating range-dependent risk.

Concerns exist about the impacts of underwater noise on marine mammals. These include auditory damage, which is a significant risk for marine mammals exposed to impulsive sounds such as explosions, pile-driving, and seismic air guns. Currently, impact assessments use different risk criteria for impulsive and non-impulsive sounds (e.g., ships, drilling). However, as impulsive sounds dissipate through the environment, they potentially lose hazardous features (e.g., sudden onset) and become non-impulsive at some distance from the source. Despite management implications, a lack of data on range-dependent characteristics currently limits their inclusion in impact assessments. We address this using acoustic recordings of seismic air guns and pile-driving to quantify range dependency in impulsive characteristics using four criteria: (1) rise time < 25 ms; (2) quotient of peak pressure and pulse duration > 5,000 Pa/s; (3) duration < 1 s; (4) crest factor > 15 dB. We demonstrate that some characteristics changed markedly within ranges of ~10 km, and that the mean probability of exceeding criteria 1 and 2 was <0.5 at ranges >3.5 km. In contrast, the mean probability of exceeding criteria 3 remained >0.5 up to ~37.0 km, and the mean probability of exceeding criteria 4 remained <0.5 throughout the range. These results suggest that a proportion of the recorded signals should be defined as impulsive based on each of the criteria, and that some of the criteria change markedly as a result of propagation. However, the impulsive nature of a sound is likely to be a complex interaction of all these criteria, and many other unrelated parameters such as duty cycle, recovery periods, and sound levels will also strongly affect the risk of hearing damage. We recommend future auditory damage studies and impact assessments explicitly consider the ranges at which sounds may lose some of their potentially hazardous characteristics.

Potential Uses of Anthropogenic Noise as a Source of Information in Animal Sensory and Communication Systems.

Although current research on the impact of anthropogenic noise has focused on the detrimental effects, there is a range of ways by which animals could benefit from increased noise levels. Here we discuss two potential uses of anthropogenic noise. First, local variations in the ambient-noise field could be used to perceive objects and navigate within an environment. Second, introduced sound cues could be used as a signal for prey detection or orientation and navigation. Although the disadvantages of noise pollution will likely outweigh any positive effects, it is important to acknowledge that such changes may benefit some species.

Grey seals use anthropogenic signals from acoustic tags to locate fish: evidence from a simulated foraging task.

Anthropogenic noise can have negative effects on animal behaviour and physiology. However, noise is often introduced systematically and potentially provides information for navigation or prey detection. Here, we show that grey seals (Halichoerus grypus) learn to use sounds from acoustic fish tags as an indicator of food location. In 20 randomized trials each, 10 grey seals individually explored 20 foraging boxes, with one box containing a tagged fish, one containing an untagged fish and all other boxes being empty. The tagged box was found after significantly fewer non-tag box visits across trials, and seals revisited boxes containing the tag more often than any other box. The time and number of boxes needed to find both fish decreased significantly throughout consecutive trials. Two additional controls were conducted to investigate the role of the acoustic signal: (i) tags were placed in one box, with no fish present in any boxes and (ii) additional pieces of fish, inaccessible to the seal, were placed in the previously empty 18 boxes, making possible alternative chemosensory cues less reliable. During these controls, the acoustically tagged box was generally found significantly faster than the control box. Our results show that animals learn to use information provided by anthropogenic signals to enhance foraging success.

GABAergic inhibition of histaminergic neurons regulates active waking but not the sleep-wake switch or propofol-induced loss of consciousness.

The activity of histaminergic neurons in the tuberomammillary nucleus (TMN) of the hypothalamus correlates with an animal's behavioral state and maintains arousal. We examined how GABAergic inputs onto histaminergic neurons regulate this behavior. A prominent hypothesis, the "flip-flop" model, predicts that increased and sustained GABAergic drive onto these cells promotes sleep. Similarly, because of the histaminergic neurons' key hub-like place in the arousal circuitry, it has also been suggested that anesthetics such as propofol induce loss of consciousness by acting primarily at histaminergic neurons. We tested both these hypotheses in mice by genetically removing ionotropic GABA(A) or metabotropic GABA(B) receptors from histidine decarboxylase-expressing neurons. At the cellular level, histaminergic neurons deficient in synaptic GABA(A) receptors were significantly more excitable and were insensitive to the anesthetic propofol. At the behavioral level, EEG profiles were recorded in nontethered mice over 24 h. Surprisingly, GABAergic transmission onto histaminergic neurons had no effect in regulating the natural sleep-wake cycle and, in the case of GABA(A) receptors, for propofol-induced loss of righting reflex. The latter finding makes it unlikely that the histaminergic TMN has a central role in anesthesia. GABA(B) receptors on histaminergic neurons were dispensable for all behaviors examined. Synaptic inhibition of histaminergic cells by GABA(A) receptors, however, was essential for habituation to a novel environment.

Acute exposure to evening blue-enriched light impacts on human sleep.

Light in the short wavelength range (blue light: 446-483 nm) elicits direct effects on human melatonin secretion, alertness and cognitive performance via non-image-forming photoreceptors. However, the impact of blue-enriched polychromatic light on human sleep architecture and sleep electroencephalographic activity remains fairly unknown. In this study we investigated sleep structure and sleep electroencephalographic characteristics of 30 healthy young participants (16 men, 14 women; age range 20-31 years) following 2 h of evening light exposure to polychromatic light at 6500 K, 2500 K and 3000 K. Sleep structure across the first three non-rapid eye movement non-rapid eye movement - rapid eye movement sleep cycles did not differ significantly with respect to the light conditions. All-night non-rapid eye movement sleep electroencephalographic power density indicated that exposure to light at 6500 K resulted in a tendency for less frontal non-rapid eye movement electroencephalographic power density, compared to light at 2500 K and 3000 K. The dynamics of non-rapid eye movement electroencephalographic slow wave activity (2.0-4.0 Hz), a functional index of homeostatic sleep pressure, were such that slow wave activity was reduced significantly during the first sleep cycle after light at 6500 K compared to light at 2500 K and 3000 K, particularly in the frontal derivation. Our data suggest that exposure to blue-enriched polychromatic light at relatively low room light levels impacts upon homeostatic sleep regulation, as indexed by reduction in frontal slow wave activity during the first non-rapid eye movement episode.

Modelling the spatial spread of COVID-19 in a German district using a diffusion model.

In this study, we focus on modeling the local spread of COVID-19 infections. As the pandemic continues and new variants or future pandemics can emerge, modelling the early stages of infection spread becomes crucial, especially as limited medical data might be available initially. Therefore, our aim is to gain a better understanding of the diffusion dynamics on smaller scales using partial differential equation (PDE) models. Previous works have already presented various methods to model the spatial spread of diseases, but, due to a lack of data on regional or even local scale, few actually applied their models on real disease courses in order to describe the behaviour of the disease or estimate parameters. We use medical data from both the Robert-Koch-Institute (RKI) and the Birkenfeld district government for parameter estimation within a single German district, Birkenfeld in Rhineland-Palatinate, during the second wave of the pandemic in autumn 2020 and winter 2020-21. This district can be seen as a typical middle-European region, characterized by its (mainly) rural nature and daily commuter movements towards metropolitan areas. A basic reaction-diffusion model used for spatial COVID spread, which includes compartments for susceptibles, exposed, infected, recovered, and the total population, is used to describe the spatio-temporal spread of infections. The transmission rate, recovery rate, initial infected values, detection rate, and diffusivity rate are considered as parameters to be estimated using the reported daily data and least square fit. This work also features an emphasis on numerical methods which will be used to describe the diffusion on arbitrary two-dimensional domains. Two numerical optimization techniques for parameter fitting are used: the Metropolis algorithm and the adjoint method. Two different methods, the Crank-Nicholson method and a finite element method, which are used according to the requirements of the respective optimization method are used to solve the PDE system. This way, the two methods are compared and validated and provide similar results with good approximation of the infected in both the district and the respective sub-districts.

The agonizing effects of uncertainty: Effects of announced vs. unannounced performance assessments on emotions and achievement.

Performance assessments play an essential role in performance diagnostics at schools. In practice, both announced and unannounced assessments are regularly used. However, it is unclear whether assessments are better administered announced or unannounced. From a theoretical perspective, it can be argued that announced assessments, mediated by the greater degree of students' subjective control that accompanies them, should have a more beneficial effect on emotions, as well as the subsequently resulting performance, than unannounced assessments. To investigate these assumptions, emotion (enjoyment, anxiety) and achievement data (grades) were collected from 414 students in 19 lower- and upper-level tracks at a German secondary school on both announced and unannounced performance assessments. Less anxiety and more enjoyment occurred on the announced assessments. Moreover, enjoyment and anxiety were predictors of performance (i.e., school grades), which was better overall on announced assessments than on unannounced ones. The results of our field study suggest that announced assessments have more beneficial effects on emotions than unannounced assessments.

[Growth trajectories of intrinsic value beliefs in mathematics and French: Relations with career orientations]. / Wachstumsverläufe der intrinsischen Wertüberzeugungen in Mathematik und Französisch: Zusammenhänge mit Berufsorientierungen.

This longitudinal study investigated different trajectories in the development of intrinsic value beliefs in the subjects Mathematics and French in Grades 9 to 11 and their correlations with career aspirations. Using data from 850 students from German-Swiss high schools (54% female, age T1: 15.6 years), five distinct growth classes were identified in a bivariate growth model. Two of these classes showed clear differentiation between intrinsic value beliefs regarding the two subjects and stable growth in the preferred subject. The other three classes were characterized by mean differences (high, medium, low intrinsic value beliefs) and moderate decline in both subjects. The five growth classes were associated with different career orientations at the end of the 11th grade, with students exhibiting particularly high career orientations in one subject when intrinsic value regarding the other subject was low. Gender differences in career orientations could be fully explained by gender membership in the five growth classes.

Repeated elicitation of the acoustic startle reflex leads to sensitisation in subsequent avoidance behaviour and induces fear conditioning.

BACKGROUND: Autonomous reflexes enable animals to respond quickly to potential threats, prevent injury and mediate fight or flight responses. Intense acoustic stimuli with sudden onsets elicit a startle reflex while stimuli of similar intensity but with longer rise times only cause a cardiac defence response. In laboratory settings, habituation appears to affect all of these reflexes so that the response amplitude generally decreases with repeated exposure to the stimulus. The startle reflex has become a model system for the study of the neural basis of simple learning processes and emotional processing and is often used as a diagnostic tool in medical applications. However, previous studies did not allow animals to avoid the stimulus and the evolutionary function and long-term behavioural consequences of repeated startling remain speculative. In this study we investigate the follow-up behaviour associated with the startle reflex in wild-captured animals using an experimental setup that allows individuals to exhibit avoidance behaviour. RESULTS: We present evidence that repeated elicitation of the acoustic startle reflex leads to rapid and pronounced sensitisation of sustained spatial avoidance behaviour in grey seals (Halichoerus grypus). Animals developed rapid flight responses, left the exposure pool and showed clear signs of fear conditioning. Once sensitised, seals even avoided a known food source that was close to the sound source. In contrast, animals exposed to non-startling (long rise time) stimuli of the same maximum sound pressure habituated and flight responses waned or were absent from the beginning. The startle threshold of grey seals expressed in units of sensation levels was comparable to thresholds reported for other mammals (93 dB). CONCLUSIONS: Our results demonstrate that the acoustic startle reflex plays a crucial role in mediating flight responses and strongly influences the motivational state of an animal beyond a short-term muscular response by mediating long-term avoidance. The reflex is therefore not only a measure of emotional state but also influences emotional processing. The biological function of the startle reflex is most likely associated with mediating rapid flight responses. The data indicate that repeated startling by anthropogenic noise sources might have severe effects on long-term behaviour. Future, studies are needed to investigate whether such effects can be associated with reduced individual fitness or even longevity of individuals.

An epidemic model integrating direct and fomite transmission as well as household structure applied to COVID-19.

This paper stresses its base contribution on a new SIR-type model including direct and fomite transmission as well as the effect of distinct household structures. The model derivation is modulated by several mechanistic processes inherent from typical airborne diseases. The notion of minimum contact radius is included in the direct transmission, facilitating the arguments on physical distancing. As fomite transmission heavily relates to former-trace of sneezes, the vector field of the system naturally contains an integral kernel with time delay indicating the contribution of undetected and non-quarantined asymptomatic cases in accumulating the historical contamination of surfaces. We then increase the complexity by including the different transmission routines within and between households. For airborne diseases, within-household interactions play a significant role in the propagation of the disease rendering countrywide effect. Two steps were taken to include the effect of household structure. The first step subdivides the entire compartments (susceptible, exposed, asymptomatic, symptomatic, recovered, death) into the household level and different infection rates for the direct transmission within and between households were distinguished. Under predefined conditions and assumptions, the governing system on household level can be raised to the community level. The second step then raises the governing system to the country level, where the final state variables estimate the total individuals from all compartments in the country. Two key attributes related to the household structure (number of local households and number of household members) effectively classify countries to be of low or high risk in terms of effective disease propagation. The basic reproductive number is calculated and its biological meaning is invoked properly. The numerical methods for solving the DIDE-system and the parameter estimation problem were mentioned. Our optimal model solutions are in quite good agreement with datasets of COVID-19 active cases and related deaths from Germany and Sri Lanka in early infection, allowing us to hypothesize several unobservable situations in the two countries. Focusing on extending minimum contact radius and reducing the intensity of individual activities, we were able to synthesize the key parameters telling what to practice.

Aversiveness of sounds in phocid seals: psycho-physiological factors, learning processes and motivation.

Aversiveness of sounds and its underlying physiological mechanisms in mammals are poorly understood. In this study we tested the influence of psychophysical parameters, motivation and learning processes on the aversiveness of anthropogenic underwater noise in phocid seals (Halichoerus grypus and Phoca vitulina). We compared behavioural responses of seals to playbacks of sounds based on a model of sensory unpleasantness for humans, sounds from acoustic deterrent devices and sounds with assumed neutral properties in different contexts of food motivation. In a captive experiment with food presentation, seals habituated quickly to all sound types presented at normalised received levels of 146 dB re. 1 microPa (r.m.s., root mean square). However, the fast habituation of avoidance behaviour was also accompanied by a weak sensitisation process affecting dive times and place preference in the pool. Experiments in the wild testing animals without food presentation revealed differential responses of seals to different sound types. We observed avoidance behaviour at received levels of 135-144 dB re. 1 microPa (sensation levels of 59-79 dB). In this experiment, sounds maximised for 'roughness' perceived as unpleasant by humans also caused the strongest avoidance responses in seals, suggesting that sensory pleasantness may be the result of auditory processing that is not restricted to humans. Our results highlight the importance of considering the effects of acoustic parameters other than the received level as well as animal motivation and previous experience when assessing the impacts of anthropogenic noise on animals.

Echolocation clicks of free-ranging Chilean dolphins (Cephalorhynchus eutropia).

In this paper, evidence is provided that Chilean dolphins (Cephalorhynchus eutropia) produce ultrasonic echolocation clicks of the narrow-band high-frequency category. Echolocation clicks emitted during approaches of the hydrophones consisted only of narrow-band (rms-BW: 12.0 kHz) single pulses with mean centroid frequencies of about 126 kHz, peak frequencies of 126 kHz, and a 20 dB duration of 82.6 micros. The maximum received level measured exceeded 165 dB re 1 microPa. In addition, high repetition-rate buzzes were recorded during foraging behavior (click interval: 2 ms), but no whistles or calls with tonal components were detected.

Ability grouping of gifted students: effects on academic self-concept and boredom.

BACKGROUND: Securing appropriate challenge or preventing boredom is one of the reasons frequently used to justify ability grouping of gifted students, which has been shown to have beneficial effects for achievement. On the other hand, critics stress psychosocial costs, such as detrimental effects on academic self-concept (contrast or big-fish-little-pond effect). AIM: The effects of full-time ability grouping in special classrooms for the gifted on students' academic self-concept and their experience of boredom in mathematics classes were investigated. SAMPLE: The sample comprised 186 ninth-grade students (106 male) from eight classes at one Austrian high school. Four of these classes were part of a gifted track beginning from school year 9 on (N=93). METHOD: Students were assessed repeatedly within the first half of the school year, three times via self-report questionnaires and once by applying a standardized IQ-test. RESULTS AND CONCLUSIONS: Students in gifted classes reported a decrease in maths academic self-concept which was most pronounced early in the academic year. Interventions to counterbalance the negative effect of exposure to a high-ability reference group should therefore be implemented when ability grouping begins. No evidence for the boredom hypothesis was found (higher levels of boredom among gifted students in regular classes). However, students clearly differed in the reasons they stated for experiencing boredom. Boredom attributions changed over time and supported the assumption that gifted classes provide more appropriate levels of challenge.

Early stage COVID-19 disease dynamics in Germany: models and parameter identification.

Since the end of 2019 an outbreak of a new strain of coronavirus, called SARS-CoV-2, is reported from China and later other parts of the world. Since January 21, World Health Organization (WHO) reports daily data on confirmed cases and deaths from both China and other countries (www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports). The Johns Hopkins University (github.com/CSSEGISandData/COVID-19/blob/master/csse_COVID_19_data/csse_COVID_19_time_series/time_series_COVID19_confirmed_global.csv) collects those data from various sources worldwide on a daily basis. For Germany, the Robert-Koch-Institute (RKI) also issues daily reports on the current number of infections and infection related fatal cases (www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Situationsberichte/Gesamt.html). However, due to delays in the data collection, the data from RKI always lags behind those reported by Johns Hopkins. In this work we present an extended SEIRD-model to describe the disease dynamics in Germany. The parameter values are identified by matching the model output to the officially reported cases. An additional parameter to capture the influence of unidentified cases is also included in the model.

Exhaustion of Skeletal Muscle Fibers Within Seconds: Incorporating Phosphate Kinetics Into a Hill-Type Model.

Initiated by neural impulses and subsequent calcium release, skeletal muscle fibers contract (actively generate force) as a result of repetitive power strokes of acto-myosin cross-bridges. The energy required for performing these cross-bridge cycles is provided by the hydrolysis of adenosine triphosphate (ATP). The reaction products, adenosine diphosphate (ADP) and inorganic phosphate (P i ), are then used-among other reactants, such as creatine phosphate-to refuel the ATP energy storage. However, similar to yeasts that perish at the hands of their own waste, the hydrolysis reaction products diminish the chemical potential of ATP and thus inhibit the muscle's force generation as their concentration rises. We suggest to use the term "exhaustion" for force reduction (fatigue) that is caused by combined P i and ADP accumulation along with a possible reduction in ATP concentration. On the basis of bio-chemical kinetics, we present a model of muscle fiber exhaustion based on hydrolytic ATP-ADP-P i dynamics, which are assumed to be length- and calcium activity-dependent. Written in terms of differential-algebraic equations, the new sub-model allows to enhance existing Hill-type excitation-contraction models in a straightforward way. Measured time courses of force decay during isometric contractions of rabbit M. gastrocnemius and M. plantaris were employed for model verification, with the finding that our suggested model enhancement proved eminently promising. We discuss implications of our model approach for enhancing muscle models in general, as well as a few aspects regarding the significance of phosphate kinetics as one contributor to muscle fatigue.

Reproductive number of the COVID-19 epidemic in Switzerland with a focus on the Cantons of Basel-Stadt and Basel-Landschaft.

The reproductive number in Switzerland was between 1.5 and 2 during the first third of March, and has consistently decreased to around 1. After the announcement of the latest strict measure on 20 March 2020, namely that gatherings of more than five people in public spaces are prohibited, the reproductive number dropped significantly below 1; the authors of this study estimate the reproductive number to be between 0.6 and 0.8 in the first third of April.