The European Physical Journal Plus

An analytical model for calculating the spread of the COVID-19 epidemic is described, and it is shown that the main patterns of epidemic development are determined by three dimensionless complexes representing the ratios of transmission rates, contact limitation due to lockdown, and population vaccination. A comparison of statistical data on the growth of the epidemic in Germany, Berlin and its various neighbourhoods shows that the development of the epidemic depends to a large extent on the ethnic composition of the population. In the same way as it is accepted in some sections of physics, it is proposed to use the methods of similarity theory to investigate the regularities of the emergence and development of the epidemic.

Diffusion comes anytime and everywhere. If there is a gradient or a potential difference of a quantity a diffusion process happens and this ends if an equilibrium is reached only. The concentration of a species maybe such quantity, or the voltage. An electric currant will be driven by a voltage difference for example. In this COVID-19 pandemic one observes both regions with low incidence and other ones with high incidence. The local different people density could be a reason for that. In populous areas like big cities or congested urban areas higher COVID-19 incidences could be observed than in rural regions. The aim of this paper consists in the application of a diffusion concept to describe one possible issue of the the COVID-19 propagation. This will be discussed for the German situation based on the quite different incidence data for the different federal states of Germany. With this ansatz some phenomenoms of the actual development of the pandemic could be confirmed. The model gives a possibility to investigate certain scenarios like border-crossings or local spreading events and their influence on the COVID-19 propagation as well.

We propose a technique of controlled manipulation with mammalian intracellular bodies by means of optical trapping in order to reveal viscoelastic properties of cell interior. Near infrared laser in the spectral range of tissue transparency was applied to study dynamics of the nucleolus-chromatin complex inside the thermodynamically non-equilibrium system of a mouse oocyte. A nucleolus of germinal vesicle (GV) oocyte as spherical probe was displaced from the equilibrium and its relaxation dynamics was observed. We developed software for subdiffraction tracking of a nucleolus position with lateral resolution up to 3 nm and applied it for different GV-oocyte chromatin configurations. We showed differences in viscoelastic properties within nucleoplasm of NSN-oocytes, visualized by Hoechst 33342 staining. Also, we demonstrate that in germ cells basic biophysical properties of nucleoplasm can be obtained by using optical trapping without disruption and modification of cellular interior.

We propose a variational method for joint motion estimation and source identification in one-dimensional image sequences. The problem is motivated by fluorescence microscopy data of laser nanoablations of cell membranes in live Drosophila embryos, which can be conveniently--and without loss of significant information--represented in space-time plots, so called kymographs. Based on mechanical models of tissue formation, we propose a variational formulation that is based on the nonhomogenous continuity equation and investigate the solution of this ill-posed inverse problem using convective regularisation. We show existence of a minimiser of the minimisation problem, derive the associated Euler-Lagrange equations, and numerically solve them using a finite element discretisation together with Newtons method. Based on synthetic data, we demonstrate that source estimation can be crucial whenever signal variations can not be explained by advection alone. Furthermore, we perform an extensive evaluation and comparison of various models, including standard optical flow, based on manually annotated kymographs that measure velocities of visible features. Finally, we present results for data generated by a mechanical model of tissue formation and demonstrate that our approach reliably estimates both a velocity and a source.

Micro-elastography is an optical technique that studies elastic waves for the mechanical characterisation of micrometric objects, such as cells. We propose to adapt this technique for the characterisation of millimetre-sized samples using a white light microscope. The objective is to perform a rapid, global characterisation of the elasticity of a biopsy. The millimetre-sized samples to be characterized are embedded in an agarose gel. A vibrator generates shear waves in this gel that transmit naturally inside the sample. This technique removes the need for precise manipulation of the wave source. A high-speed camera records the propagation of the waves in the sample. Their velocity is calculated using a noise correlation approach. Due to the lack of millimetric phantoms of calibrated elasticity, we choose to validate this method with a three step process. The experimental setup is first validated on homogeneous gels, then on biological samples of increasing elasticity, biopsies of beef liver hardened by heating, and finally on biological samples of clinical interest: biopsies of mouse endometrium. This method can be applied to all types of biological tissue, paving the way for rapid mechanical characterization of biopsies.

The SIR model of the epidemic spread is used for consideration the problem of the competition of two viruses having different contagiousness. It is shown how the more contagious strain replaces over time the less contagious one. In particular the results can be applied to the current situation when the omicron strain appeared in population affected by the delta strain. PACS number(s)02.50.-r, 05.60.-k, 82.39.-k, 87.19.Xx

In this short paper we describe a simple technique aimed to forecast the course of the spreading of Covid-19 virus infection in Italy. Data released every day by the Italian "Protezione Civile" organization have been processed with reference of the the SIR classical mathematical model by Kermack and McKendrick. The model provides a rough estimate of the time needed to completely block virus spread. The above assumptions will be valid if Covid-19 will not be recognized as capable of establishing a chronic productive infection in significant fraction of the population.

An asymmetric version of the classical Kermack-McKendrick description of an epidemic evolution is presented in terms of four independent parameters. This is enough to obtain an accurate description of the different stages of the COVID-19 pandemia in any country for the reported daily and total number of casualties due to the infection. The asymmetry accounts for lockdown effects introduced to reduce the impact of the epidemic outburst. A set of new variables allows for an analytic study of the evolution of the system before and after the lockdown measures are put in place. A continuous matching is possible for all variables in the system apart from the time dependence of the infection rate. An analytic expression is obtained for this discontinuity which is proposed as a good quantity to gauge the efficiency of the lockdown measures. A study of this variable for different countries is performed.

During embryogenesis, as cells proliferate and assemble into tissues, they undergo a sequence of transitions between distinct molecular states eventually giving rise to a cellular population consisting of an appropriate distribution of specific functional cell types. Recent progress on the dynamics underlying decision-making in developmental landscape makes it feasible to start analysing the amount of information involved in constructing such systems. To explore this we introduce the notion of potency of a developmental landscape and attempt to calculate it for two development systems of current interest, in-vitro differentiation of epiblast-like cells into neural and mesodermal progenitors and the worm vulva patterning system. Our approach integrates concepts from developmental biology, information theory and dynamical systems to estimate both the number and identity of signalling regimes that give rise to distinguishable temporal response patterns.

The mechanical properties of the nucleus play an important role in all the processes of a cell and impact greatly its decisions, functions and phenotype. It is then important to understand how internal and external stresses can modify them. To study the mechanical response of the nucleus at different timescales, a hybrid viscoelastic model integrating both continuum mechanics and soft glass matter theory is developed. It indeed accounts for the instantaneous viscoelastic response of the structural components of the nucleus as well as the active response of the nuclear envelope and the dynamic reorganization of the cytoskeleton at different timescales. This model can describe adequately the nuclear deformation caused by substrate stiffness in primary hepatocytes and HepG2 cells in culture up to 5 days. It also reveals that the increase of nuclear strain in the long term implies nuclear softening (a phenomenon intensified on stiffer substrates), simultaneously with an increase of the dissipative properties of the nucleus, offering stability. Finally, in the context of soft glassy theory, the model suggests that processes of aging and mechanical memory of the cell may be originated by the dissipative capacity of the nuclei.

The exact mechanisms behind many morphogenic processes are still a mystery. Mechanical cues, such as curvature, play an important role when tissue or cell shape is formed. In this work, we derive and analyze a mechanochemical model. This particular spatially one-dimensional model describes the deformation of a tissue- or cell surface over time, which is driven by a morphogen that locally induces curvature. The model consists of two PDEs with periodic boundary conditions; one reaction-diffusion equation for the morphogen and one PDE that describes the dynamics of the curve, derived by taking the L2-gradient flow of the Helfrich energy. We analyze the possible steady states of this model using geometric singular perturbation theory. It turns out that the strength of interaction between the morphogen and the curvature plays a key role in the type of possible steady state solutions. In the case of weak interaction, the geometry of the slow manifolds allows only for (in space) slowly changing periodic orbits that lay completely on one slow manifold. In the case of strong interaction, there exist multiple front solutions: periodic orbits that jump between different slow manifolds. The singular skeletons of the steady state solutions do not meet the required consistency conditions for the curvature, a priori indicating that the solutions might not be observable. The observability and stability are investigated further using numerical simulation.

AnnotationThe high contagiousness of the latest strains of Covid-19 qualitatively changes the behavior of the "virus vs human" system. Numerical experiments with a model of the Covid-19 epidemic in Moscow have shown that a reproduction number R0 of about 4 is critical, defining a qualitative change in the dynamics of the epidemic. Below this value (observed until 2022), the long-term forecast tends to undamped oscillations; above this value, it is described by damped oscillations: amplitudes of the epidemic waves get smaller and smaller, with a constant, very high background level of morbidity (or high-intensity vaccination) that maintains the state of natural immunity at a level close to 100% (reaching 93.7% for the current R0 value of about 16). At the limit, the system tends to a stable equilibrium point. Here we consider a reduced model of epidemic dynamics. Its study (search for equilibrium solutions, analysis of their stability, construction a bifurcation diagram and a phase portrait) confirms the presence of points of qualitative change in the behavior of the "virus vs human" system (bifurcation points). Some practical results for Moscow are given. A further increase in the contagiousness of the virus does not change the picture significantly, thus more infectious strains are not to be feared. The key parameter of the study is the function of the immunity level depending on the time after the disease. The damping of omicron waves (oscillations), observed recently in many countries, is a confirmation of the correctness of the accepted hypotheses.

We show that the standard SIR model is not effective to predict the 2019-20 coronavirus pandemic propagation. We propose a new model where the logarithm of the detected population number follows a linear dynamical system. We estimate the parameters of this system and compare models obtained with data observed from different countries. Based on the given estimator and results obtained with the Pr. Raoults treatment, we affirm with a reasonable degree of confidence that his "test-treat-noconfine" policy was less expensive in human lives than the"confine and wait for a proved treatment" policy adopted by the French government.

AO_SCPLOWBSTRACTC_SCPLOWCell migration is of major importance for the understanding of phenomena such as morphogenesis, cancer metastasis, or wound healing. In many of these situations cells are under external confinement. In this work we show by means of computer simulations with a Cellular Potts Model (CPM) that the presence of a bottleneck in an otherwise straight channel has a major influence on the internal organisation of an invading cellular monolayer and the motion of individual cells therein. Comparable to a glass or viscoelastic material, the cell sheet is found to exhibit features of both classical solids and classical fluids. The local ordering on average corresponds to a regular hexagonal lattice, while the relative motion of cells is unbounded. Compared to an unconstricted channel, we observe that a bottleneck perturbs the formation of regular hexagonal arrangements in the epithelial sheet and leads to pile-ups and backflow of cells near the entrance to the constriction, which also affects the overall invasion speed. The scale of these various phenomena depends on the dimensions of the different channel parts, as well as the shape of the funnel domain that connects wider to narrower regions.

In the course of a large-scale infectious disease a time-dependent Reproduction rate is an important parameter for political, economic and social decisions. In this paper we focus on that parameter and introduce a mathematical implementation in addition to the mostly used definition of Robert-Koch-Institute (RKI) in Germany. Such value is of particular interest in order to serve as a criterion for possible Lock-Downs and "LockUps" in society and can provide deep insights into a pandemic event. Both the definition of the new Reproduction index and the RKIs Reproduction number are compared analytically, applied to simple model calculations and finally on real Covid19 data. Clear advantages of the new Reproduction index become apparent and some weaknesses of the RKIs Reproduction number become clearly visible. In addition we propose two additional ways of displaying pandemic data to have the pandemic behaviour at a glance. We find that some signatures of the pandemic appear now very well expressed - especially in conjunction with the new Reproduction index Ri. This all could be very helpful for future political, social and economic decisions.

Ionizing radiation is one of the main threats to human space exploration beyond low Earth orbit (BLEO). It is thus of primary importance to determine safe career dose limits for astronauts involved in BLEO missions. In the first part of this work it is shown how the methods of physics and statistics can contribute to its solution. The average equivalent doses received by a hypothetical human crew are established using the data of several robotic missions to the Moon and to Mars. The probabilities of the occurrence of deterministic effects due to radiation that could impair the success of a mission or lower the life expectancy of astronauts are evaluated with the help of a statistical analysis. In the last part of this work it is argued that the use of the so-called 3D models or organoids combined with the methods of precision oncology and molecular medicine could be a good candidate of a strategy in order to predict the insurgence of stochastic effects in humans. On one side, organoids recapitulate several features of the real human organs and their in vivo surroundings. On the other side, we argue with a case study that precision oncology and molecular medicine are able to provide a deeper insight of the onset of cancer following irradiation in space.

This article presents a mathematical infection model that is designed to estimate the course of coronavirus infection in Germany for several days in advance: How many people become ill or die, what is the temporal development? If the contact restriction is perfect, then the model predicts the development of the virus infection after the initial subsidence of the infection. However, since this restriction cannot always be strictly adhered to, the model is dynamically adapted to the development. This makes it possible to estimate the number of infected people, the number of new infections and deaths in Germany about a week in advance.

We present an algorithm for dynamical fitting of a logistic curve to the Covid-19 epidemics data, with fit-parameters linearly evolving to the future. We show that the algorithm would have given reasonable short- and medium-range predictions for the mid-range evolution of the epidemics for several countries. We introduce the double-logistic curve, which provides a very good description of the epidemics data at any given time of the epidemics. We analyse the predictability properties of some naive models.

In our ongoing investigations, we have studied a specific interaction between electromagnetic fields and matter - the so-called Electromagnetic echo effect (EMEE). It enables rapid and contactless investigations of gases, liquids and solids to be performed, since the signal generated as a result of the effect is quite sensitive to all kinds of changes occurring within the studied samples. The effect can be considered universal for all matter and provides analysis in real time. We use this phenomenon to demonstrate the practical possibility to control reactions, occurring between Chicken anemia virus (CAV) and the corresponding antibodies. This methodology can be used for simple but reliable control of similar, otherwise hard to detect, antigen-antibody reactions, in order to confirm the presence of a certain viral species. The approach offers a high level of safety, since it enables measurements to be taken remotely, thus limiting exposure to contagion. We further discuss the possibility to register the presence of SARS-nCoV-2 in an attempt to address current global pandemic.

The global phytoplankton community, comprised of aquatic photosynthetic organisms, is acknowledged for being responsible for half of the global oxygen production Prominent among these is the pico-eukaryote Micromonas commoda (formally Micromonas pusilla of the genus Micromonas), which can be found in marine and coastal environments across the globe. Cell death of phytoplankton has been identified as contributing to the largest carbon transfers on the planet moving 109 tonnes of carbon in the oceans every day. During a cell death organic matter is released into the local environment which can act as both a food source and a warning signal for nearby organisms. Here we present a novel motility response to single cell death in populations of Micromonas sp., where the death of a single cell releases a chemical patch triggers surrounding cells to escape the immediate affected area. These so-called "burst events" are then modelled and compared with a spherically symmetric diffusing patch which is found to faithfully reproduce the observed behaviour. Finally, laser ablation of single cells reproduces the observed avoidance response, confirming that Micromonas sp. has evolved a specific motility response in order to escape harmful environments for example nearby predator-prey interactions or virus lysis induced cell death.