In this review, we successively present the methods for phenomenological modeling of the evolution of reported and unreported cases of COVID-19, both in the exponential phase of growth and then in a complete epidemic wave. After the case of an isolated wave, we present the modeling of several successive waves separated by endemic stationary periods. Then, we treat the case of multi-compartmental models without or with age structure. Eventually, we review the literature, based on 260 articles selected in 11 sections, ranging from the medical survey of hospital cases to forecasting the dynamics of new cases in the general population. This review favors the phenomenological approach over the mechanistic approach in the choice of references and provides simulations of the evolution of the number of observed cases of COVID-19 for 10 states (California, China, France, India, Israel, Japan, New York, Peru, Spain and United Kingdom).

The automotive industry is entering a digital revolution, driven by the need to develop new products in less time that are high-quality and environmentally friendly. A proper manufacturing process influences the performance of the door grommet during its lifetime. In this work, uniaxial tensile tests based on molecular dynamics simulations have been performed on an ethylene-propylene-diene monomer (EPDM) material to investigate the effect of the crosslink density and its variation with temperature. The Mooney-Rivlin (MR) model is used to fit the results of molecular dynamics (MD) simulations in this paper and an exponential-type model is proposed to calculate the parameters C1(T) and C2T. The experimental results, confirmed by hardness tests of the cured part according to ASTM 1415-88, show that the free volume fraction and the crosslink density have a significant effect on the stiffness of the EPDM material in a deformed state. The results of molecular dynamics superposition on the MR model agree reasonably well with the macroscopically observed mechanical behavior and tensile stress of the EPDM at the molecular level. This work allows the accurate characterization of the stress-strain behavior of rubber-like materials subjected to deformation and can provide valuable information for their widespread application in the injection molding industry.

Silver iodide is a prototype compound of superionic conductors that allows ions to flow through its structure. It exhibits a first-order phase transition at 420 K, characterized by an abrupt change in its ionic conductivity behavior, and above this temperature, its ionic conductivity increases by more than three orders of magnitude. Introducing small concentrations of carbon into the silver iodide structure produces a new material with a mixed conductivity (ionic and electronic) that increases with increasing temperature. In this work, we report the experimental results of the ionic conductivity as a function of the reciprocal temperature for the (AgI)x - C(1-x) mixture at low carbon concentrations (x = 0.99, 0.98, and 0.97). The ionic conductivity behavior as a function of reciprocal temperature was well fitted using a phenomenological model based on a random variable theory with a probability distribution function for the carriers. The experimental data show a proximity effect between the C and AgI phases. As a consequence of this proximity behavior, carbon concentration or temperature can control the conductivity of the (AgI)x - C(1-x) mixture.

An ensemble n-sub-epidemic modeling framework that integrates sub-epidemics to capture complex temporal dynamics has demonstrated powerful forecasting capability in previous works. This modeling framework can characterize complex epidemic patterns, including plateaus, epidemic resurgences, and epidemic waves characterized by multiple peaks of different sizes. In this tutorial paper, we introduce and illustrate SubEpiPredict, a user-friendly MATLAB toolbox for fitting and forecasting time series data using an ensemble n-sub-epidemic modeling framework. The toolbox can be used for model fitting, forecasting, and evaluation of model performance of the calibration and forecasting periods using metrics such as the weighted interval score (WIS). We also provide a detailed description of these methods including the concept of the n-sub-epidemic model, constructing ensemble forecasts from the top-ranking models, etc. For the illustration of the toolbox, we utilize publicly available daily COVID-19 death data at the national level for the United States. The MATLAB toolbox introduced in this paper can be very useful for a wider group of audiences, including policymakers, and can be easily utilized by those without extensive coding and modeling backgrounds.

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing\'s line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models (a) recapitulate the diversity of actual skin patterns, (b) capture the underlying dynamics of cellular interactions, (c) interact with tissue size and shape, (d) can lead to ordered sequential patterning, (e) generate cellular automaton dynamics in lizards and snakes, (f) predict actual patterns beyond their statistical features, and (g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.

Interaction between membrane proteins and ligands plays a key role in governing a wide spectrum of cellular processes. These interactions can provide a cooperative-type regulation of protein function. A wide variety of proteins, including enzymes, channels, transporters, and receptors, displays cooperative behavior in their interactions with ligands. Moreover, the ligands involved encompass a vast diversity and include specific molecules or ions that bind to specific binding sites. In this review, our particular focus is on the interaction between integral membrane proteins and ligands that can present multiple \"binding sites\", such as protons or membrane phospholipids. The study of the interaction that protons or lipids have with membrane proteins often presents challenges for classical mechanistic modeling approaches. In this regard, we show that, like Hill\'s pioneering work on hemoglobin regulation, phenomenological modeling constitutes a powerful tool for capturing essential features of these systems.

Brain stimulation is an increasingly popular neuromodulatory tool used in both clinical and research settings; however, the effects of brain stimulation, particularly those of non-invasive stimulation, are variable. This variability can be partially explained by an incomplete mechanistic understanding, coupled with a combinatorial explosion of possible stimulation parameters. Computational models constitute a useful tool to explore the vast sea of stimulation parameters and characterise their effects on brain activity. Yet the utility of modelling stimulation in-silico relies on its biophysical relevance, which needs to account for the dynamics of large and diverse neural populations and how underlying networks shape those collective dynamics. The large number of parameters to consider when constructing a model is no less than those needed to consider when planning empirical studies. This piece is centred on the application of phenomenological and biophysical models in non-invasive brain stimulation. We first introduce common forms of brain stimulation and computational models, and provide typical construction choices made when building phenomenological and biophysical models. Through the lens of four case studies, we provide an account of the questions these models can address, commonalities, and limitations across studies. We conclude by proposing future directions to fully realise the potential of computational models of brain stimulation for the design of personalized, efficient, and effective stimulation strategies.

BACKGROUND: The age of infection plays an important role in assessing an individual\'s daily level of contagiousness, quantified by the daily reproduction number. Then, we derive an autoregressive moving average model from a daily discrete-time epidemic model based on a difference equation involving the age of infection. Novelty: The article\'s main idea is to use a part of the spectrum associated with this difference equation to describe the data and the model.
RESULTS: We present some results of the parameters\' identification of the model when all the eigenvalues are known. This method was applied to Japan\'s third epidemic wave of COVID-19 fails to preserve the positivity of daily reproduction. This problem forced us to develop an original truncated spectral method applied to Japanese data. We start by considering ten days and extend our analysis to one month.
CONCLUSIONS: We can identify the shape for a daily reproduction numbers curve throughout the contagion period using only a few eigenvalues to fit the data.

Caffeine and theophylline are compounds with important applications in the pharmaceutical industry and other fields of the chemical industry. These purine derivatives have simple chemical structures, therefore, the evaluation of their sublimation process contributes to the development of mass transfer analysis methods that can later be applied to other compounds with more complex structures. With the help of thermogravimetric analysis in isothermal conditions, the kinetic study of the sublimation of caffeine and theophylline, along with the evaluation of kinetic parameters (activation energy and the pre-exponential factor), was carried out. Global mass transfer coefficients were determined, which vary for caffeine between 53 × 10-8 and 631 × 10-8 mol/s·m2·Pa, and for theophylline between 68 × 10-8 and 441 × 10-8 mol/s·m2·Pa. The dimensionless equations of the form: Sh=a+b·Rec·Scd have been proposed, which allow the determination of individual mass transfer coefficients at temperatures between 130 and 160 °C for caffeine and between 170 and 200 °C for theophylline.

It was important to understand the accurate mechanical properties of soft tissue for the evaluation of its injury, provide reliable protective ways or design effective human resist-injury devices. There was little study that clarified the difference between phenomenological models based on strain invariant and the principal stretches variables respectively although some quasi-static constitutive models of soft tissue were developed. In this study, we enumerate several typical hyperelastic models and derive the tensor equation of stress-strain based on continuum mechanics to fit the experimental data of human brain specimens under multiple loading modes in previous studies and give the coefficient of determination based on the least square fitting. It was suggested that two variable forms of phenomenological models with only the first strain invariant are consistent under uniaxial compression and tension, but the Cauchy stress tensor expressed by strain is completely different under simple shear loading. Also, the shear stress derived from the constitutive model based on strain invariants and principal stretchs has multiple relationships related to shear strain. The results in this study would be used to understand the more accurate mechanical characterization of soft tissue, which will allow us to evaluate the injury and develop much accurate injury criteria for soft tissue.