Duchenne Muscular Dystrophy (DMD) is a common X-linked disease, caused by mutations in the gene encoding dystrophin and characterized by widespread muscle damage that invariably leads to paralysis ...and death. Lack of dystrophin in the muscles of DMD patients determines an increased fragility of muscle fibers, leading to repeated cycles of necrosis and regeneration that result in failed regeneration, increased fibrosis and progressive loss of muscle function.
In this work, we propose a three-dimensional chemo-mechanical mathematical model of skeletal muscle in DMD. This model is based on stress-strain mechanical data of the muscle and studies of changes in fiber structure and interaction aiming to shade light into the biophysical mechanisms regulating muscle contraction. The results show that the model is able to reproduce the experimental data of maximum isometric force, maximum contraction velocity and concentric normalized F-V curve for the healthy and dystrophic muscle. Furthermore, the model is capable of predicting the force-velocity response of the muscle to eccentric loading without explicitly imposing its functional form in the formulation, and it is able to reproduce the concentric normalized F-V curve of the healthy fiber, as an additional proof of the predictive capabilities of the model. The resulting model represents a novel approach to study DMD pathogenesis by providing insights into the underlying mechanisms of muscle response to force associated with the impaired muscle functionality. Moreover, it could be an innovative tool for researchers to predict muscle response under conditions that are not possible to explore in the laboratory and an important step towards a new paradigm of in-silico trials that could allow identifying novel therapies bypassing the use of animal models.
In this paper, we introduce a numerical and analytical study of the HIV‐1 infection of CD4+ T‐cells conformable fractional mathematical model. This model is studied analytically by Kudryashov and ...modified Kudryashov methods and numerically by finite difference method. A comparison between the results of the analytical and numerical methods is investigated. We also give some figures that show how accurate the solutions will be obtained from analytical and numerical methods.
In the present investigations, we construct a new mathematical for the transmission dynamics of corona virus (COVID‐19) using the cases reported in Kingdom of Saudi Arabia for March 02 till July 31, ...2020. We investigate the parameters values of the model using the least square curve fitting and the basic reproduction number is suggested for the given data is ℛ0 ≈ 1.2937. The stability results of the model are shown when the basic reproduction number is ℛ0 < 1. The model is locally asymptotically stable when ℛ0 < 1. Further, we show some important parameters that are more sensitive to the basic reproduction number ℛ0 using the PRCC method. The sensitive parameters that act as a control parameters that can reduce and control the infection in the population are shown graphically. The suggested control parameters can reduce dramatically the infection in the Kingdom of Saudi Arabia if the proper attention is paid to the suggested controls.
Background & objectives: Coronavirus disease 2019 (COVID-19) has raised urgent questions about containment and mitigation, particularly in countries where the virus has not yet established ...human-to-human transmission. The objectives of this study were to find out if it was possible to prevent, or delay, the local outbreaks of COVID-19 through restrictions on travel from abroad and if the virus has already established in-country transmission, to what extent would its impact be mitigated through quarantine of symptomatic patients?
Methods: These questions were addressed in the context of India, using simple mathematical models of infectious disease transmission. While there remained important uncertainties in the natural history of COVID-19, using hypothetical epidemic curves, some key findings were illustrated that appeared insensitive to model assumptions, as well as highlighting critical data gaps.
Results: It was assumed that symptomatic quarantine would identify and quarantine 50 per cent of symptomatic individuals within three days of developing symptoms. In an optimistic scenario of the basic reproduction number (R0) being 1.5, and asymptomatic infections lacking any infectiousness, such measures would reduce the cumulative incidence by 62 per cent. In the pessimistic scenario of R0=4, and asymptomatic infections being half as infectious as symptomatic, this projected impact falls to two per cent.
Interpretation & conclusions: Port-of-entry-based entry screening of travellers with suggestive clinical features and from COVID-19-affected countries, would achieve modest delays in the introduction of the virus into the community. Acting alone, however, such measures would be insufficient to delay the outbreak by weeks or longer. Once the virus establishes transmission within the community, quarantine of symptomatics may have a meaningful impact on disease burden. Model projections are subject to substantial uncertainty and can be further refined as more is understood about the natural history of infection of this novel virus. As a public health measure, health system and community preparedness would be critical to control any impending spread of COVID-19 in the country.
For the LCL-type grid-connected inverter, there are basically three current control schemes, namely the grid current control, the inverter-side inductor current control, and the weighted average ...current control. This paper builds a general mathematical model to describe the three current control schemes. In this model, the grid current is an equivalent target control variable, the capacitor current feedback serves as a damping solution, and the computation and pulse-width modulation delays are taken into account. Based on the general mathematical model, a comparative analysis of different control schemes is carried out in terms of the grid current stability. It reveals that when the inverter-side inductor current is controlled, the grid current shows the same stability as the inverter-side inductor current; but when the weighted average current is controlled, both the grid current and the inverter-side inductor current are critically stable even though the weighted average current can be easily stabilized. Moreover, the general mathematical model also provides a unified perspective to design different control schemes, which makes the controller parameter tuning more straightforward and effective. In this way, a set of controller parameters which yields high robustness against the grid-impedance variation can be selected for all the three current control schemes. Finally, a 6-kW prototype is built, and experiments are performed to verify the theoretical analysis.
Viral coinfections are responsible for a significant portion of cases of patients hospitalized with influenza-like illness. As our awareness of viral coinfections has increased, researchers have ...started to experimentally examine some of the virus–virus interactions underlying these infections. One mechanism of interaction between viruses is through the innate immune response. This seems to occur primarily through the interferon response, which generates an antiviral state in nearby uninfected cells, a phenomenon know as the bystander effect. Here, we develop a mathematical model of two viruses interacting through the bystander effect. We find that when the rate of removal of cells to the protected state is high, growth of the first virus is suppressed, while the second virus enjoys sole access to the protected cells, enhancing its growth. Conversely, growth of the second virus can be fully suppressed if its ability to infect the protected cells is limited.
•A system of ODEs is used to examine the role of protected cells during coinfection.•The rate at which the immune response protects cells can alter which virus is dominant.•An immune response protecting against one virus can enhance availability of cells for a second virus.
A 305-d lactation followed by a 60-d dry period has traditionally been considered economically optimal, yet dairy cows in modern intensive dairy systems are frequently dried off while still producing ...significant quantities of milk. Managing cows for an extended lactation has reported production, welfare, and economic benefits, but not all cows are suitable for an extended lactation. Implementation of an extended lactation strategy on-farm could benefit from use of a decision support system, based on a mathematical lactation model, that can identify suitable cows during early lactation that have a high likelihood of producing above a target milk yield (MY) at 305 d in milk (DIM). Therefore, our objectives were (1) to compare the suitability of 3 commonly used lactation models for modeling extended lactations (Dijkstra, Wood, and Wilmink) in primiparous and multiparous cows under a variety of lactation lengths, and (2) to determine the amount of early-lactation daily MY data needed to accurately forecast MY at d 305 by using the most suitable model and determine whether this is sufficient for identifying cows suitable for an extended lactation before the end of a typical voluntary waiting period (50–90 d). Daily MY data from 467 individual Holstein-Friesian lactations (DIM >305 d; 379 ± 65-d lactation length mean ± SD) were fitted by the 3 lactation models using a nonlinear regression procedure. The parameter estimates of these models, lactation characteristics (peak yield, time to peak yield, and persistency), and goodness-of-fit were compared between parity and different lactation lengths. The models had similar performance, and differences between parity groups were consistent with previous literature. Then, data from only the first i DIM for each individual lactation, where i was incremented by 30 d from 30 to 150 DIM and by 50 d from 150 to 300 DIM, were fitted by each model to forecast MY at d 305. The Dijkstra model was selected for further analysis, as it had superior goodness-of-fit statistics for i= 30 and 60. The data set was fit twice by the Dijkstra model, with parameter bounds either unconstrained or constrained. The quality of predictions of MY at d 305 improved with increasing data availability for both models and assisting the model fitting procedure with more biologically relevant constraints on parameters improved the predictions, but neither was reliable enough for practical use on-farm due to the high uncertainty of forecasted predictions. Using 90 d of data, the constrained model correctly classified 66% of lactations as being above or below a target MY at d 305 of 25 kg/d, with a probability threshold of 0.95. The proportion of correct classifications became smaller at lower targets of MY at d 305 and became greater when using more lactation days. Overall, further work is required to develop a model that can forecast late-lactation MY with sufficient accuracy for practical use. We envisage that a hybridized machine learning and mechanistic model that incorporates additional historical and genetic information with early-lactation MY could produce meaningful lactation curve forecasts.
Three approaches to modelling the heating and evaporation of monocomponent droplets are compared. Firstly, the heat rate supplied to the droplets to raise their internal energy is calculated based on ...the observation that steady-state equations for heat and mass balance in the gas phase should lead to the same droplet evaporation rates. The direct calculation of the above-mentioned heat rate is used in the second approach; the value of this rate is then used for the estimation of the droplet evaporation rate using the Spalding heat transfer number. In the third approach, the same algorithm as in the second approach is used to calculate the heat rate but the mass evaporation rate in this approach is inferred from the coupled solution to the momentum, mass and energy conservation equations in the gas phase; the gas mixture density in this approach depends on temperature. The predictions of the numerical algorithms for these approaches are compared with experimentally observed time dependencies of the rates of change of radii and average temperatures of n-decane droplets at initial temperatures and radii equal to 300 K and 0.85 mm, respectively, placed in a gas at temperatures 500 K and 760 K. It is shown that the algorithm for the third approach predicts values which are close to the experimental data.
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•Three modelling approaches to droplet heating and evaporation are analysed.•The solution to conservation equations in gas phase is considered.•The models are validated for the rates of change in droplet radii and temperatures.•Importance of accuracy of the gas phase model is emphasised.
We investigate the relationship between the frequency spectrum of image data and the generalization behavior of convolutional neural networks (CNN). We first notice CNN's ability in capturing the ...high-frequency components of images. These high-frequency components are almost imperceptible to a human. Thus the observation leads to multiple hypotheses that are related to the generalization behaviors of CNN, including a potential explanation for adversarial examples, a discussion of CNN's trade-off between robustness and accuracy, and some evidence in understanding training heuristics.
Personnel scheduling: Models and complexity Brucker, Peter; Qu, Rong; Burke, Edmund
European journal of operational research,
05/2011, Letnik:
210, Številka:
3
Journal Article
Recenzirano
Odprti dostop
Due to its complexity, its challenging features, and its practical relevance, personnel scheduling has been heavily investigated in the last few decades. However, there is a relatively low level of ...study on models and complexity in these important problems. In this paper, we present mathematical models which cover specific aspects in the personnel scheduling literature. Furthermore, we address complexity issues by identifying polynomial solvable and NP-hard special cases.
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