Applied Mathematical Modelling最新文献

It is well known that, during replication, RNA viruses spontaneously generate defective viral genomes (DVGs). DVGs are unable to complete an infectious cycle autonomously and depend on coinfection with a wild-type helper virus (HV) for their replication and/or transmission. The study of the dynamics arising from a HV and its DVGs has been a longstanding question in virology. It has been shown that DVGs can modulate HV replication and, depending on the strength of interference, result in HV extinctions or self-sustained persistent fluctuations. Extensive experimental work has provided mechanistic explanations for DVG generation and compelling evidences of HV-DVGs virus coevolution. Some of these observations have been captured by mathematical models. Here, we develop and investigate an epidemiological-like mathematical model specifically designed to study the dynamics of betacoronavirus in cell culture experiments. The dynamics of the model is governed by several degenerate normally hyperbolic invariant manifolds given by quasineutral planes - i.e., filled by equilibrium points. Three different quasineutral planes have been identified depending on parameters and involving: (i) persistence of HV and DVGs; (ii) persistence of non-infected cells and DVG-infected cells; and (iii) persistence of DVG-infected cells and DVGs. Key parameters involved in these scenarios are the maximum burst size (B), the fraction of DVGs produced during HV replication (β), and the replication advantage of DVGs (δ). More precisely, in the case $0<B<1+\beta$ the system displays tristability, where all three scenarios are present. In the case $1+\beta <B<1+\beta +\delta$ this tristability persists but attracting scenario (ii) is reduced to a well-defined half-plane. For $B>1+\beta +\delta$, the scenario (i) becomes globally attractor. Scenarios (ii) and (iii) are compatible with the so-called self-curing since the HV is removed from the population. Sensitivity analyses indicate that model dynamics largely depend on DVGs production rate (β) and their replicative advantage (δ), and on both the infection rates and virus-induced cell deaths. Finally, the model has been fitted to single-passage experimental data using an artificial intelligence methodology based on genetic algorithms and key virological parameters have been estimated.

This work introduces an innovative strategy for mitigating shadow effects in images through the utilization of a time-fractionated anisotropic osmosis equation. The method goes beyond conventional approaches by incorporating a newly derived bilateral total variation (BTV) term, coupled with a nonlinear anisotropic transport component. Theoretical insights are rigorously presented, accompanied by a meticulous exposition of the discretization scheme based on finite differences. In addition to the theoretical foundation, the paper conducts comprehensive numerical experiments to validate the proposed model's efficacy. These experiments not only affirm the qualitative advantages of the anisotropic osmosis model but also provide quantitative evidence of its superiority over existing state-of-the-art techniques.

This work delves into the study of stresses induced in a non-homogeneous pre-stressed nearly incompressible elastic substrate with irregularity as a result of a normal load moving on its rough surface. The irregularity on the free surface of the substrate is considered in the form of parabolic irregularity. The solution methodology features the applicability of perturbation method along with substitution method to obtain the displacement components. The expressions of the induced shear and normal stresses have been established in closed form, and their expressions for special cases of the considered problem have also been deduced, which concur well with the existing literature. The influences of affecting parameters viz., non-homogeneity, frictional coefficient, irregularity factor, irregularity depth, hydrostatic stress and depth of the substrate on shear and normal stresses have been depicted graphically by means of numerical computation. The computational results have been manifested for distinct cases of irregularity zone involving parabolic as well as rectangular irregularities present in the considered geometrical model. It has been figured out that the presence of non-homogeneity in the irregular substrate has significant impact on the developed stresses.

This paper proposes two realistic and biologically viable methods for Wolbachia-based biocontrol of Aedes aegypti mosquitoes, assuming imperfect maternal transmission of the Wolbachia bacterium, incomplete cytoplasmic incompatibility, and direct loss of Wolbachia infection caused by thermal stress. Both methods are based on optimization approaches and allow for the stable persistence of Wolbachia-infected mosquitoes in the wild Ae. aegypti populations in a minimum time and using the smallest quantity of Wolbachia-carrying insects to release. The first method stems from the continuous-time optimal release strategy, which is further transformed into a sequence of suboptimal impulses mimicking instantaneous releases of Wolbachia-carrying insects. The second method constitutes a novel alternative to all existing techniques aimed at the design of release strategies. It is developed using metaheuristics (ϵ-constraint method combined with the genetic algorithm) and directly produces a discrete sequence of decisions, where each element represents the quantity of Wolbachia-carrying mosquitoes to be released instantaneously and only once per a specified time unit. It turns out that a direct discrete-time optimization (second method) renders better quantifiable results compared to transforming a continuous-time optimal release function into a sequence of suboptimal impulses (first method). As an illustration, we provide examples of daily, weekly, and fortnightly release strategies designed by both methods for two Wolbachia strains, wMel and wMelPop.

The precise quantification of the internal force field in MEMS piezoresistive sensor micro structure is crucial for ensuring accurate signal output. This paper proposes and proves the complementary energy principle associated with modified couple stress theory (MCST) based on the linear elasticity assumption. And this principle is used to discuss and analyze whether there is a size effect in the internal force field of functionally graded (FG) micro beams for the MEMS piezoresistive sensor. The results show that the size effects exist in the internal forces and the stationary point coordinate x of the total moment for the micro beam. The size effects are related to the dimensionless material scale parameter l/h, the supported spring stiffness, the temperature and the support rotational movements. Intuitive explanations of the size effects are given for the internal force fields and its stationary point coordinates. Behaviors of the solutions agree with the published data when the MCST degenerates into the classical theory (CT).

With the acceleration of urbanization and aging process, an increasing number of Chinese senior citizens are suffering from cardiovascular diseases (CVDs). Therefore, reducing the prevalence and mortality of CVD has become one of the priorities of the public health department. And the scientific prediction of CVD morality is of great significance in the prevention and treatment of CVD among the elderly. Given the characteristics of “small sample, complex causes and long duration” of CVD among the senior citizens, grey prediction models which aim at handling the data with “small sample, poor information” are more feasible in forecasting its developing trend. In this paper, a new discrete grey prediction model is designed to forecast the CVD morality among Chinese senior citizens, in which a non-linear function is introduced to expand the model structure and the order and background value coefficient are optimized. In all the three sets of experiments, the errors of the new model are close to but smaller than those of the other three mainstream grey prediction models, indicating that the simulation and prediction performance of the new model is more accurate and stable. The research provides a new modelling approach to predicting the CVD mortality among Chinese senior citizens, which is conducive to the prevention of CVD prevalence and the sustainable development of public health.

The move towards a circular economy represents an urgent need for production and distribution systems. For this reason, traditional supply chains must rearrange their structures and configurations to reduce virgin material extraction, as well as production and end-of-life products that are sent to landfill. However, many questions regarding the dynamic behavior of circular supply chains remain unsolved. The aim of this work is to contribute to the literature on circular supply chains by investigating their dynamics when there are several reverse loops, i.e., the products delivered to the final customer have been either produced from virgin materials, by the remanufacturing of end-of-life products, or by the use of by-products generated in another supply chain. Using a full factorial design of experiments and a difference equation modelling approach, a wide range of supply chain scenarios with different return and by-product usage rates are analyzed, and their dynamic and economic performance is evaluated. Our results suggest that there is a combined effect of the return rate and the by-product rate on the dynamic behavior of the supply chain. When their combination exceeds a stability threshold, the order amplification disappears, at the expense of unmanageable inventories. However, they also show that, below this threshold, circular supply chains can outperform traditional ones.

In order to solve the problem of the deterioration of the vehicle vertical vibration caused by the introduction of hub motor, to study the interaction mechanism between the electric vehicle (EV) and the road, to analyze the coupling relationship between vehicle vibration and unbalanced electromagnetic force, road surface irregularity, road vibration and other factors and their influence on the vertical performance of the vehicle, the hub motor driving EV and sandwich plate road coupling model is proposed and established. The electromagnetic excitation of switched reluctance motor (SRM) is obtained with Maxwell's tensor theory, the vertical dynamic response of viscoelastic sandwich plat road system is derived analytically by the methods of Galerkin and Duhamel integral, and then the proposed solution is verified by comparing the measurement data in the references. On this basis, the effects of motor excitation, road surface irregularity, vehicle-road coupling vibration and vehicle speed on road and vehicle response are analyzed. The results show that motor excitation has greater influence on the road response, followed by the influence of vehicle-road coupling, and motor excitation make the road response increase and fluctuate. Motor excitation has greater effects on tire dynamic load, body acceleration and roll angle acceleration, followed by suspension dynamic deformation and pitch angle acceleration, and the influence of vehicle-road coupling on vehicle response is relatively small. Moreover, when driving at low speed and smooth road, the effects of motor excitation and vehicle-road coupling vibration on vehicle response is more prominent and should be taken seriously. The negative effects introduced by the comprehensive excitations need to be considered in actual engineering and vertical dynamic analysis of hub motor driving EVs.

In practice, transient gas transport problems frequently have to be solved for large-scale gas networks. Gas network optimization problems typically belong to the class of Mixed-Integer Nonlinear Programming Problems (MINLP). However current state-of-the-art MINLP solvers are not yet mature enough to solve large-scale real-world instances. Therefore, an established approach in practice is to solve the problems with respect to a coarser representation of the network and thereby reducing the size of the underlying model. Two well-known aggregation methods that effectively reduce the network size are parallel and serial pipe merges. However, these methods have only been studied in stationary gas transport problems so far. This paper closes this gap and presents parallel and serial pipe merging methods for transient gas transport problems. An empirical evaluation indicates that the developed methods perform very accurately on a huge set of fine-grained real-world data taken from one of the largest transmission system operators in Europe.

The non-Gaussian rough surface simulation method with desired spatial distribution and height distribution is generally used to analyse the contact characteristics of rough surfaces under different contact conditions. Conventional surface simulation methods have disadvantages in terms of their range, accuracy, and stability. In this study, the analytical function method is enhanced to generate non-Gaussian random number matrices. The enhanced method was combined with the spectral representation method and an iterative algorithm to accurately and stably generate rough surfaces characterized by extensive skewness, kurtosis and autocorrelation lengths. The skewness and kurtosis range of the generated rough surface includes skewness and kurtosis of most engineering surfaces, such as worn surfaces and various machined surface and irregular engineering surfaces. A rough surface is easily generated ≤ 10 s.