Analysis and Dynamics of Fractional Order Mathematical Model of COVID-19in Nigeria Using Atangana-Baleanu Operator

We propose a mathematical model of the coronavirus disease 2019(COVID-19)to investigate the transmission and control mechanism of the disease in the community of Nigeria.Using stability theory of differential equations,the qualitative behavior of model is studied.The pandemic indicator represented by basic reproductive number R0 is obtained from the largest eigenvalue of the next-generation matrix.Local as well as global asymptotic stability conditions for the disease-free and pandemic equilibrium are obtained which determines the conditions to stabilize the exponential spread of the disease.Further,we examined this model by using Atangana–Baleanu fractional derivative operator and existence criteria of solution for the operator is established.We consider the data of reported infection cases from April 1,2020,till April 30,2020,and parameterized the model.We have used one of the reliable and efficient method known as iterative Laplace transform to obtain numerical simulations.The impacts of various biological parameters on transmission dynamics of COVID-19 is examined.These results are based on different values of the fractional parameter and serve as a control parameter to identify the significant strategies for the control of the disease.In the end,the obtained results are demonstrated graphically to justify our theoretical findings.

Non-Linear Mathematical Model of the Interaction between Tumor and Oncolytic Viruses

A mathematical modeling of tumor therapy with oncolytic viruses is discussed. The model consists of two coupled, deterministic differential equations allowing for cell reproduction and death, and cell infection. The model is one of the conceptual mathematical models of tumor growth that treat a tumor as a dynamic society of interacting cells. In this paper, we obtain an approximate analytical expression of uninfected and infected cell population by solving the non-linear equations using Homotopy analysis method (HAM). Furthermore, the results are compared with the numerical simulation of the problem using Matlab program. The obtained results are valid for the whole solution domain.

Mass and heat transfer mechanism in wood during radio frequency/vacuum drying and numerical analysis

The mass and heat transfer mechanisms during radio frequency/vacuum （RF/V） drying of square-edged timber were analyzed and discussed in detail, and a new one-dimensional mathematical model to describe the transport phenomena of mass and heat during continuous RF/V drying was derived from conservation equations based on the mass and heat transfer theory of porous materials The new model provided a relatively fast and efficient way to simulate vacuum drying behavior assisted by dielectric heating. Its advantages compared with the conventional models include： （1） Each independent vari- able has a separate control equation and is solved inde- pendently by converting the partial differential equation into a difference equation with the finite volume method; （2） The calculated data from different parts of the specimen can be displayed in the evolution curves, and the change law of the,parameters can be better described. After analyzing the calculated results, most of the important phenomena observed during RF/V drying were adequately described by this model.

STRUCTURAL DAMAGE MODEL OF UNSATURATED EXPANSIVE SOIL AND ITS APPLICATION IN MULTI-FIELD COUPLE ANALYSIS ON EXPANSIVE SOIL SLOPE

Focused on the sensitivity to climate change and the special mechanical characteristics of undisturbed expansive soil, an elasto-plastic damage constitutive model was proposed based on the mechanics of unsaturated soil and the mechanics of damage. Undisturbed expansive soil was considered as a compound of non-damaged part and damaged part. The behavior of the non-damaged part was described using non-linear constitutive model of unsaturated soil. The property of the damaged part was described using a damage evolution equation and two yield surfaces, i.e., loading yield （LY） and shear yield （SY）. Furthermore, a consolidation model for unsaturated undisturbed expansive soil was established and a FEM program named UESEPDC was designed. Numerical analysis on solid-liquid-gas tri-phases and multi-field couple problem was conducted for four stages and fields of stress, displacement, pore water pressure, pore air pressure, water content, suction, and the damage region as well as plastic region in an expansive soil slope were obtained.

SOLID-GAS INTERACTION MODELLING FOR MINING SAFETY RANGE AND NUMERICAL SIMULATIONS

Coal and gas outburst is one of the most serious natural calamities in collieries. And protective layer mining is an effective regional method for preventing and controlling coal outburst. However, how to rationally determine the mining safety range in coal mining of protective layer with quantitative analysis is a difficult problem in rock mechanics and mining engineering so far. Then in this paper applied solid gas interaction mechanics for gas leakage flow, the solid gas interaction analysis for the safety range of up protective layer mining has been achieved with the results of experimental research and in situ measurements so that the result of numerical simulation for the difficult problem is closer to reality. Furthermore, the safety range of up protective layer mining can be determined with time dependent based on the result of numerical simulation.

Numerical modelling and simulation analysis of wind blades:a critical review

Wind energy has emerged as a promising renewable energy source and wind turbine technology has developed rapidly in recent years.Improved wind turbine performance depends heavily on the design and optimization of wind blades.This work offers a critical evaluation of the state of the art in the field of numerical modelling and simulation analysis,which have become crucial for the design and optimization of wind blades.The evaluation of the literature includes considerable research on the application of numerical methods for the structural and aerodynamic performance of wind blades under various operating situations,as well as for analysis and optimization of wind blades.The article illustrates how numerical techniques can be used to analyse wind blade performance and maximize design efficiency.The study of blade performance under various wind conditions has also been made possible through the use of simulation analysis,thus enhancing the efficiency and dependability of wind turbines.Improvements in wind turbine efficiency and dependability,and ultimately the move towards a more sustainable energy future,will be greatly helpful for the development of numerical modelling and simulation techniques.

Perturbation Analysis of the Attached Water Mass Effect on Offshore Platform Dynamic Response

Theoretically speaking, it is impossible to make the differential equation of motion uncoupled for the natural modes of a system in consideration of the attached water. The hydro-elastic structure is equal to the non-proportional damping system. In this paper a perturbation analysis method is put forward. The structure motion equation is strictly solved mathematically, and the non-proportional damping problem is transformed into a series of proportional damping ones in the superposition form. The paper also presents the calculation formula of the dynamic response of the structure being subjected to harmonic and arbitrary load. The convergence of the proposed method is also studied in this paper, and the corresponding convergence conditions are given. Finally, the proposed method is used to analyze the displacement response of a real offshore platform. The calculation results show that this method has the characteristics of high accuracy and fast convergence.

Square-Root Dynamics of a SIR-Model in Fractional Order

In this paper, we consider an SIR-model for which the interaction term is the square root of the susceptible and infected individuals in the form of fractional order differential equations. First the non-negative solution of the model in fractional order is presented. Then the local stability analysis of the model in fractional order is discussed. Finally, the general solutions are presented and a discrete-time finite difference scheme is constructed using the nonstandard finite difference (NSFD) method. A comparative study of the classical Runge-Kutta method and ODE45 is presented in the case of integer order derivatives. The solutions obtained are presented graphically.

Mathematical analysis of a tuberculosis model with imperfect vaccine

Since 1921,the Bacille Calmette Guerin(BCG)vaccine continues to be the most widely used vaccine for the prevention of Tuberculosis(TB).However,the immunity induced by BCG wanes out after some time making the vaccinated individual susceptible to TB infection.In this work,we formulate a mathematical model that incorporates the vaccination of newly born children and older susceptible individuals in the transmission dynamics of TB in a population,with a vaccine that can confer protection on older susceptible individuals.In the absence of disease-induced deaths,the model is shown to undergo the phenomenon of backward bifurcation where a stable disease-free equilibrium(DFE)co-exists with a stable positive(endemic)equilibrium when the associated repro-duction number is less than unity.It is shown that this phenomenon does not exist in the absence of imperfect vaccine,exogenous reinfection,and reinfection of prev iously treated individuals.It is further shown that a special case of the model has a unique endemic equilibrium point(EEP),which is globally asymptotically stable when the associated reproduction number exceeds unity.Uncertainty and sensitivity analysis are carried out to identify key parameters that have the greatest infuence on the transmission dynamics of TB in the population using the total population of latently infected individuals,total number of actively infected individuals,disease incidence,and the effective reproduc-tion number as output responses.The analysis shows that the top five parameters of the model that have the greatest influence on the effective reproduction number of the model are the transmission rate,the fraction of fast disease progression,modification parame-ter which accounts for reduced likelihood to infection by vaccinated individuals due to imperfect vaccine,rate of progression from latent to active TB,and the treatment rate of actively infected individuals,with other key parameters infuencing the outcomes of the other output responses.Numerical simulations suggest that with higher vaccination rate of older susceptible individuals,fewer new born children need to be vaccinated,in order to achieve disease eradication.

“有限元-数学模型”融合驱动的地铁下穿既有桥梁变形预测研究

为探究地铁盾构穿越既有桥梁的影响,建立安全有效的变形控制体系,确定更加精准的施工过程变形预测方法。依托乌鲁木齐2号线盾构下穿人民路立交桥工程,采用MIDAS/GTX进行施工过程数值模拟并验证其准确性。通过数值模拟对改变土舱压力、地面预埋袖阀管注浆等方法进行安全控制措施的有效性分析。针对数值模拟+实测数据采用基于小波分析—自适应卡尔曼滤波组合模型进行变形预测,与实测数据及基于实测数据的模型预测值进行对比,探究最佳预测模型。结果表明:数值模拟与实测数据在盾构穿越后各墩台沉降误差及单/双线盾构通过后监测误差均不超过10%,初步验证数值模拟的准确性。利用数值模拟探究土舱压力、地面注浆等方法的有效性,并与实测数据对比进一步验证模型有效性。通过对基于数值模拟+实测数据的小波分析—自适应卡尔曼滤波组合模型预测结果与实测数据及基于实测数据的模型预测结果进行对比分析,发现基于数值模拟+实测数据的组合模型预测结果精度更佳,平均绝对误差与均方误差分别为0.10、0.01 mm,更加接近实测值,为类似工程提供参考。

A Comparative Study of Adomian Decomposition Method with Variational Iteration Method for Solving Linear and Nonlinear Differential Equations

This study compares the Adomian Decomposition Method (ADM) and the Variational Iteration Method (VIM) for solving nonlinear differential equations in engineering. Differential equations are essential for modeling dynamic systems in various disciplines, including biological processes, heat transfer, and control systems. This study addresses first, second, and third-order nonlinear differential equations using Mathematica for data generation and graphing. The ADM, developed by George Adomian, uses Adomian polynomials to handle nonlinear terms, which can be computationally intensive. In contrast, VIM, developed by He, directly iterates the correction functional, providing a more straightforward and efficient approach. This study highlights VIM’s rapid convergence and effectiveness of VIM, particularly for nonlinear problems, where it simplifies calculations and offers direct solutions without polynomial derivation. The results demonstrate VIM’s superior efficiency and rapid convergence of VIM compared with ADM. The VIM’s minimal computational requirements make it practical for real-time applications and complex system modeling. Our findings align with those of previous research, confirming VIM’s efficiency of VIM in various engineering applications. This study emphasizes the importance of selecting appropriate methods based on specific problem requirements. While ADM is valuable for certain nonlinearities, VIM’s approach is ideal for many engineering scenarios. Future research should explore broader applications and hybrid methods to enhance the solution’s accuracy and efficiency. This comprehensive comparison provides valuable guidance for selecting effective numerical methods for differential equations in engineering.

五轴数控机床综合误差建模分析

分析了机床运动副的误差运动学原理 ,利用齐次坐标变换对一台包含 3个移动副和 2个转动副的五轴加工中心建立了误差综合数学模型 .模型中不仅包含了几何误差且包含了热误差 ,共计 5 7个误差元素 .本分析方法可为其他类型的多轴数控机床。

大冶铁矿露天转地下开采的离散元数值模拟研究

离散单元方法特别适合于节理比较发育的岩体。对于模拟和分析矿山中因采矿引起的围岩松动和冒落等力学行为是比较有效的。用离散单元法研究了大冶铁矿狮子山采区露天转地下开采,采用充填法、崩落法采掘对露天边坡和围岩的影响及围岩变形规律,并得出了相应的结论,为设计和方案的选用提供了一些有益的根据。

基于云模型理论的蚁群算法改进研究

近几年优化领域中新出现的蚁群算法采用分布式并行计算机制,易于与其它方法结合,具有较强的鲁棒性,但易限于局部最优解是其最突出的缺点.云模型是一种新的实现定性概念和定量数值之间转换的有力工具,本文在介绍云模型理论的基础上,提出了一种利用云模型来有效限制蚁群算法陷入局部最优解的方法,最后将基于云模型理论的改进蚁群算法与未改进的蚁群算法分别应用于著名的CHC144TSP进行实验.改进后的蚁群算法采用升半正态云规则进行控制,并选取了500个云滴,仿真计算结果证明了该方法的有效性和可行性.

考虑气固耦合填埋场沉降数学模型

为研究城市生活垃圾填埋场孔隙气压对沉降的影响程度,把填埋场简化为非稳定单向气体渗流场,采用Gibson和Lo一维压缩模型及U.S.EPALandgem产气方程,结合达西定律、气体状态方程、有效应力原理和多孔介质流体动力学理论,建立了考虑气固耦合的填埋场沉降计算模型。填埋场的沉降按封场前和封场后2个阶段分别计算,封场前填埋场接受垃圾,堆填压力增加,而封场后的堆填压力保持不变。运用差分法求解的结果表明,填埋场垃圾体内孔隙气压与深度、时间和透气率等因素有关。封场前,气压随深度和时间的增加而增加;封场后,气压随时间逐渐消散。高透气率的填埋场有较高的气体消散速率。封场前气压的增加减小了填埋场沉降速率,从而导致填埋场的容量减少。提出在填埋场沉降计算和边坡稳定分析时考虑气压影响的必要性。

序列运算的扩展及其数字特征

在已建立的序列运算理论基础上进行了进一步扩展。首先提出了一种新的序列运算———合并运算 ,分析了其相应的性质 ;提出了部分概率序列的概念及其与合并运算之间的关系 ,分析了部分概率序列的物理含义。这些内容作为原始的 4种序列运算的补充 ,已经在实际应用中发挥了重要作用。研究了序列运算的逆运算问题 ,提出了反卷和运算的计算方法和存在条件。给出了序列的矩与投影度的概念和数学描述 ,并着重研究了其运算性质。文中的结果 ,使得序列运算理论进一步完善 。

搅拌摩擦焊接热输入数值模型

根据搅拌摩擦焊接特点,建立了轴肩、柱形搅拌针和锥形搅拌针热输入数值模型,并分别讨论了搅拌针锥角对轴肩和锥形搅拌针热输入的影响。结果表明,锥角增大,轴肩热输入降低;锥形搅拌针侧面热输入增大;搅拌针端面热输入降低;搅拌针总的热输入先下降,然后迅速上升。

挡土墙后土体拱效应分析

考虑墙土摩擦角对挡土墙后土体滑裂面倾角的影响,对小主应力拱形状进行了理论分析.根据土拱形状计算平均竖直应力,由此得到了对应不同内摩擦角和墙土摩擦角的侧土压力系数,将其用于水平微分单元法求解挡土墙主动土压力,得到了挡土墙主动土压力强度、土压力合力和合力作用点的理论公式,并与库仑土压力理论和模型试验数据进行了比较分析.结果表明,挡土墙主动土压力强度为非线性分布,与模型试验结果基本吻合;土压力合力与库仑土压力合力相等.

非稳态油品蒸发的数值分析 Ⅱ.数值分析及应用实例

利用已建立的油品蒸发过程油气摩尔分数分布计算数学模型,在确定相关参数后,对储油容器进油及储油过程中油品蒸发和油气排放规律进行数值分析。结果表明,对于正常操作下以自然扩散为主的传质体系,计算值与实测值较吻合。

基于ACK和NAK的可靠组播传输协议的性能分析和比较

本文在目前各种可靠组播传输协议的基础上 ,归纳构建了两类基本的可靠组播传输协议—基于确认(ACK)的和基于否定确认 (NAK)的可靠组播传输协议 .在典型的组播网络系统模型基础上 ,对这两类协议以及一种主要的改进协议在占用网络带宽和可扩展性方面的性能特点进行了定性的分析和比较 .性能分析结果表明 ,基于否定确认且采用否定确认压缩策略 (NAKCompression)的可靠组播传输协议成功传输组播数据包所需要的带宽较小 。