Stochastic Numerical Analysis for Impact of Heavy Alcohol Consumption on Transmission Dynamics of Gonorrhoea Epidemic

This paper aims to perform a comparison of deterministic and stochastic models. The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model. Also, the deterministic solution is itself mean of the stochastic solution of the model. For numerical analysis, first, we developed some explicit stochastic methods, but unfortunately, they do not remain consistent in certain situations. Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model. The proposed method is independent of the choice of parameters and behaves well in all scenarios. So, some theorems and simulations are presented in support of the article.     

一个计算机病毒传播数学模型的建立与研究

基于流行病数学模型的建模方法,建立了一个对等网中的关于计算机病毒传播的时滞微分方程模型,模型中考虑了计算机病毒的潜伏期与反病毒技术出现时间。利用微分动力系统理论研究了单种计算机病毒的传播规律,得到了病毒是否消除的阈值。最后对论文结果进行了讨论与数值模拟。论文的研究成果为计算机病毒控制提供理论基础。     

A Reliable Stochastic Numerical Analysis for Typhoid Fever Incorporating With Protection Against Infection

In this paper, a reliable stochastic numerical analysis for typhoid fever incorporating with protection against infection has been considered. We have compared the solutions of stochastic and deterministic typhoid fever model. It has been shown that the stochastic typhoid fever model is more realistic as compared to the deterministic typhoid fever model. The effect of threshold number T* hold in stochastic typhoid fever model. The proposed framework of the stochastic non-standard finite difference scheme (SNSFD) preserves all dynamical properties like positivity, bounded-ness and dynamical consistency defined by Mickens, R. E. The stochastic numerical simulation of the model showed that increase in protection leads to low disease prevalence in a population.     

一类具有垂直传播的HIV模型的稳定性分析

根据艾滋病的传播规律,本文建立了一类传染病模型.在模型中,HIV携带者分为幼年和成年两类,HIV可垂直传染,艾滋病患者有额外死亡.我们用再生矩阵求出了模型的基本再生数,并得出当基本再生数小于1时,模型只有无病平衡点,而当基本再生数大于1时,模型还有地方病平衡点.最后,应用第二加性复合矩阵等理论,文中证明了各平衡点全局渐近稳定性.     

Structure-Preserving Dynamics of Stochastic Epidemic Model with the Saturated Incidence Rate

The structure-preserving features of the nonlinear stochastic models are positivity, dynamical consistency and boundedness. These features have a significant role in different fields of computational biology and many more. Unfortunately, the existing stochastic approaches in literature do not restore aforesaid structure-preserving features, particularly for the stochastic models. Therefore, these gaps should be occupied up in literature, by constructing the structure-preserving features preserving numerical approach. This writing aims to describe the structure-preserving dynamics of the stochastic model. We have analysed the effect of reproduction number in stochastic modelling the same as described in the literature for deterministic modelling. The usual explicit stochastic numerical approaches are time-dependent. We have developed the implicitly driven explicit approach for the stochastic epidemic model. We have proved that the newly developed approach is preserving the structural, dynamical properties as positivity, boundedness and dynamical consistency. Finally, convergence analysis of a newly developed approach and graphically illustration is also presented.     

Spatio-Temporal Dynamics and Structure Preserving Algorithm for Computer Virus Model

The present work is related to the numerical investigation of the spatio-temporal susceptible-latent-breaking out-recovered (SLBR) epidemic model. It describes the computer virus dynamics with vertical transmission via the internet. In these types of dynamics models, the absolute values of the state variables are the fundamental requirement that must be fulfilled by the numerical design. By taking into account this key property, the positivity preserving algorithm is designed to solve the underlying SLBR system. Since, the state variables associated with the phenomenon, represent the computer nodes, so they must take in absolute. Moreover, the continuous system (SLBR) acquires two steady states i.e., the virus-free state and the virus existence state. The stability of the numerical design, at the equilibrium points, portrays an exceptional aspect about the propagation of the virus. The designed discretization algorithm sustains the stability of both the steady states. The computer simulations also endorse that the proposed discretization algorithm retains all the traits of the continuous SLBR model with spatial content. The stability and consistency of the proposed algorithm are verified, mathematically. All the facts are also ascertained by numerical simulations.     

Deterministic and Stochastic Fractional-Order Hastings-Powell Food Chain Model

In this paper, a deterministic and stochastic fractional-order model of the tri-trophic food chain model incorporating harvesting is proposed and analysed. The interaction between prey, middle predator and top predator population is investigated. In order to clarify the characteristics of the proposed model, the analysis of existence, uniqueness, non-negativity and boundedness of the solutions of the proposed model are examined. Some sufficient conditions that ensure the local and global stability of equilibrium points are obtained. By using stability analysis of the fractional-order system, it is proved that if the basic reproduction number , the predator free equilibrium point is globally asymptotically stable. The occurrence of local bifurcation near the equilibrium points is investigated with the help of Sotomayor’s theorem. Some numerical examples are given to illustrate the theoretical findings. The impact of harvesting on prey and the middle predator is studied. We conclude that harvesting parameters can control the dynamics of the middle predator. A numerical approximation method is developed for the proposed stochastic fractional-order model.     

Computer Aided Model for Casting Aluminium Using Die-Casting

Computer aided casting of aluminum using die-casting was developed. A piston, which is an automobile part and very important in internal combination engine, was chosen for the research. Pistons are made of aluminum alloy. Models of the products were developed to aid the casting process. Mathematical models that show the dimensions of the casting were also developed. Since the project is about using computer to aid casting process, a program using visual basic （VB） Language was developed. The program was used to incorporate die-casting process into computer system. The written program was tested and the model of the casting product （piston） was displayed. The result shows that computer which is faster with accurate result can be used as an aid in the production of aluminum piston using die-casting process, for accurate planning in the manufacture of the product.     

An Effective Numerical Method for the Solution of a Stochastic Coronavirus (2019-nCovid) Pandemic Model

Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model. The comparison of the results of deterministic and stochastic models is also presented. Our proposed efficient computational method well preserves the essential properties of the model. Comparison and convergence analyses of the method are presented.     

随机调幅Rattling振动的二级传动模型

迫击 (Rattling)振动是汽车齿轮传动中不期望产生的振动 ,它是由于齿轮传动过程中在空载作用下产生的 ,目前已得到许多专家与学者的关注。本文研究随机调幅二级传动的 Rattling振动 ,直接采用非高斯截断技术 ,导出一个用平均映射描述的离散随机模型 ,并通过平均庞加莱图和平均速度的功率谱密度揭示随机调幅 Rattling振动的二级传动随机模型的性质 ,同时通过最大李雅普诺夫指数给出混沌发生的参数域。     

Gaussian Surrogates for Computer Models With Time-Varying Inputs and Outputs

Computer models of dynamic systems produce outputs that are functions of time; models that solve systems of differential equations often have this character. In many cases, time series output can be usefully reduced via principal components to simplify analysis. Time-indexed inputs, such as the functions that describe time-varying boundary conditions, are also common with such models. However, inputs that are functions of time often do not have one or a few “characteristic shapes” that are more common with output functions, and so, principal component representation has less potential for reducing the dimension of input functions. In this article, Gaussian process surrogates are described for models with inputs and outputs that are both functions of time. The focus is on construction of an appropriate covariance structure for such surrogates, some experimental design issues, and an application to a model of marrow cell dynamics.     

非对称随机波动模型的参数估计及其实证

研究非对称随机波动模型参数的贝叶斯估计问题,提出一种计算参数贝叶斯估计量的MCMC (Markov Chain Monte Carlo)算法。并利用此算法对中国股市波动的非对称现象进行了实证分析。     

随机网络瓶颈容量扩张的期望值模型

在不确定的环境下,怎样去增加一组边的容量到一个指定的瓶颈容量,以至于网络瓶颈扩张的费用最小。假定每一条边的单位扩张费用形是一个随机的变量,它服从正态分布。带有随机单位扩张费用W的网络瓶颈客量扩张问题可以根据一些概率统计规则,列出它的期望值模型的通用表达式。随后,网络瓶颈容量算法、随机模拟方法和遗传算法将合成在一起,设计出该问题的混合智能算法。最后。给出数值案例。     

不确定车数的随机车辆路径问题模型及算法

研究了一类有时间约束、车辆数量不确定的随机车辆路径问题;建立了该类问题的随机规划数学模型;设计了模型求解的遗传算法、禁忌搜索算法和遗传-禁忌混合算法.禁忌算法采用了对当前解的车辆-顾客分配结构和解的路径顺序分别禁忌的双层禁忌算法,使算法全局性更好,同时也降低了搜索时间.把禁忌算法作为变异算子应用于遗传算法形成了混合算法.最后给出了计算示例,对算法进行了比较分析.     

随机潜蚤病模型的动力学行为分析

潜蚤病是贫困地区的一种人畜共患病,其发病过程极易受到随机波动环境因素的影响。因此,建立并讨论了一类以正确卫生习惯为控制策略的随机潜蚤病模型。首先,通过构造恰当的Lyapunov函数并利用It$\hat{\rm o}$公式证明了随机系统全局正解的存在唯一性。其次,在一定的条件下证明了随机系统的正解围绕在确定性系统平衡点附近的振荡行为。最后,通过数值模拟验证了理论结果的正确性。数值结果表明,当随机干扰强度足够大时将会导致疾病灭绝。     

随机局部弹性与分批连续进货的随机存储模型

利用随机局部弹性的概念及运算法则,研究了分批连续进货并允许缺货的存储模型中,总费用对随机最高存储量与随机采购周期的局部弹性,给出了总费用弹性的联合概率密度的一般表达式,通过实例证明了当最高存储量与采购周期的分布特性已知时,总费用的弹性分布和弹性变化范围及弹性在该变化范围的可信度。     

A Stochastic EM Algorithm for Progressively Censored Data Analysis

Progressive censoring technique is useful in lifetime data analysis. Simple approaches to progressive data analysis are crucial for its widespread adoption by reliability engineers. This study develops an efficient yet easy‐to‐implement framework for analyzing progressively censored data by making use of the stochastic EM algorithm. On the basis of this framework, we develop specific stochastic EM procedures for several popular lifetime models. These procedures are shown to be very simple. We then demonstrate the applicability and efficiency of the stochastic EM algorithm by a fatigue life data set with proper modification and by a progressively censored data set from a life test on hard disk drives. Copyright © 2013 John Wiley & Sons, Ltd.