Partial Differential Equations in Applied Mathematics最新文献_第2页

Optimizing control strategies for monkeypox through mathematical modeling 通过数学建模优化猴痘控制策略

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-26 DOI: 10.1016/j.padiff.2024.100996

Mohamed Baroudi , Imane Smouni , Hicham Gourram , Abderrahim Labzai , Mohamed Belam

Monkeypox is a zoonotic viral disease similar to smallpox, has emerged as a major global health concern following the COVID-19 pandemic. This study presents a novel mathematical model aimed at analyzing various epidemiological factors, particularly the less-explored transmission from humans to monkeys, where both species act as carriers. Our approach integrates comprehensive awareness campaigns, strict security measures, and targeted health interventions to limit transmission between hosts, with the goal of reducing human infections and eliminating the virus among animal populations. The model utilizes the continuous-time Pontryagin maximum principle to determine and apply optimal control strategies, with iterative simulations conducted in Matlab. Our results, derived from these simulations, show that implementing all proposed preventative strategies—such as public awareness efforts, isolation of infected monkeys, and vaccination—simultaneously is the most effective method to control the virus’s spread. We observed a significant reduction in both human and animal infections when these strategies were combined. The study’s conclusions provide important insights into the transmission dynamics of monkeypox, highlighting the critical role of multifaceted intervention strategies in controlling outbreaks. These findings are expected to support more effective public health management and contribute to the global effort to contain and ultimately eradicate monkeypox.

猴痘是一种类似于天花的人畜共患病毒性疾病，在 COVID-19 大流行之后已成为全球关注的主要健康问题。本研究提出了一个新颖的数学模型，旨在分析各种流行病学因素，尤其是较少被研究的人猴传播，因为人猴都是病毒携带者。我们的方法整合了全面的宣传活动、严格的安全措施和有针对性的健康干预措施，以限制宿主之间的传播，从而达到减少人类感染和消灭动物群体中病毒的目的。该模型利用连续时间庞特里亚金最大原则来确定和应用最优控制策略，并在 Matlab 中进行迭代模拟。模拟结果表明，同时实施所有建议的预防策略，如提高公众意识、隔离受感染的猴子和接种疫苗，是控制病毒传播的最有效方法。我们观察到，当这些策略结合使用时，人类和动物的感染率都大幅下降。这项研究的结论为我们了解猴痘的传播动态提供了重要依据，突出了多方面干预策略在控制疫情爆发中的关键作用。这些发现有望为更有效的公共卫生管理提供支持，并有助于全球遏制并最终根除猴痘的努力。

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引用次数: 0

Numerical investigation of fractional order SEIR models with newborn immunization using Vieta–Fibonacci wavelets 使用 Vieta-Fibonacci 小波对带有新生儿免疫的分数阶 SEIR 模型进行数值研究

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-23 DOI: 10.1016/j.padiff.2024.100995

Naied A. Nayied , Firdous A. Shah , Mukhtar A. Khanday , Kottakkaran Sooppy Nisar

In this article, we investigate the dynamics of a fractional-order SEIR epidemic model with special emphasis on the vaccination of newborns. By incorporating vaccination directly into the SEIR framework, newborns bypass the susceptible stage and enter the immune class directly, which enhances herd immunity and contributes to the overall reduction in disease spread. A novel operational matrix method based on Vieta–Fibonacci wavelets is developed to approximate the fractional-order SEIR model that includes newborn immunization, where the fractional derivative is taken in the Caputo sense. To begin with, the operational matrices of fractional-order integration are obtained via block-pulse functions. These matrices convert the underlying model into a system of algebraic equations that can solved using any classical method, such as Newton’s iterative method, Broyden’s method, or fsolve command in MATLAB software. The Haar wavelet method is also discussed to show its applicability and efficiency. The obtained results lucidly illustrate the dynamics of susceptible, exposed, infected, and recovered populations during an infectious outbreak. The decline in susceptible and infected individuals reflects the disease’s progression, while vaccination significantly reduces infection peaks. Variations in the fractional parameter

α

and transmission factor

β

reveal the influence of these variables on the disease outbreak, with higher values of

β

leading to rapid transmission. The chaotic attractors of the fractional-order SEIR epidemic model with newborn immunization are graphically represented using Vieta–Fibonacci wavelets.

在本文中，我们研究了分数阶 SEIR 流行病模型的动力学，并特别强调了新生儿的疫苗接种。通过将疫苗接种直接纳入 SEIR 框架，新生儿可以绕过易感阶段，直接进入免疫阶段，从而增强群体免疫力，有助于全面减少疾病传播。本文开发了一种基于 Vieta-Fibonacci 小波的新型运算矩阵方法，用于近似包含新生儿免疫的分数阶 SEIR 模型，其中分数导数是在 Caputo 意义上取的。首先，通过块脉冲函数获得分数阶积分的运算矩阵。这些矩阵将基础模型转换为代数方程系统，可使用任何经典方法求解，如牛顿迭代法、布罗伊登法或 MATLAB 软件中的 fsolve 命令。此外，还讨论了哈小波方法，以显示其适用性和效率。所得结果清楚地说明了传染病爆发期间易感人群、暴露人群、感染人群和康复人群的动态变化。易感人群和感染人群的减少反映了疾病的进展，而疫苗接种则显著降低了感染高峰。分形参数 α 和传播因子 β 的变化揭示了这些变量对疾病爆发的影响，β 值越高，传播速度越快。使用 Vieta-Fibonacci 小波对带有新生儿免疫的分数阶 SEIR 流行模型的混沌吸引子进行了图解。

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引用次数: 0

Comprehensive analysis of noise behavior influenced by random effects in stochastic differential equations 随机微分方程中受随机效应影响的噪声行为综合分析

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-23 DOI: 10.1016/j.padiff.2024.100997

Maryam Kousar , Adil Jhangeer , Muhammad Muddassar

Stochastic differential equations are practical tools for modeling systems in which stochastic effects prevail, distinguishing it from deterministic models. Qualitative and quantitative analyses of a specific observed model are possible with the help of a thorough discrimination framework of such systems. The effectiveness of the method is supported by exact results derived from the model using necessary constraint conditions. This study looks at how model parameters influence solution behavior with two and three dimensions. In addition, numerical studies are conducted to validate the theoretical findings and determine the stability of the system under different circumstances. Therefore, when the model is reformulated as a dynamical system, we get the Hamiltonian and topological characteristics, bifurcation theory, Lyapunov coefficients, quasiperiodic, and chaos. The analysis of the sustained chaotic behavior by outer forms of control offers greater insight into the dynamics of the proposed model. The findings further indicate possible uses of this model in areas such as climatology where stochastic disturbances play a major role in system behavior. Hence, the current study shares enough methodological improvement for analytical problems in engineering, physics, and mathematics, especially the non-linearities solved with stochastic models.

随机微分方程是模拟系统的实用工具，在这些系统中，随机效应占主导地位，有别于确定性模型。借助对此类系统的全面判别框架，可以对特定观测模型进行定性和定量分析。利用必要的约束条件从模型中得出的精确结果支持了该方法的有效性。本研究探讨了模型参数如何影响二维和三维的求解行为。此外，还进行了数值研究，以验证理论结论，并确定系统在不同情况下的稳定性。因此，当模型被重新表述为一个动力学系统时，我们得到了哈密顿和拓扑特征、分岔理论、Lyapunov 系数、准周期和混沌。通过对外部控制形式的持续混沌行为的分析，我们对所提模型的动力学有了更深入的了解。研究结果进一步表明，该模型可用于气候学等领域，因为随机干扰在系统行为中发挥着重要作用。因此，当前的研究为工程、物理和数学领域的分析问题，尤其是用随机模型求解的非线性问题，提供了足够的方法改进。

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引用次数: 0

Blow-up study of a nonlinear hyperbolic system with delay 带延迟的非线性双曲系统的爆炸研究

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-23 DOI: 10.1016/j.padiff.2024.100984

Mohammad Kafini, Mohammad M. Al-Gharabli, Adel M. Al-Mahdi

This work examines a system of wave equations that feature frictional damping and nonlinear sources. The two equations are affected by constant delay. By demonstrating that there exist solutions with negative initial energy that blow up in a finite amount of time, we prove a blow-up result. Levine’s concavity approach is a basis of the proof. Additionally, by estimating the lower bound, we dominate the blow-up time from below.

这项工作研究的是以摩擦阻尼和非线性源为特征的波方程系统。这两个方程受到恒定延迟的影响。通过证明存在在有限时间内炸毁的负初始能量解，我们证明了炸毁结果。莱文的凹性方法是证明的基础。此外，通过对下限的估计，我们从下往上控制了炸毁时间。

引用次数: 0

New general single, double and triple conformable integral transforms: Definitions, properties and applications 新的一般单、双和三保形积分变换：定义、性质和应用

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-22 DOI: 10.1016/j.padiff.2024.100991

Mohammad Hossein Akrami , Abbas Poya , Mohammad Ali Zirak

This study introduces an innovative general adaptive integral transform in single, double and triple types. This article outlines the definitions of these new transformations and establishes their main characteristics in each species. In addition, it examines the connections between newly introduced generic transformations and existing transformations. It is shown that previously developed adaptive transforms, including Laplace, Sumodo, Elzaki, G-transforms, Pourreza, and Aboodh, appear as special cases of this general adaptive transform. Furthermore, the effectiveness of the conformal generalized transform is demonstrated through its application in solving different types of linear and nonlinear fractional differential equations. Such as Black–Scholes and Berger’s equations, to demonstrating its proficiency in this domain. The proposed approach demonstrates versatility by encompassing nearly all conformable integral transforms of orders one, two, and three. As a result, it eliminates the need to derive new formulas for single, double, and triple conformable integral transforms, streamlining the process and enhancing the efficiency of solving related problems.

本研究介绍了一种创新性的通用自适应积分变换，分为单一、双重和三重类型。本文概述了这些新变换的定义，并确定了它们在各类型中的主要特征。此外，文章还探讨了新引入的通用变换与现有变换之间的联系。研究表明，以前开发的自适应变换，包括拉普拉斯变换、苏莫多变换、埃尔扎基变换、G 变换、普雷扎变换和阿布德变换，都是这种通用自适应变换的特例。此外，保角广义变换在求解不同类型的线性和非线性分数微分方程中的应用也证明了它的有效性。如布莱克-斯科尔斯方程和伯格方程，以证明其在这一领域的熟练程度。所提出的方法涵盖了几乎所有一阶、二阶和三阶的保形积分变换，展示了其多功能性。因此，它消除了为单、双和三保形积分变换推导新公式的需要，简化了过程并提高了解决相关问题的效率。

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引用次数: 0

Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations 百日咳 SVEIQRP 模型的分形分数微分方程系统动力学行为

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-19 DOI: 10.1016/j.padiff.2024.100990

Razia Begum , Sajjad Ali , Nahid Fatima , Kamal Shah , Thabet Abdeljawad

In this work, the application of the system of fractal fractional differential equations is exploited. Infectious diseases modeling of non-integer order attracts many mathematicians and biological scientists. The presentation of an advanced fractal fractional model for studying the exact dynamical behavior of infectious diseases in epidemiology is necessary. In this study, a new version of a mathematical model for whooping cough is presented. Whooping cough is a disease and can be transmitted from humans to humans through various means, i.e., touch, cough, and air droplets. In this study, we considered the whooping cough model with a new permanent compartment. Our modified model after incorporating the permanent recovered compartment explains better regarding the individuals who have developed long term immunity against whooping cough. This addition to the model enhances the model’s accuracy towards real world scenarios. The considered model was analyzed by using a system of fractal fractional differential equations, and numerical simulation was established for the findings of this study. The fixed point theorem was used to determine the existence, uniqueness, and Hyers–Ulam stability of the model. Numerical results of the dynamical behavior of the model are also recorded in tables.

这项工作利用了分形分微分方程系统的应用。非整数阶的传染病模型吸引了众多数学家和生物科学家。有必要提出一种先进的分形分数模型，用于研究流行病学中传染病的精确动力学行为。本研究提出了百日咳数学模型的新版本。百日咳是一种疾病，可通过接触、咳嗽和空气飞沫等多种途径在人与人之间传播。在这项研究中，我们考虑了百日咳模型，并增加了一个新的永久隔室。加入永久恢复区后，我们修改后的模型能更好地解释对百日咳产生长期免疫力的个体。对模型的这一补充增强了模型在现实世界中的准确性。我们使用分形分数微分方程系统分析了所考虑的模型，并对研究结果进行了数值模拟。利用定点定理确定了模型的存在性、唯一性和 Hyers-Ulam 稳定性。模型动力学行为的数值结果也记录在表格中。

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引用次数: 0

The effect of surface tension on axisymmetric confined viscous gravity currents 表面张力对轴对称封闭粘性重力流的影响

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-16 DOI: 10.1016/j.padiff.2024.100992

A.J. Hutchinson

We consider the radial spreading of an axisymmetric viscous gravity current, in which fluid released from a point source at a constant flux is confined vertically to a narrow gap between two horizontal plates. A grounding line forms where the free surface of the current intersects with the top plate, creating two regions of flow: an inner, circular contact region near to the source where the fluid fills the entire gap between the two plates; and an outer annular region where the free surface of the gravity current lies below the top plate. Mathematical models of such flows involve solving a partial differential equation for the height of the free surface, subject to appropriate boundary conditions at the grounding line and at the leading edge of the current. In many cases, these systems admit similarity solutions. I will present one such model where the effects of surface tension are included locally at the grounding line and at the leading edge, leading to similarity solutions that depend on two dimensionless parameters,

J

and

S

, which measure the impact of confinement and the effects of surface tension, respectively. Introducing the surface tension parameter

S

is shown to provide better agreement between theory and experiment.

我们考虑的是轴对称粘性重力流的径向扩散问题，在这种情况下，流体以恒定的流量从点源释放，被垂直限制在两块水平板之间的狭窄间隙中。流体的自由表面与顶板相交处形成一条接地线，从而形成两个流动区域：一个是靠近流体源的内部圆形接触区域，流体充满了两块板之间的整个间隙；另一个是重力流的自由表面位于顶板下方的外部环形区域。这种流动的数学模型需要求解自由表面高度的偏微分方程，并在接地线和电流前缘处设置适当的边界条件。在许多情况下，这些系统都有相似解。我将介绍一个这样的模型，其中在接地线和前缘局部加入了表面张力的影响，从而得到取决于两个无量纲参数 J 和 S 的相似性解，这两个参数分别用于测量约束的影响和表面张力的影响。结果表明，引入表面张力参数 S 可使理论与实验之间的一致性更好。

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引用次数: 0

A mathematical study of the influence of media on the asymptotic dynamics of diseases 介质对疾病渐进动态影响的数学研究

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-15 DOI: 10.1016/j.padiff.2024.100982

Lahcen Boulaasair , Hassane Bouzahir , N. Seshagiri Rao , Salma Haque , Nabil Mlaiki

This study explores the asymptotic behavior of a stochastic epidemic model that accounts for the impact of media coverage. The initial focus lies on determining the conditions leading to the exponential extinction of the disease. Additionally, we investigate the weak convergence of the probability distribution of the stochastic process

N (t)

, representing the total population, to a one-dimensional stochastic process with density calculated through the Fokker–Planck equation. Subsequently, we demonstrate the persistent nature of the disease and utilize Has’minskii theory to establish the presence of a unique ergodic stationary distribution for our stochastic epidemic model. Finally, numerical simulations are conducted to validate the theoretical findings.

本研究探讨了一种考虑到媒体报道影响的随机流行病模型的渐进行为。最初的重点在于确定导致疾病指数式消亡的条件。此外，我们还研究了代表总人口的随机过程 N(t) 的概率分布向通过福克-普朗克方程计算密度的一维随机过程的弱收敛性。随后，我们证明了疾病的持续性，并利用 Has'minskii 理论确定了我们的随机流行病模型存在唯一的遍历静态分布。最后，我们进行了数值模拟来验证理论结论。

引用次数: 0

New crossover lumpy skin disease: Numerical treatments 新型交叉性肿块皮肤病：数字疗法

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-13 DOI: 10.1016/j.padiff.2024.100986

NH Sweilam , Waleed Abdel Kareem , SM Al-Mekhlafi , Muner M Abou Hasan , Taha H El-Ghareeb , TM Soliman

This work expands on a novel piecewise mathematical model of Lumpy Skin Disease (LSD) in three time intervals by utilizing fractional stochastic derivatives and variable-order differential equations. The LSD model is developed into two crossover hybrid variable-order derivatives. This study's piecewise mathematical model representation of lumpy skin disease has revealed a property that has never been taken into account or seen in previous research employing mathematical models based on classical, different fractional derivatives and variable order fractional derivatives. The Caputo derivative and the Riemann-Liouville integral are merged linearly to produce the hybrid fractional order derivative. The variable-order fractional and hybrid fractional operators are approximated using the Grünwald-Letnikov approximation. We introduce the hybrid variable-order operator combined with the non-standard finite difference method. The stability, boundedness, positivity, and existence of the suggested model are examined. The effectiveness of the techniques and the validity of the theoretical results were verified through a number of numerical experiments.

这项研究利用分数随机导数和变阶微分方程，扩展了一个新颖的分段式结节性皮肤病（LSD）数学模型。LSD 模型被发展成两个交叉混合变阶导数。本研究对块状皮肤病的片断数学模型表征揭示了一种特性，这种特性在以往采用基于经典、不同分数导数和变阶分数导数的数学模型的研究中从未被考虑或出现过。卡普托导数和黎曼-刘维尔积分通过线性合并产生了混合分数阶导数。变阶分式算子和混合分式算子使用格吕内瓦尔德-列特尼科夫近似法进行近似。我们介绍了与非标准有限差分法相结合的混合变阶算子。我们考察了所建议模型的稳定性、有界性、实在性和存在性。通过大量数值实验验证了这些技术的有效性和理论结果的正确性。

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引用次数: 0

Mathematical modeling and simulation of magnetized bioconvective nanoliquid flow capturing Brownian motion, multiple slip, thermophoresis and gyrotactic microorganisms configured by rotating disk 磁化生物对流纳米液流的数学建模与仿真，捕获布朗运动、多重滑移、热泳和由旋转盘配置的陀螺触觉微生物

Q1 Mathematics

Partial Differential Equations in Applied Mathematics

Pub Date : 2024-11-13 DOI: 10.1016/j.padiff.2024.100989

Hakim AL Garalleh , Sami Ullah Khan , M. Waqas , Nurnadiah Zamri , Barno Abdullaeva , Manish Gupta

This analysis describes the bioconvective flow of nanofluid due to rotation of disk. A uniform suspension of nanofluid between microorganisms is considered to analyze the applications of bioconvection. The nanofluid assumed to be electrically conducting with amplification of magnetic force. The problem is entertained in presence of different slip features including velocity, temperature, concentration and microorganisms. The formulation of problem in simplified form is attained via dimensionless variables. Shooting numerical scheme is used to compute the simulations. Physical interpretation and visualization of results is observed in view of parameters. The observations concluded that interaction of slip effects reduces the velocity profile but enhances nanofluid temperature and concentration profiles. The temperature profile increases with thermophoresis parameter. Current results comprise applications in cooling of electronics devices, thin film coating, gas turbines engine, energy systems etc.

该分析描述了纳米流体因圆盘旋转而产生的生物对流。分析生物对流的应用时，考虑了微生物之间均匀悬浮的纳米流体。假定纳米流体导电并具有磁力放大作用。在存在不同滑动特征（包括速度、温度、浓度和微生物）的情况下，对该问题进行了讨论。通过无量纲变量实现了问题的简化表述。使用射击数值方案进行模拟计算。根据参数对结果进行物理解释和可视化观察。观察得出的结论是，滑移效应的相互作用降低了速度曲线，但增强了纳米流体的温度和浓度曲线。温度曲线随着热泳参数的增加而增加。目前的研究成果包括在电子设备冷却、薄膜涂层、燃气涡轮发动机、能源系统等方面的应用。

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引用次数: 0