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

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

{"title":"Optimizing control strategies for monkeypox through mathematical modeling","authors":"Mohamed Baroudi , Imane Smouni , Hicham Gourram , Abderrahim Labzai , Mohamed Belam","doi":"10.1016/j.padiff.2024.100996","DOIUrl":"10.1016/j.padiff.2024.100996","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100996"},"PeriodicalIF":0.0,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142721256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

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

{"title":"Numerical investigation of fractional order SEIR models with newborn immunization using Vieta–Fibonacci wavelets","authors":"Naied A. Nayied , Firdous A. Shah , Mukhtar A. Khanday , Kottakkaran Sooppy Nisar","doi":"10.1016/j.padiff.2024.100995","DOIUrl":"10.1016/j.padiff.2024.100995","url":null,"abstract":"<div><div>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 <em>fsolve</em> 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 <span><math><mi>α</mi></math></span> and transmission factor <span><math><mi>β</mi></math></span> reveal the influence of these variables on the disease outbreak, with higher values of <span><math><mi>β</mi></math></span> leading to rapid transmission. The chaotic attractors of the fractional-order SEIR epidemic model with newborn immunization are graphically represented using Vieta–Fibonacci wavelets.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100995"},"PeriodicalIF":0.0,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142721255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-23 DOI: 10.1016/j.padiff.2024.100997

Maryam Kousar , Adil Jhangeer , Muhammad Muddassar

{"title":"Comprehensive analysis of noise behavior influenced by random effects in stochastic differential equations","authors":"Maryam Kousar , Adil Jhangeer , Muhammad Muddassar","doi":"10.1016/j.padiff.2024.100997","DOIUrl":"10.1016/j.padiff.2024.100997","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100997"},"PeriodicalIF":0.0,"publicationDate":"2024-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

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

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

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

{"title":"New general single, double and triple conformable integral transforms: Definitions, properties and applications","authors":"Mohammad Hossein Akrami , Abbas Poya , Mohammad Ali Zirak","doi":"10.1016/j.padiff.2024.100991","DOIUrl":"10.1016/j.padiff.2024.100991","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100991"},"PeriodicalIF":0.0,"publicationDate":"2024-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142721254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

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

{"title":"Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations","authors":"Razia Begum , Sajjad Ali , Nahid Fatima , Kamal Shah , Thabet Abdeljawad","doi":"10.1016/j.padiff.2024.100990","DOIUrl":"10.1016/j.padiff.2024.100990","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100990"},"PeriodicalIF":0.0,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

Partial Differential Equations in Applied Mathematics Pub Date : 2024-11-16 DOI: 10.1016/j.padiff.2024.100992

A.J. Hutchinson

{"title":"The effect of surface tension on axisymmetric confined viscous gravity currents","authors":"A.J. Hutchinson","doi":"10.1016/j.padiff.2024.100992","DOIUrl":"10.1016/j.padiff.2024.100992","url":null,"abstract":"<div><div>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, <span><math><mi>J</mi></math></span> and <span><math><mi>S</mi></math></span>, which measure the impact of confinement and the effects of surface tension, respectively. Introducing the surface tension parameter <span><math><mi>S</mi></math></span> is shown to provide better agreement between theory and experiment.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100992"},"PeriodicalIF":0.0,"publicationDate":"2024-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698705","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

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

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

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

{"title":"New crossover lumpy skin disease: Numerical treatments","authors":"NH Sweilam , Waleed Abdel Kareem , SM Al-Mekhlafi , Muner M Abou Hasan , Taha H El-Ghareeb , TM Soliman","doi":"10.1016/j.padiff.2024.100986","DOIUrl":"10.1016/j.padiff.2024.100986","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100986"},"PeriodicalIF":0.0,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698199","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

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

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

{"title":"Mathematical modeling and simulation of magnetized bioconvective nanoliquid flow capturing Brownian motion, multiple slip, thermophoresis and gyrotactic microorganisms configured by rotating disk","authors":"Hakim AL Garalleh , Sami Ullah Khan , M. Waqas , Nurnadiah Zamri , Barno Abdullaeva , Manish Gupta","doi":"10.1016/j.padiff.2024.100989","DOIUrl":"10.1016/j.padiff.2024.100989","url":null,"abstract":"<div><div>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.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"12 ","pages":"Article 100989"},"PeriodicalIF":0.0,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142698200","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0