Fractal Fractional Order Operators in Computational Techniques for Mathematical Models in Epidemiology

New fractional operators, the COVID-19 model has been studied in this paper. By using different numericaltechniques and the time fractional parameters, the mechanical characteristics of the fractional order model areidentified. The uniqueness and existence have been established. Themodel’sUlam-Hyers stability analysis has beenfound. In order to justify the theoretical results, numerical simulations are carried out for the presented methodin the range of fractional order to show the implications of fractional and fractal orders.We applied very effectivenumerical techniques to obtain the solutions of themodel and simulations. Also, we present conditions of existencefor a solution to the proposed epidemicmodel and to calculate the reproduction number in certain state conditionsof the analyzed dynamic system. COVID-19 fractional order model for the case of Wuhan, China, is offered foranalysis with simulations in order to determine the possible efficacy of Coronavirus disease transmission in theCommunity. For this reason, we employed the COVID-19 fractal fractional derivative model in the example ofWuhan, China, with the given beginning conditions. In conclusion, again the mathematical models with fractionaloperators can facilitate the improvement of decision-making for measures to be taken in the management of anepidemic situation.

Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

The relationship between compartment models and their stochastic counterparts:A comparative study with examples of the COVID-19 epidemic modeling

Deterministic compartment models(CMs)and stochastic models,including stochastic CMs and agent-based models,are widely utilized in epidemic modeling.However,the relationship between CMs and their corresponding stochastic models is not well understood.The present study aimed to address this gap by conducting a comparative study using the susceptible,exposed,infectious,and recovered(SEIR)model and its extended CMs from the coronavirus disease 2019 modeling literature.We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations.Based on this equivalence,we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment.The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics.However,it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs.Additionally,we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents.This model offered a balance between computational efficiency and accuracy.The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling.Furthermore,the results had implications for the development of hybrid models that integrated the strengths of both frameworks.Overall,the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.

Prospect Theory Based Individual Irrationality Modelling and Behavior Inducement in Pandemic Control

Understanding and modeling individuals’behaviors during epidemics is crucial for effective epidemic control.However,existing research ignores the impact of users’irrationality on decision-making in the epidemic.Meanwhile,existing disease control methods often assume users’full compliance with measures like mandatory isolation,which does not align with the actual situation.To address these issues,this paper proposes a prospect theorybased framework to model users’decision-making process in epidemics and analyzes how irrationality affects individuals’behaviors and epidemic dynamics.According to the analysis results,irrationality tends to prompt conservative behaviors when the infection risk is low but encourages risk-seeking behaviors when the risk is high.Then,this paper proposes a behavior inducement algorithm to guide individuals’behaviors and control the spread of disease.Simulations and real user tests validate our analysis,and simulation results show that the proposed behavior inducement algorithm can effectively guide individuals’behavior.

A NOVEL STOCHASTIC HEPATITIS B VIRUS EPIDEMIC MODEL WITH SECOND-ORDER MULTIPLICATIVE α-STABLE NOISE AND REAL DATA

This work presents an advanced and detailed analysis of the mechanisms of hepatitis B virus(HBV)propagation in an environment characterized by variability and stochas-ticity.Based on some biological features of the virus and the assumptions,the corresponding deterministic model is formulated,which takes into consideration the effect of vaccination.This deterministic model is extended to a stochastic framework by considering a new form of disturbance which makes it possible to simulate strong and significant fluctuations.The long-term behaviors of the virus are predicted by using stochastic differential equations with second-order multiplicative α-stable jumps.By developing the assumptions and employing the novel theoretical tools,the threshold parameter responsible for ergodicity(persistence)and extinction is provided.The theoretical results of the current study are validated by numerical simulations and parameters estimation is also performed.Moreover,we obtain the following new interesting findings:(a)in each class,the average time depends on the value ofα;(b)the second-order noise has an inverse effect on the spread of the virus;(c)the shapes of population densities at stationary level quickly changes at certain values of α.The last three conclusions can provide a solid research base for further investigation in the field of biological and ecological modeling.

A Stochastic Model to Assess the Epidemiological Impact of Vaccine Booster Doses on COVID-19 and Viral Hepatitis B Co-Dynamics with Real Data

A patient co-infected with COVID-19 and viral hepatitis B can be atmore risk of severe complications than the one infected with a single infection.This study develops a comprehensive stochastic model to assess the epidemiological impact of vaccine booster doses on the co-dynamics of viral hepatitis B and COVID-19.The model is fitted to real COVID-19 data from Pakistan.The proposed model incorporates logistic growth and saturated incidence functions.Rigorous analyses using the tools of stochastic calculus,are performed to study appropriate conditions for the existence of unique global solutions,stationary distribution in the sense of ergodicity and disease extinction.The stochastic threshold estimated from the data fitting is given by:R_(0)^(S)=3.0651.Numerical assessments are implemented to illustrate the impact of double-dose vaccination and saturated incidence functions on the dynamics of both diseases.The effects of stochastic white noise intensities are also highlighted.

An Improved CREAM Model Based on DS Evidence Theory and DEMATEL

Cognitive Reliability and Error Analysis Method(CREAM)is widely used in human reliability analysis(HRA).It defines nine common performance conditions(CPCs),which represent the factors thatmay affect human reliability and are used to modify the cognitive failure probability(CFP).However,the levels of CPCs are usually determined by domain experts,whichmay be subjective and uncertain.What’smore,the classicCREAMassumes that the CPCs are independent,which is unrealistic.Ignoring the dependence among CPCs will result in repeated calculations of the influence of the CPCs on CFP and lead to unreasonable reliability evaluation.To address the issue of uncertain information modeling and processing,this paper introduces evidence theory to evaluate the CPC levels in specific scenarios.To address the issue of dependence modeling,the Decision-Making Trial and Evaluation Laboratory(DEMATEL)method is used to process the dependence among CPCs and calculate the relative weights of each CPC,thus modifying the multiplier of the CPCs.The detailed process of the proposed method is illustrated in this paper and the CFP estimated by the proposed method is more reasonable.

A Hybrid SIR-Fuzzy Model for Epidemic Dynamics:A Numerical Study

This study focuses on the urgent requirement for improved accuracy in diseasemodeling by introducing a newcomputational framework called the Hybrid SIR-Fuzzy Model.By integrating the traditional Susceptible-Infectious-Recovered(SIR)modelwith fuzzy logic,ourmethod effectively addresses the complex nature of epidemic dynamics by accurately accounting for uncertainties and imprecisions in both data and model parameters.The main aim of this research is to provide a model for disease transmission using fuzzy theory,which can successfully address uncertainty in mathematical modeling.Our main emphasis is on the imprecise transmission rate parameter,utilizing a three-part description of its membership level.This enhances the representation of disease processes with greater complexity and tackles the difficulties related to quantifying uncertainty in mathematical models.We investigate equilibrium points for three separate scenarios and perform a comprehensive sensitivity analysis,providing insight into the complex correlation betweenmodel parameters and epidemic results.In order to facilitate a quantitative analysis of the fuzzy model,we propose the implementation of a resilient numerical scheme.The convergence study of the scheme demonstrates its trustworthiness,providing a conditionally positive solution,which represents a significant improvement compared to current forward Euler schemes.The numerical findings demonstrate themodel’s effectiveness in accurately representing the dynamics of disease transmission.Significantly,when the mortality coefficient rises,both the susceptible and infected populations decrease,highlighting the model’s sensitivity to important epidemiological factors.Moreover,there is a direct relationship between higher Holling type rate values and a decrease in the number of individuals who are infected,as well as an increase in the number of susceptible individuals.This correlation offers a significant understanding of how many elements affect the consequences of an epidemic.Our objective is to enhance decision-making in public health by providing a thorough quantitative analysis of the Hybrid SIR-Fuzzy Model.Our approach not only tackles the existing constraints in disease modeling,but also paves the way for additional investigation,providing a vital instrument for researchers and policymakers alike.

A particle-resolved heat-particle-fluid coupling model by DEM-IMB-LBM

Multifield coupling is frequently encountered and also an active area of research in geotechnical engineering.In this work,a particle-resolved direct numerical simulation(PR-DNS)technique is extended to simulate particle-fluid interaction problems involving heat transfer at the grain level.In this extended technique,an immersed moving boundary(IMB)scheme is used to couple the discrete element method(DEM)and lattice Boltzmann method(LBM),while a recently proposed Dirichlet-type thermal boundary condition is also adapted to account for heat transfer between fluid phase and solid particles.The resulting DEM-IBM-LBM model is robust to simulate moving curved boundaries with constant temperature in thermal flows.To facilitate the understanding and implementation of this coupled model for non-isothermal problems,a complete list is given for the conversion of relevant physical variables to lattice units.Then,benchmark tests,including a single-particle sedimentation and a two-particle drafting-kissing-tumbling(DKT)simulation with heat transfer,are carried out to validate the accuracy of our coupled technique.To further investigate the role of heat transfer in particle-laden flows,two multiple-particle problems with heat transfer are performed.Numerical examples demonstrate that the proposed coupling model is a promising high-resolution approach for simulating the heat-particle-fluid coupling at the grain level.

Cartographic Study and Modeling of the Bakwanga Kimberlite Massive 5 at Kasai Oriental in the Democratic Republic of Congo

Bakwanga kimberlite massive 5 in Kasai Oriental is part of a set of 13 kimberlite massives numbered according to the order in which they were discovered. They are located on an alignment with a more or less W-E direction making up the Northern group known as Bakwanga. The importance of the Bakwanga kimberlite massives on the country’s economy in the production of diamonds sufficiently proves the interest of geological research work in this area. The objective of this work is to determine a mathematical model of the shape of the massive as close as possible to reality and through cartography. The cartographic study and modeling of this kimberlite massive were carried out using data from core samples taken on longitudinal and transverse profiles of the 50 × 50 meter mesh drilling plan intersecting this kimberlite massive. We intend to deduce the structure and lithostratigraphy of the kim-berlitic facies and the direct environment of massive 5. As a result, we note that the majority of surveys on the extent of this massive have intersected: Red clayey sand - Polymorphic sandstone - Nodular sandstone, with kaolin blocks and nodules - Epiclastic Kimberlite - Xenokimberlite - Massive Kimberlite - Mesozoic sandstone - Dolomite (enclosing). The shape of the Massive 5 model is vaguely elliptical with a W-E longitudinal axis of 575 m and N-S axis of 275 meters. Surveys have shown that Massive 5 is in fact composed of two pipes, located in the W (western pipe) and E (eastern pipe) ends of the massif. The two chimneys of the two pipes have walls ranging from subvertical at the eastern pipe to very steep walls of around 70˚ to 80˚ for the western pipe and the average diameter of the two pipes is ±50 meters. At level 600, the massive has an area of ±10.5 hectares and it gradually decreases in depth and the modeling of the latter shows a concentric decrease in the volume of the massive from the surface to depth in the shape of a mushroom. 3 eruptive phases established this Kimber-litic massive, the first two phases (old) of which formed the crater of the western pipe and the third formed the crater of the eastern pipe in the dolomites. These dolomites constitute everywhere the surrounding area of the massive;the distinction of these 3 phases is made possible thanks to Epiclastic deposits, Xenokim-berlites and massive Kimberlites.

Stability of a Delayed Stochastic Epidemic COVID-19 Model with Vaccination and with Differential Susceptibility

In this paper, we treat the spread of COVID-19 using a delayed stochastic SVIRS (Susceptible, Infected, Recovered, Susceptible) epidemic model with a general incidence rate and differential susceptibility. We start with a deterministic model, then add random perturbations on the contact rate using white noise to obtain a stochastic model. We first show that the delayed stochastic differential equation that describes the model has a unique global positive solution for any positive initial value. Under the condition R0 ≤ 1, we prove the almost sure asymptotic stability of the disease-free equilibrium of the model.

Exploring International Media and Information Literacy Initiatives: Insights From DW Akademie’s MIL Model

Media and Information Literacy(MIL)is one of the most important topics in today’s mediatized world.Under the leadership of United Nations Educational,Scientific and Cultural Organization(UNESCO),many international organizations in the world,as foreign donors,annually announce many projects and grants for the promotion and development of the field of MIL in the countries of the world.One of the main actors of this movement is DW Akademie with different media and MIL projects several countries of the world.This research paper delves into the role of DW Akademie’s MIL model in shaping a media-savvy generation.The study explores the theoretical underpinnings and practical applications of Deutsche Welle(DW)Akademie’s MIL model,analysing its effectiveness in fostering media literacy skills.The research employs a multi-faceted approach,incorporating case studies to assess the model’s impact across diverse demographics.The paper also considers the model’s alignment with global educational policies and proposes recommendations for its integration into broader frameworks.By investigating DW Akademie’s MIL model,this research contributes to the ongoing discourse on media literacy education,providing valuable insights for educators,policymakers,and researchers.The findings offer a nuanced understanding of the model’s position in cultivating a media-savvy generation poised to navigate the complexities of the information age.

基于倾斜三维模型与机载LiDAR点云的DEM快速更新

随着倾斜摄影技术的发展和实景三维建设的不断推进,地形级实景三维地理场景对DEM现势性要求日益提高。为了解决传统方法更新DEM成本高、工作量大的问题,本文提出了利用倾斜三维模型成果转换点云,融合两期DSM和DOM进行变化检测,替换已有机载LiDAR点云,快速更新DEM的方法,并通过项目验证了该方法的可行性,极大地节约了生产成本,为DEM更新提供了思路。

矿区沉陷DEM多重滤波方法研究

针对传统地表移动监测方法周期较长、工作量大的问题,通过无人机LiDAR和点云滤波获取地面点云,并构建沉陷DEM,实现地表沉陷监测的方法具有快速、高效的优势;由于现有点云滤波和插值算法构建的沉陷DEM模型仍会包含噪声,限制了该技术在矿区的普及,因此,进一步研究了沉陷DEM噪声的去除方法,对比分析了多重滤波与经典滤波方法。实验分析结果表明:在几种去噪方法中,中值滤波组合维纳滤波的去噪效果最好,保留了下沉盆地的细节特征,能够满足矿区地表形变监测的基本要求。

一种DEM辅助下的LiDAR点云PTD滤波改进算法

针对传统渐进加密不规则三角网(PTD)滤波算法在复杂地形环境下需要反复调试地面点判断参数才能获得较好结果的局限性,以往期DEM数据提取的地形高程和地形梯度为辅助,改进PTD中初始地面种子点的选取方法,优化地面点判断参数,并对往期DEM数据和现势LiDAR点云数据之间的地形变化进行检测和处理,适用于不同坡度地形条件的复杂地形,滤波效果较好。对比分析实验数据精度可知,该算法能有效降低I类与II类误差,且样本分类精度均在90%以上,说明DEM辅助可切实提高PTD滤波算法的精度。

基于CFD-DEM的流-固耦合数值建模方法研究进展

随着土体渗流侵蚀研究的逐渐深入,对土颗粒流失和变形破坏机理的研究方法呈现出多尺度的特点。其中,计算流体力学-离散元耦合方法(CFD-DEM)为在细观尺度上研究流-固耦合相互作用对土体宏观力学特性的影响提供了一种行之有效的方法。针对CFD-DEM耦合方法在岩土工程领域应用现状,本文系统总结现有流-固耦合计算方法的优缺点,重点论述CFD-DEM耦合方法的建模策略,包括固相颗粒形状建模与粒间接触模型、流体相控制方程及参数计算方法,以及CFD-DEM耦合计算,并就相关问题进行深入探讨,最后提出了CFD-DEM耦合方法未来的发展方向。

基于DEM的旋转给料器叶片磨损特性研究

为探究旋转给料器工作时,颗粒在给料器内流动对给料器的磨损特性,使用SoildWorks软件构建旋转给料器叶片结构,借助EDEM软件对仿真模型进行离散建模分析,分别研究旋转给料器不同转速、不同叶片数下给料器叶片磨损情况,得出给料器叶片数相同,叶片转速为230 r/min、267 r/min与305 r/min时,随着叶片转速的增加,磨损量反而减小。当转速都为230 r/min,叶片数量为4、6和8时,6叶片的情况下给料器叶片的磨损程度最小。综合得出的结果,给料器可以设计成叶片数量为6、额定转速为305 r/min,这样对叶片的磨损程度不大,可以提高给料器的使用寿命。

流场涡旋中颗粒碰撞黏附机制的CFD-DEM(XDLVO)模拟

混凝装备中流场的涡旋特征是影响煤泥水等微细颗粒絮凝效果的关键因素之一。为解析流场涡旋影响颗粒混凝碰撞与黏附机制,以圆柱绕流产生的涡街为代表性涡旋流场,采用CFD方法模拟了流速和圆柱直径对流场涡旋强度和尺度的影响;引入XDLVO理论辅助描述离散元方法中颗粒间的相互作用力,对粒径为25~100μm颗粒在上述流场中的碰撞与黏附过程进行CFD-DEM模拟,并试验验证。结果表明,在流速0.06~0.12 m/s、圆柱直径2~6 mm、雷诺数为120~720条件下,圆柱绕流场中的涡旋半径(r)与圆柱直径(D)的关系近似为r=0.133 3D+0.421 4,与流速无显著相关性;涡旋中心的最大涡量与流速成正比,涡旋强度与圆柱直径的2次方正相关。CFD-DEM(XDLVO)模拟方法获得的黏附聚集体的特征参数与试验结果吻合较好,说明其可较准确地描述圆柱绕流场中颗粒的碰撞与黏附过程。对流场涡旋分布特征和聚集体在流场分区中分布特征的分析表明,流场中的涡旋通过惯性离心力使颗粒远离涡旋中心向涡旋周边的黏性剪切区富集,在改变颗粒运动方向的同时,增加了颗粒在黏性区的局部浓度,从而提高了颗粒的碰撞概率,有效促进了颗粒的黏附并大。当涡旋尺度为物料粒径的10倍左右时最有利于颗粒的碰撞黏附,因此可根据应用场景的物料粒度来优化设计绕流圆柱直径,使其达到最好的黏附效果。

基于CFD-DEM的物料转运过程诱导风流场与产尘因素分析

为了揭示颗粒物料在皮带机转运过程中的粉尘运移规律问题,推导了含有水平初速度的颗粒物料转运过程中的诱导气流方程,并采用CFD-DEM耦合方法对转运过程中的颗粒分布与诱导风流场特性进行了研究,分析了颗粒物料的落料高度、质量流量和初速度对颗粒逸散与诱导气流的影响。结果表明:颗粒在弧形下落阶段速度逐渐提高,挤压碰撞阶段颗粒速度先降低后提高,最后趋于稳定,部分颗粒出现逸散现象;含尘气流在颗粒物料弧形下落阶段和挤压碰撞阶段扩散较为明显;诱导气流速度与颗粒物料质量流量和初始速度呈正比关系,颗粒物料质量流量与诱导气流速度呈幂函数关系,拟合曲线幂指数为0.6~0.74。

基于DEM-FEM耦合方法的碎屑流对桥墩最大冲击力的影响因素研究

碎屑流是我国山区最危险的地质灾害之一,山区桥墩常受到碎屑流冲击而开裂、倾斜甚至倒塌,给山区桥梁建设、运营带来严重的安全隐患。采用离散元方法(discrete element method,DEM)和有限元方法(finite element method,FEM)耦合的三维数值模拟方法模拟了碎屑流对双柱式桥墩的冲击效应,并结合斜槽试验,验证了耦合方法的准确性,进一步分析了碎屑流冲击坡度、距离和体积密度对桥墩冲击力的影响规律。结果表明,最大冲击力与碎屑流冲击坡度、距离和体积密度分别呈幂函数(指数大于1)、幂函数(指数小于1)和线性正相关。冲击坡度、距离和体积密度对最大冲击力的敏感度值分别为3.012、0.202、0.804,在桥梁碎屑流灾害防治时需重视冲击坡度和体积密度的影响。将冲击力的数值模拟值与流体动力学模型预测值对比分析表明,流体动力学模型理论公式能较好地预测桥墩所受的最大冲击力,最大预测误差低于23.6%。相关研究结果可为山区桥梁碎屑流灾害防治与设计提供一定的参考依据。