Dynamics of a Stochastic Epidemic Model with Age-group

A stochastic epidemic model with two age groups is established in this study,in which the susceptible(S),the exposed(E),the infected(I),the hospitalized(H)and the recovered(R)are involved within the total population,the aging rates between two age groups are set to be constant.The existence-and-uniqueness of global positive solution is firstly showed.Then,by constructing several appropriate Lyapunov functions and using the high-dimensional Itô’s formula,the sufficient conditions for the stochastic extinction and stochastic persistence of the exposed individuals and the infected individuals are obtained.The stochastic extinction indicator and the stochastic persistence indicator are less-valued expressions compared with the basic reproduction number.Meanwhile,the main results of this study are modified into multi-age groups.Furthermore,by using the surveillance data for Fujian Provincial Center for Disease Control and Prevention,Fuzhou COVID-19 epidemic is chosen to carry out the numerical simulations,which show that the age group of the population plays the vital role when studying infectious diseases.

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.

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.

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.

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.

基于DEM-MBD耦合的马铃薯排种性能提升研究

针对播种所用的切块薯形状不规则、流动性差,导致充种困难、排种效果差等问题,在测定切块薯物料特性的基础上,对种勺取种过程进行仿真分析,阐明了加设偏心抬种装置可提高排种性能的机理。通过DEM-MBD耦合单因素仿真试验,分析播种转速、种层高度、偏心抬种装置转速的改变对排种性能的影响;在此基础上,以播种转速、种层高度、偏心抬种装置转速为试验因素,以排种器的合格指数、重种指数、漏种指数为试验指标,进行了二次回归正交旋转组合的台架试验,建立了3个指标的回归模型,并利用模型对排种器的工作参数进行了优化。试验结果表明:当播种速度为1.986 km/h、偏心抬种装置转速为41.91 r/min、种层高度为177.549 mm时排种性能达到最佳,合格指数为91.21%,漏种指数为2.02%,重种指数为6.76%,满足马铃薯种植要求。

Projecting the Dynamic Trends of Human Immunodeficiency Virus/Acquired Immunodeficiency Syndrome:Modeling the Epidemic in Sichuan Province, China

Objective Our study aimed to provide a comprehensive overview of the current status and dynamic trends of the human immunodeficiency virus(HIV)prevalence in Sichuan,the second most heavily affected province in China,and to explore future interventions.Methods The epidemiological,behavioral,and population census data from multiple sources were analyzed to extract inputs for an acquired immunodeficiency syndrome(AIDS)epidemic model(AEM).Baseline curves,derived from historical trends in HIV prevalence,were used,and the AEM was employed to examine future intervention scenarios.Results In 2015,the modeled data suggested an adult HIV prevalence of 0.191%in Sichuan,with an estimated 128,766 people living with HIV/AIDS and 16,983 individuals with newly diagnosed infections.Considering current high-risk behaviors,the model predicts an increase in the adult prevalence to 0.306%by 2025,projecting an estimated 212,168 people living with HIV/AIDS and 16,555 individuals with newly diagnosed infections.Conclusion Heterosexual transmission will likely emerge as the primary mode of AIDS transmission in Sichuan.Furthermore,we anticipate a stabilization in the incidence of AIDS with a concurrent increase in prevalence.Implementing comprehensive intervention measures aimed at high-risk groups could effectively alleviate the spread of AIDS in Sichuan.

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.

Student Academic Performance Predictive Model Based on Dual-stream Deep Network

Blended teaching is one of the essential teaching methods with the development of information technology.Constructing a learning effect evaluation model is helpful to improve students’academic performance and helps teachers to better implement course teaching.However,a lack of evaluation models for the fusion of temporal and non-temporal behavioral data leads to an unsatisfactory evaluation effect.To meet the demand for predicting students’academic performance through learning behavior data,this study proposes a learning effect evaluation method that integrates expert perspective indicators to predict academic performance by constructing a dual-stream network that combines temporal behavior data and non-temporal behavior data in the learning process.In this paper,firstly,the Delphi method is used to analyze and process the course learning behavior data of students and establish an effective evaluation index system of learning behavior with universality;secondly,the Mann-Whitney U-test and the complex correlation analysis are used to analyze further and validate the evaluation indexes;and lastly,a dual-stream information fusion model,which combines temporal and non-temporal features,is established.The learning effect evaluation model is built,and the results of the mean absolute error(MAE)and root mean square error(RMSE)indexes are 4.16 and 5.29,respectively.This study indicates that combining expert perspectives for evaluation index selection and further fusing temporal and non-temporal behavioral features that for learning effect evaluation and prediction is rationality,accuracy,and effectiveness,which provides a powerful help for the practical application of learning effect evaluation and prediction.

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.

Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal cord.It is a devastating disease and remains a significant public health challenge.This study investigates a bacterial meningitis model through deterministic and stochastic versions.Four-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and recovered.The model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric perturbations.Also,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known theorems.Standard and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic model.Unfortunately,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step size.In addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is zero.The simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

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.

基于CFD-DEM方法的煤气化渣气流分级提炭模拟研究

【目的】煤气化渣提炭分质是实现其减量化、无害化、资源化利用的重要手段,气流分级法因其能够高效处理细粒级物料且无废水、废气排放而具有独特优势。【方法】基于CFD-DEM模拟,研究卧式涡轮气流分级机内气固流动状况,探明进气方向和涡轮转向的匹配关系,明确炭颗粒和灰颗粒的流动机制。优化涡轮气流分级机中进气口方向,预测入口气速和涡轮转速对气化细渣气流分级提炭效率的影响。【结果】结果表明:涡轮气流分级机的进气方向对流场分布和气化细渣提炭效率有显著影响。切向进气口易导致在分级区和淘洗区产生相互干扰的次级漩涡,影响气化渣炭和灰颗粒分离效率。优化切向进气为垂直向上后,避免了淘洗区和分级区相互干扰,消除了涡轮和叶片之间次级漩涡,改善并稳定了分级区内的流场,提高了气化细渣提炭效率。在优化后的涡轮气流分级机中,通过匹配入口气速与涡轮转速,富炭渣产品中的炭含量可达80.95%,炭回收率可达59.83%。

基于CFD-DEM的种子联合收获机气流清种仿真分析

针对现有种子联合收获机在收获后籽粒输运搅龙、杂余搅龙和卸粮搅龙处会残留种子的问题,在上述部位添加了清种气流,并分析在这些机构内使用气流清理残留种粒的可行性。从螺旋搅龙转速和清种入口气流速度这两个因素对清种效果的影响进行研究,开展卸粮搅龙机构内气固两相流的数值仿真,并基于计算流体力学-离散单元法(CFD-DEM)进行耦合求解,获得了清种过程中气相与颗粒相的速度分布及运动轨迹。结果表明:螺旋搅龙的运动状态对清种气流的通过性有显著影响;当螺旋搅龙处在高转速状态时,清种气流衰减速度较快,此状态下难以有效地利用气流进行清种;气流速度对清种效果影响显著,余种数量和清种所用时间随气流速度升高而降低,但当气流速度过快时会使种子撞击在螺旋搅龙叶片上产生反流和飞溅现象,从而影响清种效果。仿真表明,最优清种气流速度为50 m/s。

Numerical Simulation and Parameter Estimation of Fractional-Order Dynamic Epidemic Model for COVID-19

The outbreak of COVID-19 in 2019 resulted in numerous infections and deaths. In order to better study the transmission of COVID-19, this article adopts an improved fractional-order SIR model. Firstly, the properties of the model are studied, including the feasible domain and bounded solutions of the system. Secondly, the stability of the system is discussed, among other things. Then, the GMMP method is introduced to obtain numerical solutions for the COVID-19 system and combined with the improved MH-NMSS-PSO parameter estimation method to fit the real data of Delhi, India from April 1, 2020 to June 30, 2020. The results show that the fitting effect is quite ideal. Finally, long-term predictions were made on the number of infections. We accurately estimate that the peak number of infections in Delhi, India, can reach around 2.1 million. This paper also compares the fitting performance of the integer-order COVID-19 model and the fractional-order COVID-19 model using the real data from Delhi. The results indicate that the fractional-order model with different orders, as we proposed, performs the best.

Stochastic Bifurcation of an SIS Epidemic Model with Treatment and Immigration

In this paper, we investigate an SIS model with treatment and immigration. Firstly, the two-dimensional model is simplified by using the stochastic averaging method. Then, we derive the local stability of the stochastic system by computing the Lyapunov exponent of the linearized system. Further, the global stability of the stochastic model is analyzed based on the singular boundary theory. Moreover, we prove that the model undergoes a Hopf bifurcation and a pitchfork bifurcation. Finally, several numerical examples are provided to illustrate the theoretical results. .

Research on the Dynamic Volatility Relationship between Chinese and U.S. Stock Markets Based on the DCC-GARCH Model under the Background of the COVID-19 Pandemic

This study utilizes the Dynamic Conditional Correlation-Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) model to investigate the dynamic relationship between Chinese and U.S. stock markets amid the COVID-19 pandemic. Initially, a univariate GARCH model is developed to derive residual sequences, which are then used to estimate the DCC model parameters. The research reveals a significant rise in the interconnection between the Chinese and U.S. stock markets during the pandemic. The S&P 500 index displayed higher sensitivity and greater volatility in response to the pandemic, whereas the CSI 300 index showed superior resilience and stability. Analysis and model estimation suggest that the market’s dependence on historical data has intensified and its sensitivity to recent shocks has heightened. Predictions from the model indicate increased market volatility during the pandemic. While the model is proficient in capturing market trends, there remains potential for enhancing the accuracy of specific volatility predictions. The study proposes recommendations for policymakers and investors, highlighting the importance of improved cooperation in international financial market regulation and investor education.