Analysis of an Epidemic Model with Age of Vaccination

A simple SI epidemic model with age of vaccination is discussed in this paper.Both vexing birth rate, the mortality rate caused by disease and vaccine waning rate areconsidered in this model. We prove that the global dynamics is completely determined bythe basic reproductive number R（ψ）（ψ denotes per capita vaccination rate）. If R（0） 〈 1,the disease-free equilibrium is a global attractor; If R（ψ） 〈： 1, the disease-free equilibriumis locally asymptotically stable; If R（ψ） ：〉 1, an unique endemic equilibrium exists and islocally asymptotically stable under certain condition.

ANALYSIS OF AN SI EPIDEMIC MODEL WITH NONLINEAR TRANSMISSION AND STAGE STRUCTURE

A disease transmission model of SI type with stage structure is formulated. The stability of disease free equilibrium, the existence and uniqueness of an endemic equilibrium, the existence of a global attractor are investigated.

ANALYSIS OF AN SIS EPIDEMIOLOGIC MODEL WITH VARIABLE POPULATION SIZE AND A DELAY

Epidemiologic model of SIS type has a delay corresponding to the infectious period and disease related deaths,so that the population size is variable.The population dynamics structure is recruitment and natural births with natural deaths.The incidence term is of the standard incidence.Here the thresholds and equilibria are detemined,and stabilities are examined.The persistence of the infectious disease and disease related deaths can lead to a new equilibrium population size below the carrying capacity.

COEXISTENCE FOR MULTIPLE LARGEST REPRODUCTION RATIOS OF A MULTI-STRAIN SIS EPIDEMIC MODEL

In this paper, to complete the global dynamics of a multi-strains SIS epidemic model, we establish a precise result on coexistence for the cases of the partial and complete duplicated multiple largest reproduction ratios for this model.

Oscillatory Behavior of a Network Epidemic SIS Model with Nonlinear Infectivity

In this paper, an epidemic SIS model with nonlinear infectivity on heterogeneous networks and time delays is investigated. The oscillatory behavior of the solutions is studied. Two sufficient conditions are provided to guarantee the oscillatory behavior for the solutions. Some computer simulations are demonstrated.

Simulation of Typhoon Muifa using a mesoscale coupled atmosphere–ocean model

A mesoscale coupled atmosphere–ocean model has been developed based on the GRAPES（Global and Regional Assimilation and Prediction System） regional typhoon model（GRAPES_TYM） and ECOM-si（estuary, coast and ocean model（semi-implicit））. Coupling between the typhoon and ocean models was conducted by exchanging wind stress, heat, moisture fluxes, and sea surface temperatures（SSTs） using the coupler OASIS3.0. Numerical prediction experiments were run with and without coupling for the case of Typhoon Muifa in the western North Pacific. To investigate the impact of using more accurate SST information on the simulation of the track and the intensity of Typhoon Muifa, experiments were also conducted using increased SST resolution in the initial condition field of the control test. The results indicate that increasing SST resolution in the initial condition field somewhat improved the intensity forecast, and use of the coupled model improved the intensity forecast significantly, with mean absolute errors in maximum wind speed within 48 and 72 h reduced by 32% and 20%, respectively. Use of the coupled model also resulted in less pronounced over-prediction of the intensity of Typhoon Muifa by the GRAPES_TYM. Moreover, the effects of using the coupled model on the intensity varied throughout the different stages of the development of Muifa owing to changes in the oceanic mixed layer depth. The coupled model had pronounced effects during the later stage of Muifa but had no obvious effects during the earlier stage. The SSTs predicted by the coupled model decreased by about 5–6℃ at most after the typhoon passed, in agreement with satellite data. Furthermore, based on analysis on the sea surface heat flux, wet static energy of the boundary layer, atmospheric temperature, and precipitation forecasted by the coupled model and the control test, the simulation results of this coupled atmosphere–ocean model can be considered to reasonably reflect the primary mechanisms underlying the interactions between tropical cyclones and oceans.

An SIS epidemic model with diffusion

The aim of this paper is to study the diffusion. We first study the well-posedness of the dynamics of an SIS epidemic model with model. And then, by using linearization method and constructing suitable Lyapunov function, we establish the local and global stability of the disease-free equilibrium and the endemic equilibrium, respectively. Furthermore, in view of Schauder fixed point theorem, we show that the model admits traveling wave solutions con- necting the disease-free equilibrium and the endemic equilibrium when R0 〉 1 and c 〉 c^＊. And also, by virtue of the two-sided Laplace transform, we prove that the model has no traveling wave solution connecting the two equilibria when R0 〉 1 and c ∈（0, c^＊）.

The Game-Theoretical Model of Using Insecticide-Treated Bed-Nets to Fight Malaria

Malaria infection is a major problem in many countries. The use of the Insecticide-Treated Bed-Nets (ITNs) has been shown to significantly reduce the number of malaria infections;however, the effectiveness is often jeopardized by improper handling or human behavior such as inconsistent usage. In this paper, we present a game-theoretical model for ITN usage in communities with malaria infections. We show that it is in the individual’s self interest to use the ITNs as long as the malaria is present in the community. Such an optimal ITN usage will significantly decrease the malaria prevalence and under some conditions may even lead to complete eradication of the disease.

基于SI模型的病毒传播动力学分析

创建了SI传播动力学模型,重点讨论了系统平衡点的存在性和稳定性,并运用连续动态系统分岔理论,利用MATLAB软件对系统的分岔情况进行了深入分析,同时考察了参数变化对系统的影响.在数值模拟阶段,对具有Holling IV型功能反应的病毒传播系统进行了详细分析,研究了疾病传播的特点和演变规律.

基于SI-SB系统安全模型的多层级边缘智能管控模式

为探索信息化、智能化技术赋能下的创新型安全生产管控模式,从安全信息学的角度分析安全管控过程中的信息流动特点,提出安全生产多层级边缘智能管控模式;基于安全信息-安全行为(SI-SB)系统安全模型分析安全管控过程中安全决策偏差和滞后的机制,提出安全管控系统性能改进的思路;结合安全生产组织管理体系特点和数字化技术优势,阐述数字化技术在信息感知传递、安全信息解释和安全行为引导等3个方面的赋能依据,以及数字化感知、智能化决策和多层级管控等3个方面的赋能途径,并提出具备智能决策、敏捷响应、弹性扩展和人机协同特点的安全生产多层级边缘智能管控模式;在紧急事件、短周期管控、长周期管控3类场景中,对应用智能管控模式前后的安全事件响应进行时效性计算和对比。结果表明:所提出的多层级边缘智能管控模式能够显著提高安全管控效能。

A Nonstandard Finite Difference Scheme for SIS Epidemic Model with Delay: Stability and Bifurcation Analysis

A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the linearized system, we can provide the stable regions in the appropriate parameter plane. It is shown that the conditions for those equilibria to be asymptotically stable are consistent with the continuous model for any size of numerical time-step. Furthermore, we also establish the existence of Neimark-Sacker bifurcation (also called Hopf bifurcation for map) which is controlled by the time delay. The analytical results are confirmed by some numerical simulations.

Prediction of ILI following the COVID-19 pandemic in China by using a partial differential equation

The COVID-19 outbreak has significantly disrupted the lives of individuals worldwide.Following the lifting of COVID-19 interventions,there is a heightened risk of future outbreaks from other circulating respiratory infections,such as influenza-like illness(ILI).Accurate prediction models for ILI cases are crucial in enabling governments to implement necessary measures and persuade individuals to adopt personal precautions against the disease.This paper aims to provide a forecasting model for ILI cases with actual cases.We propose a specific model utilizing the partial differential equation(PDE)that will be developed and validated using real-world data obtained from the Chinese National Influenza Center.Our model combines the effects of transboundary spread among regions in China mainland and human activities’impact on ILI transmission dynamics.The simulated results demonstrate that our model achieves excellent predictive performance.Additionally,relevant factors influencing the dissemination are further examined in our analysis.Furthermore,we investigate the effectiveness of travel restrictions on ILI cases.Results can be used to utilize to mitigate the spread of disease.

Thickness-averaged model for numerical simulation of electroosmotic flow in three-dimensional microfluidic chips

The microfiuidic system is a multi-physics interaction field that has at- tracted great attention. The electric double layers and electroosmosis are important flow-electricity interaction phenomena. This paper presents a thickness-averaged model to solve three-dimensional complex electroosmotic flows in a wide-shallow microchan- nel/chamber combined （MCC） chip based on the Navier-Stokes equations for the flow field and the Poisson equation to the electric field. Behaviors of the electroosmotic flow, the electric field, and the pressure are analyzed. The quantitative effects of the wall charge density （or the zeta potential） and the applied electric field on the electroosmotic flow rate are investigated. The two-dimensional thickness-averaged flow model greatly simplifies the three-dimensional computation of the complex electroosmotic flows, and correctly reflects the electrookinetic effects of the wall charge on the flow. The numerical results indicate that the electroosmotic flow rate of the thickness-averaged model agrees well with that of the three-dimensional slip-boundary flow model. The flow streamlines and pressure distribution of these two models are in qualitative agreement.

具有饱和发生率的SIS传染病模型稳定性

考虑了一类具有易感人群饱和发生率的SIS传染病数学模型,定义了基本再生数,证明了地方病平衡点的存在唯一性、局部和全局渐近稳定性,分析了饱和发生率参数对模型动力学行为的影响,并通过数值模拟验证了所得结论的准确性。

Evaluation of Component Activities in C-Mn-Fe-Si with Model Self-SReM4

A sub-regular solution model SELFSReM4 used to evaluate activities of the components in a homogeneous region of a quaternary system has been developed in Shanghai Enhanced Lab of Ferrometallurgy. This paper introduces the application of SELFSReM4 in evaluating activities of the components in C-Mn-Fe-Si system without SiC precipitation.

单纯复形上的随机SIS传染病模型

该文考虑了噪声影响下单纯复形上的随机SIS传染病模型,比较了1单形传染强度(λ)或2单形传染强度(λ_(△))受噪声扰动后的模型在随机稳定性和随机分岔方面的区别.结果表明:对于随机模型而言,噪声作用于λ所在的低次项后传染病依概率1灭绝的阈值与噪声强度有关,反之作用于λ_(△)所在的高次项则对阈值无影响;增大λ_(△),会使稳态概率密度函数靠近1处出现峰值、峰值变大或峰值趋近于1,即:增大λ_(△),会促进疾病的传播.

一类具有垂直传染的随机SIS模型的稳定性

研究一类具有饱和发生率和垂直传染的随机SIS传染病模型,分别考虑外部环境对于易感者和染病者出生率、死亡率的扰动,证明了模型存在唯一的全局正解,通过构造Lyapunov函数证明了传染病的灭绝,得到疾病持久的充分条件。

一类具有空间异质性SIS传染病模型的阈值动力学分析

本文研究了空间异质性下水平传播和垂直传播的SIS传染病模型的问题.利用半群理论、下一代再生算子谱半径的定义、Lyapunov函数、渐近自治半流理论以及数值模拟的方法,获得了空间异质性下水平传播和垂直传播的SIS传染病模型的动力学行为和传播规律的结果.这些结果推广了之前的相关研究结果,为理解此类传染病模型提供了更深入的理论依据.

Numerical modeling for electron-beam evaporated process of magnetic alloy Fe-6.5%Si

Based on Langmuir equation and thermodynamic properties of iron-silicon binary alloy, a mathematical model about the process of electron-beam evaporated binary alloy Fe-6.5%Si was established. Variation of the composition of molten pool, vapor and deposit with time, length of transient time and the composition of molten pool, deposit under the steady condition were presented according to the numerical model. The experimental results on the composition of deposit were compared to the data calculated through the model. The results show that the model is applicable, after evaporating for about 50min, the compositions of the deposit are equal to those of the ingot.

海上平台SIS系统功能安全评估的方法

海上油气生产平台是海洋石油开采生产的重要设施,具有工艺系统复杂、设备布置紧凑、应急救援困难等风险特征,通常配置有安全仪表系统(SIS)作为一种重要的安全保障措施。根据IEC61511等标准要求,为了保持安全仪表系统的功能正常实现,需要对安全仪表系统开展功能安全评估。文章分别介绍了保护层分析法(LOPA)和马尔科夫模型(Markovmodel)评估方法,其中LOPA用于SIL定级评估,Markov用于SIL验证评估。对海上平台典型事故场景登平台海管压力高高联锁回路展开分析,评估结果显示该回路的配置情况可以满足预定的功能安全需求。