Stability of an equilibrium state in a multiinfectious-type SIS model on a truncated network

In a homogeneous constant population, the basic SIS model potentially has an epidemic equilibrium state with global asymptotic stability since it can be reduced to the logistic equation. On the basic SIS model with a nonhomogeneous constant population, viewed as a multitype SIS model, the global or local asymptotic stability of an epidemic equilibrium state has also been studied.^1–4 However, this kind of analysis in other models with nonhomogeneous populations has rarely been developed, even though the corresponding models with homogeneous populations are well known. In addition, recent studies of complex networks have revealed that heterogeneity of the link number of vertices drastically changes the epidemic thresholds.^5–9 For these reasons, figuring out the roles of heterogeneity is a major topic in epidemic modeling. Here, we consider a multiinfectious-type SIS model on a network, and show the (local or global) asymptotic stability of an epidemic equilibrium state whenever it exists. This work was presented in part at the 11th International Symposium of Artificial Life and Robotics, Oita, Japan, January 23–25, 2006     

小世界网络上随机SIS模型分析

考察小世界网络上疾病传播的随机SIS模型,使用拟平稳分布计算方法得到疾病传播稳态时患病节点数的分布。取分布的均值,得到与平均场方法相同的传播阈值。通过模拟所得的传染曲线解释现实传染过程中存在的波动性,传播稳态结果和平均场结果拟合较好,证实了平均场方法的合理性。     

一类脉冲动力系统的状态反馈控制

对一类具有状态反馈控制的脉冲动力系统的动力学性质进行了研究．由周期解的扰动解得到了一个Poincare映射，利用Poincare映射讨论了系统周期解的分岔，并得到了半平凡周期解和正周期-1解存在和稳定的充分条件．定性分析和数学模拟表明，半平凡周期解通过fold分岔分钻出正周期-1解，正周期-1解通过flip分岔分岔出正周期-2解，再通过一系列flip分岔通向混沌，此外，讨论了脉冲状态反馈控制的效果．     

SIS model of epidemic spreading on dynamical networks with community

We present a new epidemic Susceptible-Infected-Susceptible (SIS) model to investigate the spreading behavior on networks with dynamical topology and community structure. Individuals in themodel are mobile agentswho are allowed to perform the inter-community (i.e., long-range) motion with the probability p. The mean-field theory is utilized to derive the critical threshold (λ_C) of epidemic spreading inside separate communities and the influence of the long-range motion on the epidemic spreading. The results indicate that λ_C is only related with the population density within the community, and the long-range motion will make the original disease-free community become the endemic state. Large-scale numerical simulations also demonstrate the theoretical approximations based on our new epidemic model. The current model and analysis will help us to further understand the propagation behavior of real epidemics taking place on social networks.     

适应网络病毒传播的SIS离散模型

为有效地模拟病毒在适应网络中的传播,分析了当前适应网络病毒传播研究的现状,结合适应网络中存在的节点动力学和网络动力学相互作用、相互反馈的机制,提出了一种基于计算机仿真技术的适应网络病毒传播的SIS(susceptibleinfected-susceptible)离散模型.通过对所建模型进行仿真和分析,实验结果表明,病毒在适应网络中传播具有双稳态性;由于节点规避病毒传播而改变网络连接的行为,使得网络的度分布发生变化,该行为对病毒在网络中的传播具有抑制作用.     

On the dynamics of deterministic epidemic propagation over networks

In this work we review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network models for Susceptible-Infected (SI), Susceptible-Infected-Susceptible (SIS), and Susceptible-Infected-Recovered (SIR) settings. In each setting, we provide a comprehensive nonlinear analysis of equilibria, stability properties, convergence, monotonicity, positivity, and threshold conditions. For the network SI setting, specific contributions include establishing its equilibria, stability, and positivity properties. For the network SIS setting, we review a well-known deterministic model, provide novel results on the computation and characterization of the endemic state (when the system is above the epidemic threshold), and present alternative proofs for some of its properties. Finally, for the network SIR setting, we propose novel results for transient behavior, threshold conditions, stability properties, and asymptotic convergence. These results are analogous to those well-known for the scalar case. In addition, we provide a novel iterative algorithm to compute the asymptotic state of the network SIR system.     

基于小世界网络的甲型流感传播的研究

借助小世界网络模型和扩展的SIS传染病传播模型,建立了复杂网络的传染病传播模型,并利用此模型模拟甲型H1N1型流感病毒的传播过程,通过调节模型的不同的参数,找到影响病毒传播速度的关键因素,为研究甲型H1N1型流感病毒的传播特性和对病毒的防疫提供参考。     

时滞传染病动力学模型的脉冲接种策略研究

具有时滞的传染病模型能较好反映传染病的潜伏期、免疫期等问题．利用时滞系统的脉冲优化原理对该类模型进行分析，阐述了脉冲优化控制的基本原理和实现方法，并给出了优化脉冲接种的应用实例．结果表明该方法是有效的，并具有潜在的应用价值．     

SIS model of epidemic spreading on dynamical networks with community

We present a new epidemic Susceptible-Infected-Susceptible (SIS) model to investigate the spreading behavior on networks with dynamical topology and community structure. Individuals in themodel are mobile agentswho are allowed to perform the inter-community (i.e., long-range) motion with the probability p. The mean-field theory is utilized to derive the critical threshold (λ _C ) of epidemic spreading inside separate communities and the influence of the long-range motion on the epidemic spreading. The results indicate that λ _C is only related with the population density within the community, and the long-range motion will make the original disease-free community become the endemic state. Large-scale numerical simulations also demonstrate the theoretical approximations based on our new epidemic model. The current model and analysis will help us to further understand the propagation behavior of real epidemics taking place on social networks.     

单核单涡旋混沌系统定平面折返控制法

基于混沌细胞模型理论,提出适用于单核单涡旋混沌系统的定平面折返控制法.让混沌系统的运动轨线在确定的平面折返,并用一线性系统取代混沌系统作折返运动,从而大大降低了系统的随机性.适当选择折返平面,可控制混沌系统稳定运行于某些周期轨道上.用该控制方法对多个典型混沌系统进行数字仿真实验,获得了稳定的周期1、周期2和周期4轨道.     

Understanding dengue fever dynamics: a study of seasonality in vector-borne disease models

Dengue fever dynamics show seasonality, with the disease transmission being higher during the warmer seasons. In this paper, we analyse seasonally forced epidemic models with and without vector dynamics. We assume small seasonal effects and obtain approximations for the real response of each state variable and also for the corresponding amplitude and phase via decomposition of the sinusoidal forcing into imaginary exponential functions. The analysis begins with the simplest susceptible-infected-susceptible (SIS) model, followed by the simplest model with vector dynamics, susceptible-infected-susceptible for hosts and uninfected-vector (SISUV). Finally, we compare the more complex susceptible-infected-recovered (SIR) and susceptible-infected-recovered for hosts and uninfected-vector (SIRUV) models and conclude that the models give basically the same information when we replace, in the SIR model, the human infectivity by a function of both human and mosquito infectivities.     

脉冲推力作用下半被动双足机器人的行走动力学分析

为了提高半被动双足机器人在水平地面上行走的稳定性,研究一种脉冲推力作用下半被动双足机器人的行走动力学行为.以最简单的特殊行走模型为动力学模型,采用支撑腿脚后跟脉冲推力作为双足机器人行走动力源.鉴于系统模型的高度非线性,将连续阶段的非线性微分方程线性化;利用角动量守恒和脉冲推力构造一个二维离散映射;采用离散映射的不动点及其特征值分析系统周期步态的存在性和稳定性;接着讨论系统的倍周期分岔.在理论分析的基础上,通过Matlab软件对半被动双足机器人的行走动力学进行仿真实验. 仿真结果表明,在水平地面上行走的半被动双足机器人具有稳定的周期-1步态和周期-2步态.     

社会网络中传染病预测防控虚拟仿真实验设计

基于传染病模型和社会网络等专业知识所设计的虚拟仿真实验能够突破传统教学的时间和空间限制,为学生提供了解传染病扩散过程和参与传染病防范控制的机会。以自主研发的虚拟仿真实验平台为载体,通过SIS模型实验、SIR模型实验、SEIR模型实验和传染病防控仿真实验四个模块来模拟传染病发生时的疾病研究、战略制定、防控实施、效果评估等关键环节,从而综合培养学生在数据分析、全局决策、团队合作、社会责任感等方面的能力素养,有效推进"智能+教育"在实验教学中的落实。     

硅悬臂梁脉象传感器温度补偿

阐述了采用硅悬臂梁制造的脉象传感器结构、设计和温度补偿原理。实验结果表明:补偿后的传感器具有灵敏度高、稳定性好,线性度为1%FS(0~5 N),重复性为0.5%FS,灵敏度为50 mV/N。给出的温度补偿晶体管对该脉象传感器的灵敏度温度漂移补偿效果好,有推广应用前景。     

网格图像法提取多维脉搏特征信息

利用前期研制的基于单CCD(charge coupled device,电子耦合器件)的脉搏多维信息测量装置,采集得到脉搏动态时变图像序列.重新设计传感器触头为绘有网格点的软性双层薄膜结构,在此基础上,建立了测量原理模型,论证了该装置获取脉搏多维信息的可行性.随后,通过对网格点图像的处理,成功提取了脉搏波的形态、频率、节律及脉宽信息,所得结果与测量模型分析一致.研究表明,该系统能够有效提取多维脉搏特征信息,为脉搏信息的检测和表征提供了一种全新的手段和方法.     

传染病传播模型研究

用数学模型帮助发现传染病的传播机理,预测传染病的流行趋势已成为共识.主要简述了传染病模型的发展历程.传染病的数学模型研究分为两类:决定性模型和网络动力学模型.虽然决定论模型目前仍然具有非常重要的学术地位,但随着人工智能计算机技术的发展,目前网络动力学模型成为了新的研究热点.决定性模型主要介绍了SIS和SIR模型,网络动力学模型主要介绍了目前流行病数学模型中研究较多、应用较广的模型,包括元胞自动机、人工神经网络、无尺度网络模型.介绍了各种模型的研究方法,并且探讨了今后的研究热点,以利用其模拟结果可以更好地为传染病防治决策提供支持.     

图像化脉象仪数学建模与脉搏信息提取

为获取脉诊触觉信息,采用绘制有圆形网格点的软性薄膜加压传感探头,由单一CCD摄像头获取脉搏动态图像.在对脉搏图像传感器结构分析的基础上,建立详细的测量原理模型,论证了该图像化脉象仪获取脉搏多维信息的可行性.在此模型基础上,应用图像处理的方法提取得到脉搏波形,并给出定量分析及实验结论.研究表明,本系统能够有效提取多维脉搏特征信息,为中医诊断客观化和科学化提供了一种新的手段和方法.     

Genesio体系中的内信号随机共振

采用数值模拟的方法,研究了不同耦合方式下Genesio体系中振子的动力学行为,分别讨论了当体系处于周期-1振荡态时,单个振子、双边耦合和单边耦合情况下体系对噪声及耦合的响应情况。发现噪声强度、耦合方式及耦合强度都会对体系的内信号传递产生不同的影响。在合适的噪声水平和耦合强度及方式下,体系内信号能够被传递和放大,产生内信号随机共振现象。同时发现双边耦合比单边耦合更有利于信号的传递。本文的模拟结果将对内信号随机共振现象的试验研究有一定的意义。     

主动粘弹性控制抗冲击扰动

根据粘弹性材料耗能减振性能较好的特点,针对高频扰动、冲击扰动,本文提出了主动粘弹性控制的方法,定义了主动粘弹性控制技术的基本架构.根据粘弹性材料的耗能计算模型,提出了粘弹性控制律的选取原则.结合广义Maxwell模型,提出了3种粘弹性控制律(viscoelastic control law,VCL).并将粘弹性比例–微分(proportional derivative,PD)控制、粘弹性比例–积分–微分(proportional integral derivative,PID)控制、粘弹性自抗扰控制(active disturbance rejection control,ADRC)应用到常见的二阶系统中.研究结果表明,主动粘弹性控制技术抗高频扰动、抗冲击扰动的性能特别优异.由于主动控制的响应速度快,主动粘弹性控制的抗扰性能好,本文提出了主动控制与主动粘弹性控制相切换的控制方法,并对切换控制策略进行了研究.研究结果表明,切换控制可同时兼顾抗扰性能与响应速度.     

人体脉搏系统传递函数模型的参数估计与脉搏波仿真

为了揭示和研究人体脉搏系统的作用机理,文章从一种新的角度———系统分析和信号处理的角度建立了人体脉搏系统传递函数模型,获得脉搏系统传递函数的一般形式,结果表明传递函数只有极点而没有零点。根据脉象信号的实验测量数据对模型参数进行了估计。并运用此模型在计算机上成功地模拟了人体四种脉象信号,仿真结果与实际结果相符。