甲型H1N1流感早期传播的数学模型

根据甲型H1N1流感早期在我国的传播规律,给出了一种描述甲型H1N1流感早期在我国传播的数学模型,分析了模型的解及其性质,证明了在严格的防控措施下,发病者最终将会完全消失,但处于潜伏期者最终将会达到一个固定的比例,指出了甲型H1N1流感的防控工作是一项长期而艰巨的任务.     

具有年龄结构的传染病SIR流行病模型的研究

给出美国流感监测网络统计的2008年10月至2009年9月流感症状患者数在四个年龄段的分布,结合当前H1N1新型流感发病的特点,提出一年龄结构型的流感传播模型,讨论了这个模型的应用和优点.     

甲型H1N1流感传染人数的灰色预测模型研究

就我国甲型H1N1流感传染人数的预测运用灰色系统理论建立了GM(1,1)模型和1阶残差修正模型GMε(1,1),并分别作了精度分析研究了GMε(1,1)的变化趋势,提出了临界值和有效域概念.用MATLAB确定了模型参数及模型预测值.     

基于Kolmogorov前向方程评估甲型H1N1流感疫情的动态变化北大核心CSCD

基于个体水平的传染病模型可以揭示随机性在传染病疫情防控中的重要作用.研究此类模型的普遍方法是通过事件驱动的、大量重复的随机模拟来确定预测变量的范围.而基于Kolmogorov前向方程(KFE)研究个体水平的传染病模型,不仅不需要大量的重复模拟来确定预测变量的范围,而且可以同时考虑每种状态发生的概率.因此,基于2009年西安市第八医院甲型H1N1流感数据,建立了基于社交网络的个体决策心理模型,以确定行为改变率;进一步地,为得到传染病传播过程中各状态的概率分布,基于改进的个体SIR模型,通过Markov过程推导出KFE.结果表明:通过数值求解KFE可以得到整个爆发过程中每种状态发生的概率分布、最严重的时间段及相应的概率,从而能更快、更准确地了解甲型H1N1疫情的传播过程,因此有助于高效地进行甲型H1N1疫情防控.     

甲型H1N1流感的死亡率高吗——Bayes计量分析框架下的建模与估算

在全球甲型H1N1流感大流行背景下,本文在充分考虑各国甲流感死亡率可能存在个体混合效应、独立效应、相关效应及空间相关效应基础上,运用Bayes计量分析框架下的模型选择标准确定描述各国甲流感死亡率的最优模型,并基于该模型对不同国家甲流感死亡率进行估算。结果显示:个体独立、空间相关效应模型能很好拟合各国甲流感疫情统计数据,利用该模型估算的全球甲流感平均死亡率为0.577%。     

一类潜伏期具有常数输人率的SEIR模型在流感防控中的应用

针对流感病毒具有的潜伏性、隐性感染者的流动难于防控性、较高的病死率及治愈后拥有的免疫力等特性建立了潜伏期具有常数输入率的SEIR传染病模型.证明了疾病模型仅存在地方病平衡点,并且是全局渐近稳定的,给出了流感防控过程中总人口输入控制及针对染病者占总人数百分比不同情况下的对隐性染病者输入比例控制值的计算公式,并对甲型H1N1流感病毒相应数据数值模拟.     

甲流病毒传播的年龄结构模型的稳定性

研究甲型H1N1流感病毒的传播规律,建立年龄结构具有接种措施的SEIR流行病模型,给出了疾病流行的阈值并证明了地方病平衡点的稳定性问题.最后根据一些实际数据,进行数值模拟进而对模型的合理性加以完善,借助模型预测下一阶段甲流爆发的可能性并提出相关应对措施.     

复数阶GM(1,N)模型及其应用

针对传统和分数阶的GM(1,N)模型不能较好的调整新旧信息权重的问题,通过将模型的阶数从实数拓展到复数,则可以同时调整实部与虚部、新信息与旧信息之间的权值,建立复数阶的GM(1,N)模型(简记为CAGM^z(1,N)模型).并采用复数编码粒子群算法对数据进行求解,从而获得更好的预测结果.最后分别以某地道路交通事故、某地粮食产量数据等为例,运用CAGM^z(1,N)模型进行计算比较,结果表明:CAGM^z(1,N)较GM(1,N)模型有更低的平均误差、更好的精度.     

基于GM(0,N)模型的瓦斯涌出量简易预测

瓦斯涌出量具有非线性、时变与多变量等特点,对其进行准确预测具有很大的难度.在考虑初始数据的重要性基础上,对现有的GM(0,N)模型进行适当改进,得到改进的GM(0,N)模型.改进的GM(0,N)模型以一次累加生成算子(1-AGO)作为模型生成基础,没有引入导数,模型求解所得最小二乘解相对简便.结合某煤矿影响瓦斯涌出量的多因素数据,进行建模与预测,运行过程简易.与GM(0,N)模型、GM(1,N)模型比较,效果较为理想.     

隔离！

甲型H1N1流感疫情在全球多国爆发，至今，流感病例仍呈增加态势。由于中国政府高度重视，并采取了有效的防范与隔离措施，疫情在我国的扩散得到了最大限度的控制。     

Error estimates of H^1-Galerkin mixed finite element method for Schrodinger equation

An H1-Galerkin mixed finite element method is discussed for a class of second order SchrSdinger equation. Optimal error estimates of semidiscrete schemes are derived for problems in one space dimension. At the same time, optimal error estimates are derived for fully discrete schemes. And it is showed that the H1-Galerkin mixed finite element approximations have the same rate of convergence as in the classical mixed finite element methods without requiring the LBB consistency condition.     

A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1)

In this paper, we propose a nonlinear fractional order model in order to explain and understand the outbreaks of influenza A(H1N1). In the fractional model, the next state depends not only upon its current state but also upon all of its historical states. Thus, the fractional model is more general than the classical epidemic models. In order to deal with the fractional derivatives of the model, we rely on the Caputo operator and on the Grünwald–Letnikov method to numerically approximate the fractional derivatives. We conclude that the nonlinear fractional order epidemic model is well suited to provide numerical results that agree very well with real data of influenza A(H1N1) at the level population. In addition, the proposed model can provide useful information for the understanding, prediction, and control of the transmission of different epidemics worldwide. Copyright © 2013 John Wiley & Sons, Ltd.     

灰色预测GM(1,1)模型的一点改进

讨论了灰色预测GM(1,1)模型理论上存在的一些问题,认为在解微分方程dXdt(1)+aX(1)=b进行预测公式推导时,把-X1(1)=X11作为已知条件来确定微分方程的解是不合理的,而应根据实际情况,不局限于{X(1)(k)}序列,直接从最后的平均相对误差ε-=n1∑k=n1ε(k)入手,将-ε看作是常数cm的函数,求出满足Min{-ε(cm)}的cm值即可,并在此基础上推导出cm的计算公式,形成新的灰色预测公式,从而进一步提高预测精度,最后经过实例验证新的预测公式的正确性及可行性.     

2N+1-soliton Solutions of Boussinesq-Burgers Equation

2N+1-soliton solutions of Boussinesq-Burgers equation are obtained by using the Hi-rota bilinear derivative method and the perturbation technique. Further, we give the graphs of corresponding three-and five-soliton solutions.     

Modeling dynamics of an influenza pandemic with heterogeneous coping behaviors: case study of a 2009 H1N1 outbreak in Arizona

This paper aims to improve the accuracy of standard compartment models in modeling the dynamics of an influenza pandemic. Standard compartment models, which are commonly used in influenza simulations, make unrealistic assumptions about human behavioral responses during a pandemic outbreak. Existing simulation models with public avoidance also make a rigid assumption regarding the human behavioral response to influenza. This paper incorporates realistic assumptions regarding individuals’ avoidance behaviors in a standard compartment model. Both the standard and modified models are parameterized, implemented, and compared in the research context of the 2009 H1N1 influenza outbreak in Arizona. The modified model with heterogeneous coping behaviors forecasts influenza spread dynamics better than the standard model when evaluated against the empirical data, especially for the beginning of the 2009–2010 normal influenza season starting in October 2009 (i.e., the beginning of the second wave of 2009 H1N1). We end the paper with a discussion of the use of simulation models in efforts to help communities effectively prepare for and respond to influenza pandemics.     

Geometrical Optics Approach to Markov-Modulated Fluid Models

We analyze asymptotically a differential-difference equation, that arises in a Markov-modulated fluid model. Here, there are N identical sources that turn on and off , and when on they generate fluid at unit rate into a buffer, which processes the fluid at a rate   c < N   . In the steady-state limit, the joint probability distribution of the buffer content and the number of active sources satisfies a system of   N + 1  ODEs, that can also be viewed as a differential-difference equation analogous to a backward/forward parabolic PDE. We use singular perturbation methods to analyze the problem for   N →∞  , with appropriate scalings of the two state variables. In particular, the ray method and asymptotic matching are used.     

Asymptotic behavior of the loss probability for an M/G/1/N queue with vacations

In this paper, asymptotic properties of the loss probability are considered for an M/G/1/N queue with server vacations and exhaustive service discipline, denoted by an M/G/1/N-(V, E)-queue. Exact asymptotic rates of the loss probability are obtained for the cases in which the traffic intensity is smaller than, equal to and greater than one, respectively. When the vacation time is zero, the model considered degenerates to the standard M/G/1/N queue. For this standard queueing model, our analysis provides new or extended asymptotic results for the loss probability. In terms of the duality relationship between the M/G/1/N and GI/M/1/N queues, we also provide asymptotic properties for the standard GI/M/1/N model.