具有分段感染率的传染病模型的研究

由于媒体报道对传染率的影响有着重要作用,建立了一个受媒体影响且具有分段感染率的传染病模型的研究.首先通过运用LambertW函数解出了系统的所有平衡态;其次,分析了各平衡态的稳定性;最后,利用排除极限环的存在性证明了各平衡态的全局稳定性.     

一类受媒体影响的传染病模型的研究

媒体报道对传染病的感染率有着重要的影响,为探究这种影响建立了一个受媒体影响且具有分段感染率的传染病模型．首先,计算出模型的所有平衡态,并根据基本再生数的大小分析了各平衡态的局部稳定性．其次,通过排除极限换的存在性证明了平衡态的全局渐近稳定性．最后,对媒体影响传染病模型的动力学性态进行了讨论．     

一类具有媒体影响的媒介传染病模型的分析北大核心CSCD

建立了一类媒体报道对媒介传染病传播影响的数学模型,研究了该传染病模型的动力学性态.通过求再生矩阵谱半径的方法得到基本再生数,并给出了地方病平衡点的存在性和局部稳定性.理论分析的结果表明,系统可能存在Hopf分支.进一步,由全局Lyapunov函数的方法得到了无病平衡点和地方病平衡点全局稳定的充分条件.     

一类具有媒体影响的媒介传染病模型的分析

建立了一类媒体报道对媒介传染病传播影响的数学模型,研究了该传染病模型的动力学性态.通过求再生矩阵谱半径的方法得到基本再生数,并给出了地方病平衡点的存在性和局部稳定性.理论分析的结果表明,系统可能存在Hopf分支.进一步,由全局Lyapunov函数的方法得到了无病平衡点和地方病平衡点全局稳定的充分条件.     

一类具有时滞和空间扩散的SIR传染病模型的行波解

研究了一类具有时滞和空间扩散的SIR传染病模型,通过分析相应的特征方程,讨论了系统每个平衡态的局部稳定性,通过运用交叉迭代方法和Schauder不动点定理,把行波解的存在性转化为一对上下解的存在性,通过构造一对上下解,得到了连接无病平衡态和地方病平衡态的行波解的存在性.     

具有媒体饱和效应影响的时滞SIS模型研究

媒体报道对疾病的预防和控制有着重要的作用,其可以减少人们感染疾病的机会.通过建立具有媒体饱和的传染病时滞模型来刻画媒体报道对感染率的影响,首先计算出无病平衡点和当R_01时存在唯一的地方病平衡点;其次,分析了平衡点的稳定性,并得到当参数满足一定条件时,时滞τ超过临界值τ_0,地方病平衡点处会出现Hopf分支;最后,通过数值模拟来验证理论分析.     

疫苗接种、媒体报道和治疗措施对传染病传播影响的数学模型研究

为了探讨疫苗接种、媒体报道和治疗措施对麻疹传播影响,首先建立了具有非线性发生率的SIR传染病模型,证明了无病平衡点和地方病平衡点的全局渐近稳定性.其次,建立了具有三种控制策略新的传染病模型,得到新的基本再生数R_1.最后,为了获得更好的控制效果,对这三种控制措施进行了最优化设计,得到了相应最优控制策略.数值模拟结果显示媒体报道和疫苗接种策略在抑制麻疹的传播方面比治疗措施具有更好的控制效果.     

疾病在食饵中流行的捕食与被捕食模型的分析

分析并建立了疾病在食饵中传播的生态-传染病模型,同时考虑到两种群都受密度制约因素的影响,讨论了模型解的有界性和各平衡点的存在性,利用Routh-Hurwitz判据证明了各平衡点的局部渐进稳定性,通过构造Lyapunov函数分析了各平衡点的全局渐进稳定性,得到了疾病存在与否的充分性条件.     

年龄结构乙肝传染病模型及稳定性

本文讨论一年龄结构乙肝传染病模型,得出基本再生数■的表达式,证明:当■1时,无病平衡态局部渐近稳定且全局渐近稳定;当■ 1时,存在唯一的地方病平衡态,并给出地方病平衡态的局部渐近稳定性条件,这些条件对于控制疾病的传播具有重要的理论及实际意义.     

具有媒体报道影响的SIRS模型分析

本文研究了一个具有媒体报道影响的感染率的SIRS传染病模型,得到了基本再生数?_0及模型平衡点的存在性.当?_0?_0~*1时,通过构造Lyapunov函数得到了无病平衡点的全局稳定性.进一步,本文研究由媒体报道引起的对易感者通过降低传染率进行管理控制的最优措施,证明了最优控制的存在性且得到最优控制的显式表达式.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Laminations minimales résiduellement à 2 bouts

Résumé On décrit toutes les feuilles des laminations minimales dont un ensemble résiduel de feuilles ont 2 bouts.