一类具有脉冲免疫传染病模型SIVS的全局稳定性

讨论了一类具有脉冲免疫的媒介传播的SⅣS流行病模型.疾病的进程依赖感染年龄,时刻t传染率受时刻t-τ媒介种群的影响.模型存在一无病周期解.分析表明存在依赖于脉冲周期和脉冲免疫比例的基本再生数R_0(p,T),当R_0(p,T)<1时,无病周期解是全局稳定的.     

一类具有时滞的随机SIS传染病模型

本文研究一类具有时滞的随机SIS传染病模型,并定性分析种群灭绝和持久的充分条件.获得了阈值R_0,当R_01时,种群灭绝.当R_01时,种群持久.并通过了数值模拟验证了上述理论结果.     

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.     

一类具有logistic增长的SIR时滞传染病模型的稳定性分析

研究了一类具有logistic增长的时滞SIR传染病模型,得到了决定疾病爆发和消亡的阈值R_0,证明了当R_01时,对于任意的时滞τ,无病平衡点都是全局渐近稳定的,此时疾病消亡;当R_01时,系统会出现一个临界值τ_0,当ττ_0时,地方病平衡点不稳定;当ττ_0,且满足给定的条件时,地方病平衡点局部渐近稳定;当τ=τ_0时,系统发生Hopf分支.通过数值模拟,验证了上述结论的正确性,且做了参数的敏感度分析.     

一类具时滞SIR传染病模型的动力行为

分析传染病模型的稳定性,并考虑到已感染者对易感染者的作用的时滞影响.文中首先在R_01时,构造一个Lyapunov泛函,证明了无病平衡点的全局渐近稳定性.当R_01时,证明了正平衡点的局部渐近稳定性和持久性.     

一类自调节免疫的时滞病毒感染模型分析

针对病毒在感染宿主的过程中,细胞免疫的时间滞后、非线性发生率、自调节免疫等因素往往同时出现的问题,建立了具有饱和发生率和自调节免疫的时滞病毒感染模型,证明了当R_0≤1,τ为任意值时,无病平衡点局部渐近稳定,当R_01时,存在唯一正平衡点,且在一定的条件下,存在-σ_00,当ττ_0时,正平衡点局部渐近稳定;当ττ_0时,正平衡点不稳定.最后,通过数值模拟验证了理论结果的正确性.     

一类具有两次接种的时滞SVIR传染病模型

首先建立了具有两次不同免疫率的SVIR传染病模型,并用时滞分析接种的间隔时间.然后构造李雅普诺夫函数,证明模型的稳定性由基本再生数R_0决定:当R_0<1时,无病平衡点是全局渐近稳定的,当R_0>1时,地方病平衡点是局部渐近稳定的.最后通过数值模拟验证了以上结论.     

具有一般复发现象的疾病模型的全局稳定性

本文研究了具有一般复发现象和非线性发生率的疾病模型的动力学性质,其中模型是具有无穷分布时滞的微积分方程.该模型描述了包含疱疹等传染病的—般复发现象.利用一致持久性理论和李雅普诺夫函数,我们证明了基本再生数R_0决定的系统的全局动力学性质:当R_0≤1时,疾病灭绝;当R_01时,疾病持久生存,并且正平衡点是全局吸引的.     

一类具有非线性发生率与时滞的非局部扩散SIR模型的行波解

该文研究了一类具有非线性发生率与时滞的非局部扩散SIR传染病模型的行波解问题.利用基本再生数R_0和最小波速c~*判定行波解的存在与否.首先,当cc~*,R_01时,通过对一个截断问题使用Schauder不动点定理以及取极限的方法证明了所研究模型的行波解的存在性,其次,当0cc~*,R_01或R_0≤1时,利用双边拉普拉斯变换的性质证明了行波解的不存在性.     

无标度网络上带有时滞的SIRS模型的稳定性分析

建立了一个无标度网络上带有时滞的SIRS模型,并分析了在度不相关情况下模型的动力学性态.当基本再生数R_01时,模型只有无病平衡点,运用Jacobi矩阵和Lyapunov泛函得出无病平衡点的全局稳定性;当R_01时,无病平衡点不稳定,存在唯一地方病平衡点且是持续的.     

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.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

Qualitative Analysis of Bifurcating Solutions in the Lengyel-Epstein Model

One of the most fundamental problems in theoretical biology is to explain the mechanisms by which patterns and forms are created in the＇living world. In his seminal paper ＂The Chemical Basis of Morphogenesis＂, Turing showed that a system of coupled reaction-diffusion equations can be used to describe patterns and forms in biological systems. However, the first experimental evidence to the Turing patterns was observed by De Kepper and her associates（1990） on the CIMA reaction in an open unstirred reactor, almost 40 years after Turing＇s prediction. Lengyel and Epstein characterized this famous experiment using a system of reaction-diffusion equations. The Lengyel-Epstein model is in the form as follows     

(0,1 ;0)-INTERPOLATION ON INFINITE INTERVAL (-∞, +∞)

In this paper, we study the explicit representation and convergence of (0, 1; 0)-interpolation on infinite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values are prescribed at two set of points namely the zeros of Hn(x) and H′n(x) and the first derivatives at the zeros of H′n(x).     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

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].