带有非线性传染率的传染病模型

对一类带有非线性传染率的SEIS传染病模型,找到了其基本再生数.借助动力系统极限理论,得到当基本再生数小于1时,无病平衡点是全局渐近稳定的,且疾病最终灭绝.当基本再生数大于1时,无病平衡点是不稳定的,而唯一的地方病平衡点是局部渐近稳定的.应用Fonda定理,得到当基本再生数大于1时疾病一致持续存在.     

一类具有非线性发生率的传染病模型的稳定性

建立和研究一类具有非线性发生率的传染病模型,得到该模型基本再生数R_0的表达式,运用Lyapunov函数和第二加性复合矩阵理论证明了当R_0<1时无病平衡点全局渐近稳定,此时疾病消失,当R_0>1时地方病平衡点全局渐近稳定,此时疾病在人群中流行.     

具有饱和传染率、免疫接种和垂直传染的SIR传染病模型的稳定性

研究了一类具有饱和传染率、免疫接种和垂直传染的SIR传染病模型,确定了疾病的基本再生数,得出当疾病的基本再生数小于1时,无病平衡点是全局指数渐近稳定的,当疾病基本再生数大于1时.地方病平衡点是全局渐近稳定的,讨论了其生物意义.     

具有饱和传染率、免疫接种和垂直传染的SIR传染病模型的稳定性北大核心

研究了一类具有饱和传染率、免疫接种和垂直传染的SIR传染病模型,确定了疾病的基本再生数,得出当疾病的基本再生数小于1时,无病平衡点是全局指数渐近稳定的,当疾病基本再生数大于1时.地方病平衡点是全局渐近稳定的,讨论了其生物意义.     

年龄结构SIQR传染病模型及稳定性

讨论了年龄结构SIQR传染病模型,得出基本再生数R_0和接种再生数R(ψ)的表达式,证明了当R(ψ)1时,无病平衡点局部渐近稳定;当R_01时,无病平衡点全局渐近稳定;当R(ψ)1时,无病平衡点不稳定,此时存在唯一的地方病平衡点,并给出了地方病平衡点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,同时用再生数的表达式进一步解释了接种和隔离治疗在控制消除传染病中的作用.     

一类非线性染病年龄结构模型渐近性态

研究一类具有非线性染病年龄结构SIS流行病传播数学模型动力学性态,得到疾病绝灭和持续生存的阈值--基本再生数.当基本再生数小于或等于1时,仅存在无病平衡点,且在其小于1的情况下,无病平衡点全局渐近稳定,疾病将逐渐消除;当基本再生数大于1时,存在不稳定的无病平衡点和唯一的局部渐近稳定的地方病平衡点,疾病将持续存在.     

潜伏期和染病期均具有康复的年龄结构MSEIS流行病模型的稳定性

本文建立和研究了潜伏期和染病期均具有康复的年龄结构MSEIS流行病模型.在总人口规模不变的假设下,得到了决定疾病消亡与否的基本再生数R0的表达式,证明了当R0＜1时,无病平衡点是局部和全局渐近稳定的,此时疾病消失;当R0＞1时,无病平衡点不稳定,此时系统至少存在一个地方病平衡点,并在一定条件下证明了地方病平衡点的局部渐近稳定性.     

一类具有接种疫苗的年龄结构传染病模型分析

建立和研究了一类具有接种疫苗的年龄结构SVWIR传染病模型.在总人口规模不变的条件下,运用微分方程和积分方程中的理论和方法,得到与接种疫苗策略Ψ有关的基本再生数R(Ψ)的表达式,证明了当R(Ψ)1时,无病平衡点是局部渐近稳定的;当R(0)1时,无病平衡点是全局渐近稳定的,此时疾病消亡;当R(Ψ)1时,无病平衡点是不稳定的,此时系统存在地方病平衡点.     

一类带有非线性传染率的SEIS传染病模型的定性分析

借助极限理论和Fonda定理,研究了一类既有常数输入率又有因病死亡率的SEIS传染病模型．所考虑模型的传染率是非线性的,并且得到了该模型的基本再生数,当基本再生数小于1时,该模型仅存在唯一的无病平衡点,它是全局渐近稳定的,且疾病最终灭绝．当基本再生数大于1时,该模型除存在不稳定的无病平衡点外,还存在唯一的局部渐近稳定的地方病平衡点,并且疾病一致持续存在．     

潜伏期具有传染性的年龄结构MSEIS流行病模型的稳定性

本文讨论了潜伏期和染病期均具有传染性的年龄结构MSEIS流行病模型.在总人口规模不变的假设下,运用微分方程和积分方程中的理论和方法,得到了基本再生数 0的表达式,证明了当 0 <1时,无病平衡点是局部和全局渐近稳定的,此时疾病消亡.当 0 >1时,无病平衡点不稳定,此时系统至少存在一个地方病平衡点,并在一定条件下证明了该地方病平衡点的局部渐近稳定性.     

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.     

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     

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.     

(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].