总人口规模变化的年龄结构MSEIR流行病模型的再生数

在总人口规模变化和疾病影响死亡率的假设下,讨论了带二次感染和接种疫苗的年龄结构MSEIR流行病模型.首先给出再生数R(ψ,λ)(这里ψ(a)是接种疫苗率,λ是总人口的增长指数)的显式表达式.其次,证明了当R(ψ,λ)<1时,系统的无病平衡态是稳定的;当R(ψ,λ)>1时,无病平衡态是不稳定的.     

总人口规模变化和带接种疫苗的年龄结构TB传染病模型的再生数

本文讨论总人口规模变化和带接种疫苗的年龄结构肺结核传染病模型,给出了该模型增值数的显式表达式(R)(ψ,λ)(λ为非病染人口的增长指数),证明了若(R)(ψ,λ)＜1,则无病平衡态是线性稳定的,若(R)(ψ,λ)＞1,则无病平衡态是不稳定的.     

一类具有时滞和接种疫苗年龄的SIS模型

研究具有时滞和接种疫苗年龄的SIS流行病模型.运用微分、积分方程理论,得到再生数R(ψ)<1,且γτ1时,地方病平衡点E*的存在性.     

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.     

总人口规模变化的年龄结构SEIR流行病模型的稳定性

运用泛函分析中的谱理论和非线性发展方程的齐次动力系统理论,讨论了总人口规模变化情况下的年龄结构的SEIR流行病模型．得到了与总人口增长指数λ*有关的再生数R0的表达式,证明了当R0<1时,系统存在唯一局部渐近稳定的无病平衡态;当 R0>1时,无病平衡态不稳定,此时存在地方病平衡态,并在一定条件下证明了地方病平衡态是局部渐近稳定的．     

具有预防接种免疫力的双线性传染率SIR流行病模型全局稳定性

研究一类具有预防接种免疫力的双线性传染率 SIR流行病模型全局稳定性 ,找到了决定疾病灭绝和持续生存的阈值——基本再生数 R0 .当 R0 ≤ 1时 ,仅存在无病平衡态 E0 ;当 R0 >1时 ,存在唯一的地方病平衡态 E* 和无病平衡态 E0 .利用 Hurwitz判据及 Liapunov-Lasalle不变集原理可以得知 :当 R0 <1时 ,无病平衡态 E0 全局渐近稳定 ;当 R0 >1时 ,地方病平衡态 E*全局渐近稳定 ,无病平衡态 E0 不稳定 ;当 R0 =1时 ,计算机数值模拟结果显示 ,无病平衡态 E0 有可能是稳定的     

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.     

年龄结构SIQRS传染病模型稳定性及接种决策

讨论年龄结构SIQRS传染病模型,得出基本再生数?_0和带接种隔离再生数?(ψ)的表达式,证明了当?(ψ)1时,无病平衡点局部渐近稳定;当?01时,无病平衡点全局渐近稳定;当?(ψ)1时,无病平衡点不稳定,此时存在地方病平衡点.利用这些结果给出对于个体来说是一个年龄还是多个年龄接种的最优决策,并且给出了一次还是两次接种的最优决策.     

一个有快慢进展的TB模型的全局稳定性分析

建立了一个有快慢进展、接种和治疗的TB模型,定义了模型的基本再生数R0,通过构造Lyapunov函数来研究解的渐近性态.证明了当R01时,无病平衡点是全局渐近稳定的;也证明了当R0>1时,惟一的地方病平衡点是全局渐近稳定的.     

一类采取隔离措施的非线性传染率传染病模型的全局稳定性

讨论一类采取隔离措施的非线性传染率传染病的数学模型,得到了基本再生数Rθ的表达式,当Rθ<1时,仅存在无病平衡点,是全局渐近稳定的;当Rθ>1时,存在两个平衡点,其中无病平衡点不稳定,地方病平衡点全局渐近稳定.     

E-紧框架小波来自MRA的特征刻画

设E=■或■,■(x)∈L~2(R~2)且■_(jk)(x)=2■(E~jx-k),其中j∈Z,k∈Z~2.若{■_(jk)|jJ∈Z,k∈Z~2}构成L~2(R~2)的紧框架,则称■(x)为E-紧框架小波.本文给出E-紧框架小波是MRA E-紧框架小波的一个充要条件,即E紧框架小波■来自多尺度分析当且仅当线性空间F_■(ξ)的维数为0或1,其中F_■(ξ)=■(ξ)|j■1},■_j(ξ)={■((E~T)~j(ξ+2kπ))}_(k∈EZ~2,j■1。     

Multidimensional stability of planar waves for delayed reaction-diffusion equation with nonlocal diffusion

In this paper, we consider the multidimensional stability of planar waves for a class of nonlocal dispersal equation in $n$--dimensional space with time delay. We prove that all noncritical planar waves are exponentially stable in $L^{\infty}(\RR^n )$ in the form of $\ee^{-\mu_{\tau} t}$ for some constant $\mu_{\tau} =\mu(\tau)>0$( $\tau >0$ is the time delay) by using comparison principle and Fourier transform. It is also realized that, the effect of time delay essentially causes the decay rate of the solution slowly down. While, for the critical planar waves, we prove that they are asymptotically stable by establishing some estimates in weighted $L^1(\RR^n)$ space and $H^k(\RR^n) (k \geq [\frac{n+1}{2}])$ space.     

具热效应的半导体方程组的初边值问题

证明了热了流模型半导体方程组整体光滑解的存在唯一性。如果区域在某一方向充分窄，则我们证明了平衡解的存在唯一性和解的渐近性。     

Transplantation Theorems for Ultraspherical Polynomials in Re H 1 and BMO

We consider the uniformly bounded orthonormal system of functions $$ u_n^{(\l)}(x)= \varphi_n^{(\lambda)}(\cos x)(\sin x)^\lambda, \qquad x\in [0,\pi], $$ where $\{\varphi_n^{(\lambda)}\}_{n=0}^\infty \,\, (\lambda > 0)$ is the normalized system of ultraspherical polynomials. R. Askey and S. Wainger proved that the $L^p$-norm $(1 < p < \infty)$ of any linear combination of the first $N+1$ functions $u_n^{(\lambda)}(x)$ is equivalent to the $L^p$-norm of the even trigonometric polynomial of degree $N$ with the same coefficients. This theorem fails if $p=1 $ or $p=\infty.$ Studying these limiting cases, we prove (for $0 < \lambda < 1$) similar transplantation theorems in $\mbox{Re } H^1$ and $\mbox{BMO}.$     

EXPANSIONS OF STEP-TRANSITION OPERATORS OF MULTI-STEP METHODS AND ORDER BARRIERS FOR DAHLQUIST PAIRS

Using least parameters, we expand the step-transition operator of any linear multi-step method （LMSM） up to O（τ^s＋5） with order s = 1 and rewrite the expansion of the steptransition operator for s = 2 （obtained by the second author in a former paper）. We prove that in the conjugate relation G3^λτ o G1^τ =G2^τ o G3^λτ with G1 being an LMSM,（1） theorder of G2 can not be higher than that of G1; （2） if G3 is also an LMSM and G2 is a symplectic B-series, then the orders of G1, G2 and G3 must be 2, 2 and 1 respectively.     

GLOBAL STABILITY IN A VIRAL INFECTION MODEL

This paper investigates the global stability of a viral infection model with lytic immune response. If the basic reproductive ratio of the virus is less than or equal to one, by the LaSalle's invariance principle, the disease-free steady state is globally asymptotically stable. If the basic reproductive ratio of the virus is greater than one but less than or equal to a constant, which is defined by the parameters of the model, then the immune-exhausted steady state is globally asymptotically stable. The endemic steady state is globally asymptotically stable if the inverse is valid.     

Ground state solution for a class fractional Hamiltonian systems

In this paper, we consider a class of Hamiltonian systems of the form $_tD_\infty^\alpha(_{-\infty} D_t^\alpha u(t))+L(t) u(t)-\nabla W(t,u(t))=0$ where $\alpha\in(\frac{1}{2},1)$, $_{-\infty}D_t^\alpha$ and $_{t}D_\infty^\alpha$ are left and right Liouville-Weyl fractional derivatives of order $\alpha$ on the whole axis $R$ respectively. Under weaker superquadratic conditions on the nonlinearity and asymptotically periodic assumptions, ground state solution is obtained by mainly using Local Mountain Pass Theorem, Concentration-Compactness Principle and a new form of Lions Lemma respect to fractional differential equations.     

Bifurcations and exact travelling wave solutions of M-N-Wang equation

By using the method of dynamical systems to Mikhailov-Novikov-Wang Equation, through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system of the derivative $\phi(\xi)$ of the wave function $\psi(\xi)$. Under different parameter conditions, for $\phi(\xi)$, exact explicit solitary wave solutions, periodic peakon and anti-peakon solutions are obtained. By integrating known $\phi(\xi)$, nine exact explicit traveling wave solutions of $\psi(\xi)$ are given.