一类有迁移的SIS流行病模型

研究一类种群有迁移的流行病模型,得到了这类模型的基本再生数R0,证明了R0＜1无病平衡点是局部渐近稳定的,而当R0＞1时无病平衡点是不稳定的.进一步讨论了疾病持续存在与无病平衡点和地方病平衡点全局稳定的条件.     

带有免疫反应的病毒动力学模型的全局稳定性

利用Lyapunov函数研究了带有免疫反应的病毒动力学模型的全局稳定性.当基本再生数R0≤1时.病毒在体内清除;当R0>1时,病毒在体内持续生存.并且模型的正解当免疫再生数R1≤1时,趋于无免疫平衡点,当R1>1.趋于地方病平衡点.     

一类带有治愈率的HIV感染的CD4＋T细胞模型的动力学性质

本文主要介绍一类带有治愈率的HIV感染的CD4 T细胞模型的动力学性质,同时证明了如果基本再生数R0＜1,HIV感染消失;如果R0＞1,HIV感染持续.然后进行数值模拟,给出了地方性平衡点E·全局稳定的参数域,得到了地方性平衡点E·不稳定时周期解存在.     

一类具免疫应答和非线性感染函数的时滞HIV-1感染模型的全局稳定性

考虑到HIV-1感染过程中免疫反应和非线性感染函数,建立了一类具有三个分布时滞的HIV-1感染动力学模型.得到了关于病毒感染的基本再生数R0和CTLs免疫反应的基本再生数R1 ＜R0.通过构造Lyapunov泛函证明了系统具有阈值动力学性质,即当R0≤1时,系统存在全局渐近稳定的无感染平衡点;当R1≤1＜R0时,系统出...     

潜伏期和染病期均具有传染性的媒介传染病模型的全局稳定性分析

讨论潜伏期和染病期均具有传染性的媒介传染病模型.得到模型基本再生数的表达式,证明了当基本再生数小于1时,无病平衡点是全局渐近稳定的,此时疾病消亡;当基本再生数大于1时,无病平衡点是不稳定的,系统存在全局渐近稳定的地方病平衡点,此时,疾病将在人群中持续存在,数值模拟验证了理论结果.     

一类SEIV模型的研究(英文)

本文主要研究一类带有饱和感染率且潜伏期也具有传染性的SEIV模型.运用微分方程中的极限理论和Busenberg-Driessche定理,建立了该模型的全局动力学性质;并且证明了当基本再生数R0≤1时,无病平衡点Q0是全局稳定的,当基本再生数R01时,疾病持续.     

带有分布时滞和非线性发生率的媒介-宿主传染病模型全局稳定性(英文)

本文分析一类带有分布时滞和非线性发生率的媒介-宿主传染病动力学性质,得到模型基本再生数R0,发现系统中平衡态的全局动力学性质能够由基本再生数来完全确定:即,如果R01,无病平衡态是全局渐近稳定的;如果R01,则系统存在唯一地方病平衡态,并且该平衡态是全局渐近稳定的.     

具有常数输入的SEIS模型的全局渐近稳定性

讨论一类具有常数输入且传染率为非线性的SEIS流行病传播数学模型,给出了决定疾病灭绝和持续生存的基本再生数R0.当R0<1时,无病平衡点全局渐近稳定;当R0>1时,利用第二加性复合矩阵证明了惟一地方病平衡点全局渐近稳定.     

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.     

一类潜伏期与传染期均传染的SEIQR传染病模型

研究了一类潜伏期和感染期均传染的SEIQR模型的全局稳定性,找到疾病绝灭和持续生存的阈值——基本再生数R0,证明了无病平衡点和地方病平衡点的存在性和全局渐近稳定性,揭示了隔离对疾病控制的积极作用。     

具有垂直传染和接触传染的传染病模型的稳定性研究

本文研究了一类具有垂直传染和接触传染的传染病模型.利用常微分方程定性与稳定性方法,分析了该模型非负平衡点的存在性及其局部稳定性.同时,利用LaSalle不变性原理和通过构造适当的Lyapunov函数,获得了平凡平衡点、无病平衡点和地方病平衡点全局渐近稳定的充分条件.结果表明当基本再生数小于等于1时,所有种群趋于灭绝;当基本再生数大于1和病毒主导再生数小于1时,病毒很快被清除;当基本再生数大于1和病毒主导再生数大于1以及满足一定条件时,病毒持续流行并将成为一种地方病.     

一类具有分布时滞和非线性发生率的媒介传染病模型的全局稳定性

建立了一类具有分布时滞和非线性发生率的SIR媒介传染病模型,分析得到了决定疾病是否一致持续存在的基本再生数．而且当基本再生数不大于1时,疾病最终灭绝;当基本再生数大于1时,模型存在惟一的地方病平衡点,并且疾病一致持续存在于种群之中．通过构造Lyapunov泛函,证明了在一定条件下地方病平衡点只要存在就全局稳定．同时指出了证明地方病平衡点全局稳定时可适用的Lyapunov泛函的不惟一性.     

Global stability of a delayed epidemic model with latent period and vaccination strategy

In this paper, a mathematical model describing the transmission dynamics of an infectious disease with an exposed (latent) period and waning vaccine-induced immunity is investigated. The basic reproduction number is found by applying the method of the next generation matrix. It is shown that the global dynamics of the model is completely determined by the basic reproduction number. By means of appropriate Lyapunov functionals and LaSalle’s invariance principle, it is proven that if the basic reproduction number is less than or equal to unity, the disease-free equilibrium is globally asymptotically stable and the disease fades out; and if the basic reproduction number is greater than unity, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic.     

Stability Analysis of an SEIS Epidemic Model with Nonlinear Incidence and Time Delay

In this paper, an SEIS epidemic model with nonlinear incidence and time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the model is established. By using suitable Lyapunov functional and LaSalle's invariance principle, it is shown that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number is less than unity. If the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global stability of the endemic equilibrium. Numerical simulations are carried out to illustrate the theoretical results.     

一类具有饱和发生率及免疫的时滞SEIR传染病模型的全局渐近稳定性

研究了一类具有饱和发生率及免疫的SEIR,传染病模型、构造适当的Lyapunov泛函并运用时滞微分方程的LaSalle型定理,证明了当基本再生数小于1时,无病平衡点是全局渐进稳定的,当基本再生数大于1时,地方病平衡点存在并且是全局渐近稳定的.     

Global dynamics of a Cholera model with age-of-immunity structure and reinfection

To understand V.Cholera transmission dynamics, in this paper, a mathematical model for the dynamics of cholera with reinfection is formulated that incorporates the duration time of the recovery individuals (age-of-immunity). The basic reproduction number $\Re_0$ for the model is identified and the threshold property of $\Re_0$ is established. By applying the persistence theory for infinite-dimensional systems, we show that the disease is uniformly persistent if the reproductive number $ \Re_0>1$. By constructing a suitable Lyapunov function, the global stability of the infection-free equilibrium in the system is obtained for $\Re_0<1$; the unique endemic equilibrium of the system is globally asymptotically stable for $\Re_0>1$.     

Dynamics of an HIV‐1 virus model with both virus‐to‐cell and cell‐to‐cell transmissions,general incidence rate,intracellular delay,and CTL immune responses

Direct cell‐to‐cell transmission of HIV‐1 is a more efficient means of virus infection than virus‐to‐cell transmission. In this paper, we incorporate both these transmissions into an HIV‐1 virus model with nonlinear general incidence rate, intracellular delay, and cytotoxic T lymphocyte (CTL) immune responses. This model admits three types of equilibria: infection‐free equilibrium, CTL‐inactivated equilibrium, and CTL‐activated equilibrium. By using Lyapunov functionals and LaSalle invariance principle, it is verified that global threshold dynamics of the model can be explicitly described by the basic reproduction numbers.     

Global Stability for a Dynamic model of Hepatitis B with Antivirus Treatment

An epidemic model on the basis of therapy of chronic Hepatitis B with antivirus treatment was introduced in this paper. By applying a comparison theorem and analyzing the corresponding characteristic equations, we obtain sufficient conditions on the parameters for the global stability of the disease-free state. It's proved that if the basic reproduction number \(R_0 &lt; 1\) , the disease-free equilibrium is globally asymptotically stable. If \(R_0 &gt; 1\), the disease-free equilibrium is unstable and the disease is uniformly permanent. Moreover, if \(R_0 &gt; 1\), sufficient conditions are obtained for the global stability of the endemic equilibrium.     

A delayed SIR epidemic model with saturation incidence and a constant infectious period

In this paper, an SIR epidemic model with saturation incidence and a time delay describing a constant infectious period is investigated. By analyzing the corresponding characteristic equations, the local stability of a disease-free equilibrium and an endemic equilibrium is established. When the basic reproduction number is greater than unity, it is proved that the disease is uniformly persistent in the population, and explicit formulae are obtained to estimate the eventual lower bound of the fraction of infectious individuals. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are derived for the global attractiveness of the endemic equilibrium. Numerical simulations are carried out to illustrate the main results.     

Stability and Hopf bifurcation of a delayed epidemic model with stage structure and nonlinear incidence rate

In this paper, a stage‐structured SI epidemic model with time delay and nonlinear incidence rate is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease‐free equilibrium, and the existence of Hopf bifurcations are established. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease‐free equilibrium is globally asymptotically stable. If the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. Copyright © 2013 John Wiley & Sons, Ltd.