具有一般发生率的疟疾传播模型的稳定性研究

研究了一类具有一般发生率的疟疾传播模型,得到了模型的平衡点和基本再生数R_0.通过构造Lyapunov函数得到当R_0≤1时,无病平衡点是全局渐近稳定的;当R_01时,正平衡点是全局渐近稳定的.通过例子说明所得的理论结果.     

具有空间效应及一般感染率的时滞病毒模型分析

考虑到时滞效应及空间扩散的影响,建立了一个具有一般传染率的病毒感染仓室模型,分析了模型的动力学性态.定义了模型的基本再生数R_0,讨论了平衡点的存在性,并通过构造Lyapunov函数分析了平衡点的稳定性.结果表明,当R_01时,无病平衡点全局渐近稳定;当R_0 1时,无病平衡点不稳定且地方病平衡点在一定条件下全局渐近稳定.同时,以Beddington-DeAngelis感染率为例的数值模拟进一步验证和扩展了理论结果.     

一类潜伏期和染病期均传染的SEIQR模型的全局稳定性

研究一类潜伏期和染病期均传染的SEIQR传染病模型,得到疾病流行与否的阈值R_0.运用Lyapunov函数方法、LaSalle不变性原理及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,当R_01时地方病平衡点全局渐近稳定.     

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.     

宿主具有垂直传染的查加斯病模型的建立与分析

查加斯病是由克氏锥虫寄生引起的,其传播媒介为锥蝽.带有病原体的锥蝽叮咬健康人是其主要的传播途径,本病也可以通过输血、母婴进行传播.建立了宿主具有垂直传染、不同的传染源采用不同传染率的查加斯病模型并进行了动力学性态分析.通过分析,给出了基本再生数R_0;当垂直传染率p=0时,若R_0<1,系统仅存在无病平衡点且局部渐近稳定,意味着疾病消亡;当R_0>1时,系统存在一个正平衡点且局部渐近稳定;当0相似文献   

考虑部分免疫和环境传播的麻疹传染病模型的全局稳定性

该文考虑一个具有部分免疫和环境传播的麻疹传染病模型,得到基本再生数R_0,并通过构造Lyapunov函数,研究了该模型的无病平衡点和地方病平衡点的全局稳定性.当R_01时,无病平衡点是全局渐近稳定的,即麻疹不会传播开;当R_01时,模型存在唯一的地方病平衡点,且是全局渐近稳定的,即麻疹的传播保持在一个稳定的状态.最后,通过数值分析说明了这些结果的合理性.该文工作对于预防和控制麻疹病毒的传播具有实际意义.     

垂直传染与环境因素对野牛布鲁氏菌传播的影响研究

研究了布鲁氏菌通过水平和垂直传染在野牛种群中传播的非线性动态模型.在SIR模型中引入了环境中的布鲁氏菌对野牛的影响,并提出了一种SIRB模型.分别算出了该模型的无病平衡点P_0和地方病平衡点P*,利用再生矩阵得到模型的阈值R_0,证明了模型平衡点的稳定性由阈值的大小所决定,即R_0 1时,通过构造合适的Lyapunov函数,证得无病平衡点全局渐近稳定.当R_0 1时,利用几何方法,证得地方病平衡点全局渐近稳定.     

一类具有非线性传染率的SEIS传染病模型的稳定性分析

研究了一类具有非线性传染率的SEIS模型,模型中包含常数输入率、自然死亡率、因病死亡率等.定义了模型的基本再生数R_0,并证明了当R_01时,无病平衡点是全局渐近稳定的.当R_01时,得到了唯一的地方平衡点是全局渐近稳定的条件.     

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.     

具有潜伏期的离散SEIR模型的稳定性

建立和研究了有年龄结构和潜伏期的离散SEIR模型,运用常差分线性方程组的理论,得到基本再生数R_0的表达式,证明了当R_0<1时,无病平衡点全局渐进稳定,当R_0>1时,无病平衡点不稳定,R_0>1且R_1<1时,地方病平衡点局部渐进稳定.     

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.     

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.     

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     

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.     

Global results for an HIV/AIDS model with multiple susceptible classes and nonlinear incidence

In this paper, an HIV/AIDS epidemic model is proposed in which there are two susceptible classes. Two types of general nonlinear incidence functions are employed to depict the scenarios of infection among cautious and incautious individuals. Qualitative analyses are performed, in terms of the basic reproduction number $\R_0$, to gain the global dynamics of the model: the disease-free equilibrium is of global asymptotic stability when $\R_0\leq 1$; a unique endemic equilibrium exists and globally asymptotically stable $\R_0> 1$. The introduction of cautious susceptible and the resulting multiple transmission functions has positive effect on HIV/AIDS prevalence. Numerical simulations are carried out to illustrate and extend the obtained analytical results.     

一类潜伏期和染病期均具有传染性的手足口病模型

根据手足口病的病理特性及传播特点,建立一类描述其传播的数学模型并对模型的动力学性态进行分析.首先利用再生矩阵的方法定义了模型的基本再生数R_0,同时通过构造Lyapunov函数和Routh-Hurwitz判据证明了当R_0≤1时无病平衡点E_0的金局渐近稳定性,R_0>1时地方病平衡点E_*的局部渐近稳定性,并进一步证明了在一定条件下地方病平衡点的全局渐近稳定性.     

Global analysis of a multi-group animal epidemic model with indirect infection and time delay

The transmission mechanism of some animal diseases is complex because of the multiple transmission pathways and multiple-group interactions, which lead to the limited understanding of the dynamics of these diseases transmission. In this paper, a delay multi-group dynamic model is proposed in which time delay is caused by the latency of infection. Under the biologically motivated assumptions, the basic reproduction number $R_0$ is derived and then the global stability of the disease-free equilibrium and the endemic equilibrium is analyzed by Lyapunov functionals and a graph-theoretic approach as for time delay. The results show the global properties of equilibria only depend on the basic reproductive number $R_0$: the disease-free equilibrium is globally asymptotically stable if $R_0\leq 1$; if $R_0>1$, the endemic equilibrium exists and is globally asymptotically stable, which implies time delay span has no effect on the stability of equilibria. Finally, some specific examples are taken to illustrate the utilization of the results and then numerical simulations are used for further discussion. The numerical results show time delay model may experience periodic oscillation behaviors, implying that the spread of animal diseases depends largely on the prevention and control strategies of all sub-populations.     

Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence

In this paper, the asymptotic behavior of solutions of an autonomous SEIRS epidemic model with the saturation incidence is studied. Using the method of Liapunov–LaSalle invariance principle, we obtain the disease-free equilibrium is globally stable if the basic reproduction number is not greater than one. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions of locally and globally asymptotically stable convergence to an endemic equilibrium are obtained base on the permanence.     

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．