具有染病年龄结构的SEIR流行病模型的稳定性

建立和研究了一类具有染病年龄结构的SEIR流行病模型.得到了该模型的基本再生数R0的表达式.证明了当R0<1时,无病平衡点E0不仅局部渐近稳定,而且全局吸引;当R0>1时,无病平衡点E0不稳定,此时存在稳定的地方病平衡点.     

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.     

具有Logistic增长和年龄结构的SIS模型

讨论具有Logistic增长和年龄结构的SIS流行病模型.运用微分、积分方程理论,得到了当再生数R0<1时,无病平衡点E0是全局渐近稳定的;当R0>1时,地方病平衡点E*是局部渐近稳定的.     

带接种疫苗和二次感染的年龄结构MSEIR流行病模型分析

本文讨论带二次感染和接种疫苗的年龄结构MSEIR流行病模型。在常数人口规模的假设下,运用微分方程和积分方程中的理论和方法,得到一个与接种疫苗策略ψ有关的再生数R(ψ)的表达式,证明了当R(ψ)<1时,无病平衡态是局部渐近稳定的;当R(ψ)>1时,无病平衡态是不稳定的,此时存在一个地方病平衡态,并且证明当R(0)<1时,无病平衡态是全局渐近稳定的。     

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.     

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.     

一类带有非线性传染率的SEIR传染病模型的全局分析

通过假设被传染的易感者一部分经过一段潜伏期后才具有传染性,而另一部分被感染的易感者直接成为传染者,建立了一类带有非线性传染率的SEIR传染病模型,得到了确定疾病是否成为地方病的基本再生数以及无病平衡点和地方病平衡点的全局稳定性.     

年龄结构乙肝传染病模型及稳定性

本文讨论一年龄结构乙肝传染病模型,得出基本再生数■的表达式,证明:当■1时,无病平衡态局部渐近稳定且全局渐近稳定;当■ 1时,存在唯一的地方病平衡态,并给出地方病平衡态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.     

一类具有饱和发生率的包虫病传播模型研究

研究一类具有饱和发生率的包虫病模型,分别讨论了无病平衡点和地方病平衡点的稳定性.分析结果表明模型的动力学行为完全由基本再生数R_0决定.最后,在讨论部分根据R_0的表达式对疾病给出一些控制策略.     

具有免疫接种且总人口规模变化的SIR传染病模型的稳定性

讨论一类具有预防免疫接种且有效接触率依赖于总人口的SIR传染病模型,给出了决定疾病灭绝和持续生存的基本再生数σ的表达式,在一定条件下证明了疾病消除平衡点的全局稳定性,得到了唯一地方病平衡点的存在性和局部渐近稳定性条件.最后研究了具有双线性传染率和标准传染率的两个具体模型,并证明了当σ>1时该模型地方病平衡点的全局渐近稳定性.     

STABILITY OF AN SEIS EPIDEMIC MODEL WITH CONSTANT RECRUITMENT AND A VARYING TOTAL POPULATION SIZE

This paper considers an SEIS epidemic model with infectious force in the latent period and a general population-size dependent contact rate. A threshold parameter R is identified. If R≤1, the disease-free equilibrium O is globally stable. If R〉1, there is a unique endemic equilibrium and O is unstable. For two important special cases of bilinear and standard incidence ,sufficient conditions for the global stability of this endemic equilibrium are given. The same qualitative results are obtained provided the threshold is more than unity for the corresponding SEIS model with no infectious force in the latent period. Some existing results are extended and improved.     

Two-group SIR epidemic model with stochastic perturbation

A stochastic two-group SIR model is presented in this paper.The existence and uniqueness of its nonnegative solution is obtained,and the solution belongs to a positively invariant set.Furthermore,the globally asymptotical stability of the disease-free equilibrium is deduced by the stochastic Lyapunov functional method if R0 ≤ 1,which means the disease will die out.While if R0 1,we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average.In addition,the intensity of the fluctuation is proportional to the intensity of the white noise.When the white noise is small,we consider the disease will prevail.At last,we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments.     

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.     

Hopf bifurcation of nonlinear incidence rates SIR epidemiological models with stage structure

1 ModelsIn standard epidethelogical modeis (ase [ll) the incidence rate (the rate of new infections)is bilinear in the infecire frartion and the susceptible fraction. There are a variet}' of reasonsthat the standard bilinear fOrm may reqfore modification (see [2. 3]). On the other hand, thereare some kinds of diseases which only spread or have more opportunities to be spread in adults(such as gollorrhea. s}philis. etc.). Consequently, realistic anaI\.sis of disease transmissiun in apopulation…     

两种群相互竞争的高维SEIR传染病模型全局渐近稳定性

研究了一类两种群相互竞争的非线性高维SEIR传染病数学模型动力学性质,综合利用Lasalle不变集原理,Lyapunov函数,Routh-Hurwitz判据和Krasnoselskii等多种方法,得到了边界平衡点的全局渐近稳定和正平衡点局部渐近稳定的阈值条件.     

TWO DIFFERENTIAL INFECTIVITY EPIDEMIC MODELS WITH NONLINEAR INCIDENCE RATE

This paper considers two differential infectivity（DI） epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely., a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity,O is globally stable and the disease always dies out. If σ〉1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover,when σ〈 1 ,the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.     

Global stability of a stage-structured epidemic model with a nonlinear incidence

In this paper, a stage-structured epidemic model with a nonlinear incidence with a factor S^p is investigated. By using limit theory of differential equations and Theorem of Busenberg and van den Driessche, global dynamics of the model is rigorously established. We prove that if the basic reproduction number R₀ is less than one, the disease-free equilibrium is globally asymptotically stable and the disease dies out; if R₀ is greater than one, then the disease persists and the unique endemic equilibrium is globally asymptotically stable. Numerical simulations support our analytical results and illustrate the effect of p on the dynamic behavior of the model.     

具有常数迁入率和非线性传染率βI~pS~q的SI模型分析

对一种具有种群动力和非线性传染率的传染病模型进行了研究,建立了具有常数迁入率和非线性传染率βI~pS~q的SI模型.与以往的具有非线性传染率的传染病模型相比,这种模型引入了种群动力,也就是种群的总数不再为常数,因此,该类模型更精确地描述了传染病传播的规律.还讨论了模型的正不变集,运用微分方程稳定性理论分析了模型平衡点的存在性及稳定性,得出了疾病消除平衡点和地方病平衡点的全局渐进稳定的充分条件.进一步的,得出了在某些参数范围内会出现Hopf分支现象,并对上述模型进行了生物学讨论.