一类具有时滞的SIRS传染病模型的Hopf分岔分析

研究了一类具有时滞的SIRS传染病模型.首先,利用特征值理论得到了模型的有病毒平衡点,然后通过分析在有病毒平衡点处的相应特征方程根的分布,得到有病毒平衡点处的局部渐近稳定和发生Hopf分岔的时滞临界点.以时滞为分岔参数,研究了SIRS传染病模型存在Hopf分岔的条件.     

一类多菌株STD模型的共存性

我们已经研究过一类拥有两种菌株的异性传播的性传染病模型.得到了边界平衡点稳定的充要条件,并确认在边界平衡点的稳定性和正平衡点的存在性之间存在着很强的联系.但是只给出了特殊条件下正平衡点稳定的充要条件,这篇文章将就以前没解决的问题,对这类模型给出完整的分析.     

具有时滞的生态-传染病模型的定性分析

针对一类疾病在食饵中传播而把食饵分为易感和染病的时滞生态-传染病模型,以时滞(即传染病在食饵种群中的潜伏期)作为分支参数,讨论了系统正平衡点在时滞τ=0时的局部渐近稳定性,在τ0时在一列临界值处发生了Hopf分支,并且对保持正平衡点稳定时时滞的范围也给出了估计.     

具有时滞的生态-传染病模型的定性分析北大核心

针对一类疾病在食饵中传播而把食饵分为易感和染病的时滞生态-传染病模型,以时滞(即传染病在食饵种群中的潜伏期)作为分支参数,讨论了系统正平衡点在时滞τ=0时的局部渐近稳定性,在τ>0时在一列临界值处发生了Hopf分支,并且对保持正平衡点稳定时时滞的范围也给出了估计.     

一类具有垂直传染和预防接种的SEIR传染病模型的定性分析

建立并分析了一类对出生时没有被染病母体垂直传染的染病者的新生儿进行免疫接种的SEIR传染病模型.得到了疾病是否灭绝的阈值R0,当R0<1时,无病平衡点全局渐近稳定的.当R0>1时,地方病平衡点局部渐近稳定的,且疾病一致持续生存.     

一类具有非线性发生率的SIR传染病模型的全局稳定性

研究一类具有非线性发生率的SIR传染病模型.应用微分方程定性理论分别得到了该系统无病平衡点、地方病平衡点全局渐近稳定的充分条件,并进行了数值模拟.     

具一般非线性隔离函数和接触率的染病年龄SIRS模型平衡点的存在性及稳定性

考虑一类具有一般非线性隔离函数和接触率的染病年龄结构SIRS传染病模型,研究平衡点的存在性及渐近稳定性,得到正平衡点指数渐近稳定的一般性条件.     

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.     

具有垂直传染的SEIA传染病模型的稳定性

建立和研究一类具有垂直传染的SEIA传染病模型,得到模型基本再生数R₀的表达式,运用Lyapunov函数和第二加性复合矩阵理论证明了当R₀〈1时无病平衡点全局渐近稳定,当R₀〉1时地方病平衡点全局渐近稳定.     

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.     

具可变种群总数的SIS传染病模型指数稳定性

本文研究了一类具可变种群总数的SIS传染病模型,利用基于比较原理的新的分析技巧,获得了一些无病平衡点和传染病平衡点全局和局部指数稳定的充分条件,同时得到了平衡点指数收敛率与指数收敛区域的估计.     

Global dynamics of a delayed eco‐epidemiological model with Holling type‐III functional response

In this paper, an eco‐epidemiological model with Holling type‐III functional response and a time delay representing the gestation period of the predators is investigated. In the model, it is assumed that the predator population suffers a transmissible disease. The disease basic reproduction number is obtained. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria and the existence of Hopf bifurcations at the disease‐free equilibrium and the endemic‐coexistence equilibrium are established, respectively. By using the persistence theory on infinite dimensional systems, it is proved that if the disease basic reproduction number is greater than unity, the system is permanent. By means of Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are obtained for the global stability of the endemic‐coexistence equilibrium, the disease‐free equilibrium and the predator‐extinction equilibrium of the system, respectively. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

具双时滞的SEIRS传染病模型指数收敛性

本文研究了一类具指数人口统计与结构的SEIRS传染病模型,利用一种新的基于比较原理的分析,获得了无病平衡点局部和全局指数稳定的两个充分条件.     

Mathematical analysis of an eco-epidemiological predator–prey model with stage-structure and latency

In this paper, an eco-epidemiological predator–prey model with stage structure for the prey and a time delay describing the latent period of the disease is investigated. By analyzing corresponding characteristic equations, the local stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the endemic equilibrium is addressed. The existence of Hopf bifurcations at the endemic equilibrium is established. By using Lyapunov functionals and LaSalle’s invariance principle, sufficient conditions are obtained for the global asymptotic stability of the trivial equilibrium, the predator-extinction equilibrium, the disease-free equilibrium and the endemic equilibrium of the model.     

Global dynamics of a delayed SEIS infectious disease model with logistic growth and saturation incidence

In this paper, a delayed Susceptible‐Exposed‐Infectious‐Susceptible (SEIS) infectious disease model with logistic growth and saturation incidence is investigated, where the time delay describes the latent period of the disease. By analyzing corresponding characteristic equations, the local stability of a disease‐free equilibrium and an endemic equilibrium is discussed. The existence of Hopf bifurcations at the endemic equilibrium is established. By using the persistence theory for infinite dimensional dynamic systems, it is proved that if the basic reproduction number is greater than unity, the system is permanent. By means of suitable Lyapunov functionals and LaSalle's invariance principle, sufficient conditions are obtained for the global stability of the disease‐free equilibrium and the endemic equilibrium, respectively. Numerical simulations are carried out to illustrate the theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

Global behavior and permanence of SIRS epidemic model with time delay

In this paper an autonomous SIRS epidemic model with time delay is studied. The basic reproductive number R₀ is obtained which determines whether the disease is extinct or not. When the basic reproductive number is greater than 1, it is proved that the disease is permanent in the population, and explicit formula are obtained by which the eventual lower bound of the fraction of infectious individuals can be computed. Throughout the total paper, we mainly use the technique of Lyapunov functional to establish the global stability of the infection-free equilibrium and the local stability of the endemic equilibrium but need another sufficient condition.     

Stability analysis for an epidemic model with stage structure

An epidemic model with stage structure is formulated. The period of infection is partitioned into the early and later stages according to the developing process of infection, and the infectious individuals in the different stages have the different ability of transmitting disease. The constant recruitment rate and exponential natural death, as well as the disease-related death, are incorporated into the model. The basic reproduction number of this model is determined by the method of next generation matrix. The global stability of the disease-free equilibrium and the local stability of the endemic equilibrium are obtained; the global stability of the endemic equilibrium is got under the case that the infection is not fatal.     

Study of a fractional-order model of chronic wasting disease

This paper studies a fractional-order modelling chronic wasting disease (CWD). The basic results on existence, uniqueness, non-negativity, and boundedness of the solutions are investigated for the considered model. The criterion for local as well as global stability of the equilibrium points is derived. A numerical analysis for Hopf-type bifurcation is presented. Finally, numerical simulations are provided to justify the results obtained.