一类具年龄结构和接种的非终生免疫型传染病模型

研究一类具年龄结构和接种的非终生免疫SIRS传染病模型平衡解的稳定性.首先利用特征线法讨论了模型平衡解的存在性,然后利用比较定理和逐次迭代法得到无病平衡解与地方病平衡解全局稳定性的充分条件.     

关于具时滞的捕食-被捕食系统的稳定性与Hopf分支

研究了一类具时滞的捕食—被捕食系统正平衡解的稳定性和Hopf分支的存在性,即以转化率l为参数,得到存在一列l_k(k=0,1,2…),使当l∈(0,l_0)时正平衡解是渐近稳定的;当l>l_0时,正平衡解是不稳定的,而每一个l_k都是该系统的Hopf分支值,改进了一些已知的工作。     

具有非线性平均增长率的离散Logistic方程的稳定性和振动性

考虑具非线性平均增长率的Ｌｏｇｉｓｔｉｃ方程 这里ｒ,ａ,ｂ都是正常数,本文证明了方程（１）的一切解关于 ｋ振动的充要条件是 ｋｒ（ａ＋２ｂｋ）＞１,其中ｋ是方程（１）的唯一的正平衡解。同时获得了方程（１）的正平衡解ｋ是渐近稳定与全局渐近稳定的充分条件．     

具有毒素的捕食-食饵系统的最优税收

本文研究了一类具有毒素的捕食-食饵系统的最优税收,通过计算雅克比矩阵的特征值以及构造适当的Lyapunov函数得出了保证系统平衡点的局部稳定性和正平衡点全局稳定性的充分性条件,并利用Pontryagin最大值原理得到了达到最优税收的最优平衡解.     

一类三阶非线性递归差分方程的全局渐近稳定性与振动性(英文)

研究了一类三阶方程x_(n+1)=x_nx_(n-2)+a/x_n+x_(n-2)+b,n=0,1,…的解的振动性和正解的全局渐近稳定性,证明了正平衡解的全局渐近稳定,非平衡解具有规律的振动性.     

三种群竞争系统的持久性

本文研究了三种群非自治周期Lotka-Volterra竞争系统的持久性,得到了正周期解的存在性和平衡振荡的条件。     

双营养Chemostat模型周期解的全局吸引性

研究含有时滞的双营养单种群Ｃｈｅｍｏｓｔａｔ模型周期解的全局吸引性,首先利用强正、凹算子理论给出了系统存在唯一正周期解的充分条件,然后利用泛函微分方程的单调理论得到了正周期解的全局吸引性。     

一类Nicholson's blowflies模型的全局吸引性和振动性

本文研究了带有多个滞后变量的Ｎｉｃｈｏｌｓｏｎ’ｓ ｂｌｏｗｆｌｉｅｓ动态模型Ｎ（ｔ）＝－δＮ（ｔ）＋ΣＰｉＮ（ｔ-τｉ）ｅ-ａｉＮ（ｔ-τｉ）的全局吸引性和振动性,获得了该方程的正平衡解为全局稳定的充分条件以及其所有正解关于该平衡解振动的充分条件．     

一类带参数的泛函微分方程的正周期解的存在性(英文)

利用锥上不动点理论,本文研究了一类非线性泛函微分方程正周期解的存在多样性和ω-周期解的不存在性.获得了一些新的结果.应用这些新的结果,讨论了一类带参数的血细胞生成模型,给出该模型的正周期解的存在性,此结果利用以前的方法是无法得到的.     

具有年龄结构的种群模型平衡解的稳定性

本文考虑具有年龄结构的种群动力系统模型,讨论系统具有多个平衡解时其解的渐近性质,最后给出了其平衡解中那些是稳定的,哪些是不稳定的.     

Qualitative analysis of an HIV transmission model.

In 1988, a multiple-group model for HIV transmission with preferred mixing was proposed by Jacquez and coworkers. In the present paper, the work done by Jacquez et al. is extended. It is shown that the stability modulus of the Jacobian matrix at the no-disease equilibrium is a threshold for this model. Furthermore, if the no-disease equilibrium is unstable, the number of infected individuals will remain above a certain positive level regardless of initial levels; that is, the disease will persist uniformly. The stability of the endemic equilibrium in the case of restricted mixing is also studied. A series of sufficient conditions for local and global asymptotic stability of the endemic equilibrium are stated.     

一类具有标准发生率的SIS型传染病模型的全局稳定性

研究一类具有标准发生率的SIS传染病模型,讨论了各类平衡点存在的条件;运用微分方程的定性理论,得到了无病平衡点E_1和地方病平衡点E_2的全局渐近稳定的充分条件.     

On the uniqueness of endemic equilibria of an HIV/AIDS transmission model for a heterogeneous population

In this paper, we examine an HIV/AIDS transmission model which has been widely used for studying the spread of HIV/AIDS through sexual contact. Some sufficient conditions are obtained for the uniqueness of endemic equilibrium. We also present a two-group model whose no-disease equilibrium is unstable but it has at least three positive endemic equilibria.     

一类含分布时滞的流行病模型的研究

提出了一类含分布时滞的流行病模型,利用构造李亚普诺夫泛函的方法,得到了无病平衡点和地方病平衡点全局稳定性的结论,揭示了平均时滞对各类平衡点稳定性的影响。     

资源与资源利用者的脉冲收获控制

研究一类资源以Cui-Lawson增长为基础的具有状态依赖脉冲收获的生态系统.首先对无脉冲作用的系统进行定性分析,得到正平衡点存在和稳定的充分条件.其次对具有状态依赖的脉冲系统,利用微分方程几何理论中后续函数法得到系统的阶一周期解存在的充分条件,证明该周期解是轨道渐近稳定的,同时利用数值模拟讨论了系统生态意义.     

变时滞SIS流行病模型的稳定性分析

研究了一类时滞SIS流行病模型,分析了该模型无病平衡点和地方平衡点的存在性,得到了无病平衡点全局指数渐近稳定和地方病平衡点局部指数渐近稳定的充分条件,同时给出了地方病平衡点吸引区域的估计。     

一类疫苗预防接种具有效期性的SIRS模型稳定性分析

研究了一类预防接种下疫苗具有有效期的SIRS传染病模型,得到了决定疾病绝灭与否的闽值,给出了无病平衡点和地方病平衡点的全局稳定性的充分条件,最后借助Matlab软件进行了数值模拟．     

一类具有广义Logistic增长的比率型捕食模型的定性分析

对具有广义Logistic增长的比率型捕食模型进行了分析,得到了系统永久持续生存的充分条件．通过对系统进行无量纲代换和应用Liapunov函数的方法,进一步得到了正平衡点全局渐近稳定的充分条件．     

Analysis of SIR epidemic models with nonlinear incidence rate and treatment

This paper deals with the nonlinear dynamics of a susceptible-infectious-recovered (SIR) epidemic model with nonlinear incidence rate, vertical transmission, vaccination for the newborns of susceptible and recovered individuals, and the capacity of treatment. It is assumed that the treatment rate is proportional to the number of infectives when it is below the capacity and constant when the number of infectives reaches the capacity. Under some conditions, it is shown that there exists a backward bifurcation from an endemic equilibrium, which implies that the disease-free equilibrium coexists with an endemic equilibrium. In such a case, reducing the basic reproduction number less than unity is not enough to control and eradicate the disease, extra measures are needed to ensure that the solutions approach the disease-free equilibrium. When the basic reproduction number is greater than unity, the model can have multiple endemic equilibria due to the effect of treatment, vaccination and other parameters. The existence and stability of the endemic equilibria of the model are analyzed and sufficient conditions on the existence and stability of a limit cycle are obtained. Numerical simulations are presented to illustrate the analytical results.     

Existence, multiplicity and stability of endemic states for an age-structured S-I epidemic model

We study an S-I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the disease-free equilibrium and guarantees the existence of an endemic equilibrium. We obtain conditions on the age-dependence of the susceptibility to infection that imply the uniqueness of the endemic equilibrium. An example with two endemic equilibria is shown. Finally, we analyse numerically how the stability of the endemic equilibrium is affected by the extra-mortality and by the possible periodicities induced by the demographic age-structure.