SARS数学模型解的存在唯一性与稳定性

讨论了一种带年龄结构的SARS疾病模型，它是一组非线性偏微分方程组，应用有界线性算子的C0一半群理论及非线性扰动理论，证明了该方程组非负解的存在唯一性及稳定性．     

一类带有隔离和接种的传染病模型的稳定性分析

建立并分析一类带有隔离和接种传染病模型,证明了系统解的非负性,利用V函数和极限方程理论,证明无病平衡点和地方病平衡点的全局渐近稳定性.     

染病者有常数输入的传染病模型

讨论在隔离措施下易感者和染病者都有常数移民的传染病模型.给出了模型的地方病平衡点,证明了地方病平衡点的稳定性.     

一类SARS传染病自治动力系统的稳定性分析

在K-M传染病模型的基础上,进一步考虑易感人群的密度制约以及患病者类的死亡与治愈率等因素,建立了描述SARS传染病的一个新的动力学模型,分析了该模型平衡点的稳定性态．证明了疾病消除平衡点在一定条件下是全局渐进稳定的,而地方病平衡点不是渐近稳定的．得到了该传染病系统在适当条件下为永久持续生存的结果．     

A two-strain epidemic model with mutant strain and vaccination

In this paper, it is assumed that the spread of a pathogen can mutate in the host to create a second, cocirculating, mutant strain. Vaccinated individuals perhaps becomes infected after being in contact with individuals infected with mutant strain. A?two-strain epidemic model with vaccination is firstly investigated. The existence and stability properties of equilibria in this model are examined. By analyzing the characteristic equation and constructing Lyapunov functions, the conditions for local and global stability of the infection-free, boundary and endemic equilibria are established. The existence of Hopf bifurcation from the endemic equilibrium is also examined as this equilibrium loses its stability. Our theoretical results are confirmed by numerical simulations.     

Global analysis of a periodic epidemic model on cholera in presence of bacteriophage

We propose and analyze a recurrent epidemic model of cholera in the presence of bacteriophage. The model is extended by general periodic incidence functions for low‐infectious bacterium and high‐infectious bacterium, respectively. A general periodic shedding function for two infected class (phage‐positive and phage‐negative) and a generalized contact and intrinsic growth function for susceptible class are also considered. Under certain biological assumptions, we derive the basic reproduction number (R₀) in a periodic environment for the proposed model. We also observe the global stability of the disease‐free equilibrium, existence, permanence, and global stability of the positive endemic periodic solution of our proposed model. Finally, we verify our results with specific functional form. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

A Positivity-preserving Mickens-type Discretization of an Epidemic Model

A deterministic model for the transmission dynamics of two strains of an epidemic in the presence of a preventive vaccine is considered. Theoretical results on the existence and stability of the associated equilibria of the model are given. A robust, positivity-preserving, non-standard finite-difference scheme, having the same qualitative features as the continuous model, is constructed. The theoretical and numerical analyses of the model enable the determination of a threshold level of vaccination coverage needed for community-wide eradication of the epidemic.     

Stability of a stochastic SEIS model with saturation incidence and latent period

In this paper, a stochastic SEIS epidemic model with a saturation incidence rate and a time delay describing the latent period of the disease is investigated. The model inherits the endemic steady state from its corresponding deterministic counterpart. We first show the existence and uniqueness of the global positive solution of the model. Then, by constructing Lyapunov functionals, we derive sufficient conditions ensuring the stochastic stability of the endemic steady state. Numerical simulations are carried out to confirm our analytical results. Furthermore, our simulation results shows that the existence of noise and delay may cause the endemic steady state to be unstable.     

一类带有一般接触率和常数输入的流行病模型的全局分析

借助极限系统理论和构造适当的Liapunov函数,对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论．当无染病者输入时,地方病平衡点存在的阈值被找到A·D2对相应的SIR模型,关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件;对相应的SIRS模型,得到无病平衡点和地方病平衡点全局渐近稳定的充分条件．当有染病者输入时,模型不存在无病平衡点．对相应的SIR模型,地方病平衡点是全局渐近稳定的;对相应的SIRS模型,得到地方病平衡点全局渐近稳定的充分条件．     

一类具有时滞的病菌-免疫力模型的Hopf分歧

考虑病菌的一种信息交流机制,建立一类病菌与免疫系统竞争的时滞传染病模型.分析正平衡点的存在性、渐近稳定性、Hopf分歧的存在性及方向.运用计算机数值模拟验证所得理论结果,为传染病的控制和预防提供了理论基础和数值依据.     

一类具有说服率的HIV/AIDS流行病模型

根据某市艾滋病出现的新特点,即外来人口对艾滋病的影响,给出了相应的传染病动力学模型,并进行了数值模拟.     

Backward bifurcation in a stage-structured epidemic model

A stage-structured epidemic model is proposed under the assumptions that the disease can only be transmitted among adults and that there is also intraspecific competition among them. We study the existence of equilibria and also obtain their local stability, which implies the occurrence of backward bifurcation. Moreover, sufficient conditions on the global stability of some equilibria are provided.     

An SIS Epidemic Model with Stage Structure and a Delay

A disease transmission model of SIS type with stage structure and a delay is formulated. Stability of the disease free equilibrium, and existence, uniqueness, and stability of an endemic equilibrium, are investigated for the model. The stability results arc stated in terms of a key threshold parameter. The effects of stage structure and time delay on dynamical behavior of the infectious disease are analyzed. It is shown that stage structure has no effect on the epidemic model and Hopf bifurcation can occur as the time delay increases.     

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.     

一类具有非线性传染力的阶段结构SI模型

讨论了一类具有非线性传染力的阶段结构 SI传染病模型 ,确定了各类平衡点存在的阈值条件 ,得到了各类平衡点局部稳定和全局稳定的条件 .     

THEORETICAL ANALYSIS TO A REACTION-DIFFUSION SYSTEM ARISING IN A DIFFUSIVE EPIDEMIC MODEL

This paper developes a diffusive epidemic model and investigates the globalexistence, uniform bounds, stability, asymptotic behavior and decay rate for solution ofrelated reaction-diffusion system.     

非线性接触率SIR模型脉冲接种策略研究

建立了具有非线性接触率脉冲预防接种的SIR传染病模型,利用脉冲微分方程理论,对模型的动力学性态进行了分析,给出了模型的阀值,证明了无病周期解的存在性及全局渐近稳定性.     

年龄结构的致命性传染病控制模型

本文在Ｂｒａｕｅｒ［１３］的基础上建立了一个致命性大范围传染病的年龄结构分布控制模型（这是一个具有非局部边界条件的偏微分方程组），证明了解的存在唯一性并分析了定常系统的非负平衡态的存在性，建立了相应的稳定性及其收敛性定理．     

含有免疫策略的一类计算机病毒模型稳定性分析

建立计算机病毒的动力学数学模型,可以更好地揭示计算机病毒流行的原因.考虑到免疫策略对计算机病毒动力学模型的重要影响,对一类SEIR模型进行了改进.得到了模型的无感染平衡点和感染平衡点的存在性,并分别求得两类平衡点的渐近稳定条件,通过数值模拟展示了理论成果.