一类包虫病传播动力学模型的研究

研究了一类具有终宿主产卵期和中间宿主虫卵成熟期两时滞的包虫病传播动力学模型,得到了决定系统动力学行为的阈值R_0,当R_0〈1时,证明了未感染平衡点是局部渐近稳定的;当R_0〉1时,得到了感染平衡点是局部渐近稳定的充分条件。通过数值仿真验证了理论结果并探讨了时滞对系统动力学行为的影响,且发现若时滞在一定的范围内系统存在周期解.     

一类具有非线性传染力的传染病模型的稳定性分析

研究了一类具有非线性发生率的急慢性阶段传染病模型,得到了确定模型全局动力性的阀值参数-基本再生数R_0,证明了R_01时,无病平衡点是全局渐近稳定的,疾病消失;若R_01,则存在地方病平衡点且是稳定结点,并证明了一定条件下地方病平衡点是全局渐近稳定的,疾病将蔓延.     

具有Crowley-Martin功能反应和CTL免疫反应的病毒动力学模型的全局稳定性（英文）

本文讨论了一类具有Growley-Martin功能反应和CTL免疫反应的病毒动力学模型的全局稳定性.利用Lyapunov函数和LaSalle不变原理证明:当基本再生数R_0≤1时,无病平衡点全局渐近稳定;当基本再生数R_01且免疫基本再生数R_0≤1时,免疫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.     

一个具有时滞的媒介传播流行病模型中的Hopt分支（英文）

文章研究的是一个具有时滞的媒介传播流行病模型.假定长期的发病率是双线性大规模行动的方式,确定了疾病是否流行的阈值R_0.当R_0≤1时,得到无病平衡点是全局稳定的,即疾病消失;当R_0〉1时,得到地方病平衡点.在具有时滞的微分模型中,时滞与载体转变成传染源的孵化期有关。我们研究了时滞对平衡点稳定性的影响,研究表明,在从寄生源到载体的传播过程中,时滞可以破坏动力系统并且得到了Hopt分支的周期解.     

一类具有免疫反应的HollingⅡ型发生率病毒动力学模型

建立并讨论了一类具有潜伏期、抗体免疫反应和CTL免疫反应的Holling II型发生率病毒动力学模型.定义了决定这个模型动力学性质的五个阈值,借助适当的Lyapunov函数得到:当R_(01)≤1时,无病平衡点全局渐近稳定,病毒被清除;当R_(01)1,R_(02)≤1,R_(03)≤1时,无免疫平衡点全局渐近稳定;当R_(02)1,R_(04)≤1时,CTL免疫主导平衡点全局渐近稳定;当R_(03)〉1,R_(04)≤1时,抗体免疫主导平衡点全局渐近稳定;当R_(04)1,R′_(04)1时,正平衡点全局渐近稳定.     

具有非线性发生率的SEIS模型的定性分析

研究了一类具有非线性发生率的SEIS传染病模型,给出了其基本再生数R_0.当R_01时,无病平衡点是全局渐近稳定的;当R_0〉1时,得到了唯一的地方病平衡点是全局渐近稳定的条件.     

一类具有潜伏时滞和非线性疾病发生率的SEIRS传染病模型

本文提出一类具有潜伏时滞和非线性疾病发生率的SEIRS传染病模型,通过分析对应的特征方程,运用时滞微分方程的稳定性理论得出:当基本再生数R_01时无病平衡点处的局部渐近稳定性,R_0 1时地方病平衡点处的局部渐近稳定性.通过构造Lyapunov泛函,运用LaSalle's不变集原理得到:当基本再生数R_0≤1时无病平衡点处的全局渐近稳定性;通过比较方法得到R_01时系统的一致持久性     

再生数R0的计算及其控制策略

在传染病数学模型中,一般有一个传染病消除平衡点和至少一个地方病平衡点,这些平衡点的稳定性由再生数R_0决定,当R_0<1,疾病消除平衡点稳定,此传染病可以消除;当R_0>1,疾病消除平衡点不稳定,此传染病将蔓延,所以再生数R_0是传染病数学模型中最重要的参数.本文针对乙型肝炎病毒的传播方式以及各种状态间的转化模式建立了乙型肝炎数学模型,并利用马尔可夫链的方法计算乙型肝炎数学模型中的再生数R_0,提出了通过采取降低R_0的方法对乙型肝炎数学模型施加有效控制的策略.     

具有连续接种和脉冲接种的SIVR模型研究

考虑了具有连续接种和脉冲接种的SIVR传染病模型,得到了模型的基本再生数.对于连续接种模型,证明了当基本再生数R_0~c≤1时无病平衡点是全局稳定的;当R_0~c1时,无病平衡点是不稳定的,模型存在地方病平衡点,并且当δ=0时,地方病平衡点是全局渐近稳定的.对于脉冲接种模型,得到了无病周期解的存在性和稳定性.最后,对连续接种和脉冲接种进行了比较.     

改进的病毒感染动力学模型的稳定性分析

提出一个改进的乙肝病毒感染动力学模型.本模型有三个平衡点.对于HBV感染人群,三个平衡点分别对应于三类人群：感染病毒后自愈人群、健康带毒人群、慢性乙肝患者人群.证明了当模型导出的基本复制数R_0〈1时病毒清除平衡点具有局部稳定性和全局渐近稳定性,当1〈R_0〈k_3d/（k_2λ-k_3a）＋1时持续带毒平衡点具有局部稳定性.     

具有一般形式饱和接触率SEIS模型渐近分析

研究具有一般形式饱和接触率SEIS模型渐近性态,得到决定疾病绝灭和持续的阈值-基本再生数R0。当R0 ≤ 1时,仅存在无病平衡点P^0;当R0＞1时,除存在无病平衡点P^0外,还存在惟一的地方病平衡点P^＊。当R0＜1时,无病平衡点P^0全局渐近稳定;当R0＞1时,地方病平衡点P^＊局部渐近稳定。特别地,无因病死亡时,极限方程地方病平衡点P^-＊全局渐近稳定。     

The Role of <Emphasis Type="BoldItalic">Hyalomma Truncatum</Emphasis> on the Dynamics of Rift Valley Fever: Insights from a Mathematical Epidemic Model

To date, our knowledge of Rift Valley fever (RVF) disease spread and maintenance is still limited, as flooding, humid weather and presence of biting insects such as mosquitoes, have not completely explained RVF outbreaks. We propose a model that includes livestock, mosquitoes and ticks compartments structured according to their questing and feeding behaviour in order to study the possible role of ticks on the dynamics of RVF. To quantify disease transmission at the initial stage of the epidemic, we derive an explicit formula of the basic reproductive number, \(R_0\). Using the concept of Metzler matrix, we state necessary conditions for global asymptotic stability of the disease-free equilibrium. Results suggest that although host-ticks interactions may serve as disease reservoirs or disease amplifiers, the Aedes reproductive number should be kept under unity if disease post-epizootics activities are to be controlled. Results of both local and global sensitivity analysis of selected model parameters indicate that \(R_0\) is more sensitive to the ticks attachment and detachment rates, probability of transmission from ticks to host and from host to ticks, length of infection in livestock and ticks death rate. Furthermore, when comparing the mean value of \(R_0\) with that from previous studies which did not include ticks we found that our \(R_0\) is very much larger resulting in an increase in the exponential phase of an outbreak. These findings suggest that if ticks are capable of transmitting the virus, they may be contributing to disease outbreaks and endemicity.     

一个具非单调传染率的SEIR传染病模型的全局稳定性

本文研究一类描述某种严重疾病的传染数目变大时在心理上产生影响的非单调传染率的SEIR传染病模型.研究表明模型的动力行为和疾病的爆发完全由基本再生数R0决定.当R0≤1时,无病平衡点是全局稳定的,疾病消亡;当R0〉1时,地方病平衡点是全局稳定的,疾病持续且发展成地方病.     

A Stuctured Discrete Model for Dengue Fever Infections and the Determination of R_0 from Age-Stratified Serological Data

A time discrete age-structured model for modeling the spread of Dengue fever is built. The demographic dynamics is introduced trough the Leslie model. The basic reproductive number is introduced, and an approximation for it is built. The final age distributions for the susceptibles, infected and removed are obtained, and we show how they can be used to produce an actual estimate for \(R_0\) from stratified serological data. An application is made using data from Recife, Brazil, and explicit estimates for \(R_0\) are given.     

一类具有垂直传染和预防接种的传染病模型的稳定性

考虑了垂直传染和预防接种因素对传染病流行影响的SEIRS模型,主要研究了系统的平衡点及其稳定性,得出当预防接种水平超过某一个阈值时疾病可以根除,若接种水平低于阈值时疾病将流行.     

一类带有非线性感染率传染病模型的动力学性质（英文）

主要介绍了一类带有非线性感染率的传染病模型.并且证明了当基本再生数Ro≤1时,无病平衡点是全局稳定的,当基本再生数R_0〉1时,疾病持续.     

一个带有ATL过程的HTL V-I感染的时滞模型

本文提出并分析了两个关于人体T-细胞淋巴回归Ⅰ型病毒（HTL V-I）感染并带有坏死白血病细胞（ATL）进程的数学模型,一个常微分方程模型,一个离散时滞模型.首先对常微分方程模型进行了分析,运用相应的特征方程得到一个阈值Ro（CD4⁺ T-细胞的基本再生数）.当R₀≤1时,仅有未染病平衡态存在,并且给出了其稳定性;当R₀>1时,有一个染病稳定态存在,并且此时它是稳定的.然后,我们在常微分方程模型中引入了一个离散时滞,通过对时滞模型的超越特征方程的分析,导出了与常微分方程模型中同样的稳定性条件,即时滞模型平衡态的稳定性与时滞的具体值无关.     

On the evolution of specialization with a mechanistic underpinning in structured metapopulations

We analyze the evolution of specialization in resource utilization in a discrete-time metapopulation model using the adaptive dynamics approach. The local dynamics in the metapopulation are based on the Beverton-Holt model with mechanistic underpinnings. The consumer faces a trade-off in the abilities to consume two resources that are spatially heterogeneously distributed to patches that are prone to local catastrophes. We explore the factors favoring the spread of generalist or specialist strategies. Increasing fecundity or decreasing catastrophe probability favors the spread of the generalist strategy and increasing environmental heterogeneity enlarges the parameter domain where the evolutionary branching is possible. When there are no catastrophes, increasing emigration diminishes the parameter domain where the evolutionary branching may occur. Otherwise, the effect of emigration on evolutionary dynamics is non-monotonous: both small and large values of emigration probability favor the spread of the specialist strategies whereas the parameter domain where evolutionary branching may occur is largest when the emigration probability has intermediate values. We compare how different forms of spatial heterogeneity and different models of local growth affect the evolutionary dynamics. We show that even small changes in the resource dynamics may have outstanding evolutionary effects to the consumers.     

Reproduction Number and Asymptotic Stability for the Dynamics of a Honey Bee Colony with Continuous Age Structure

A system of partial differential equations is derived as a model for the dynamics of a honey bee colony with a continuous age distribution, and the system is then extended to include the effects of a simplified infectious disease. In the disease-free case, we analytically derive the equilibrium age distribution within the colony and propose a novel approach for determining the global asymptotic stability of a reduced model. Furthermore, we present a method for determining the basic reproduction number \(R_0\) of the infection; the method can be applied to other age-structured disease models with interacting susceptible classes. The results of asymptotic stability indicate that a honey bee colony suffering losses will recover naturally so long as the cause of the losses is removed before the colony collapses. Our expression for \(R_0\) has potential uses in the tracking and control of an infectious disease within a bee colony.