一类具有空间扩散的SEIAV模型及其阈值动力学研究

本文在现有的模型基础上,考虑无症状感染者、游离病毒的传播及空间扩散等因素的影响,建立了一个扩展的SEAIV模型.在研究模型正解的存在性,并给出作为阈值的基本再生数R₀的前提下,对疾病的灭绝及持久的情况进行讨论,得到当R₀<1时模型的无病平衡点的稳定性以及R₀>1时地方病平衡点的稳定性,同时利用数值模拟进行验证.进一步讨论在R₀=1的情况下,模型的无病平衡点的全局吸引性.     

宁夏彭阳县包虫病传播动力学建模及分析

包虫病是严重影响人类身体健康和社会经济发展的人畜共患病.彭阳县是宁夏回族自治区包虫病比较严重的地区,基于彭阳县囊型包虫病的传播机理,本文建立了包虫病在人,羊,犬及环境中传播的数学模型,预测彭阳县包虫病流行趋势并评估防控措施对疾病传播的影响.理论结果表明包虫病的流行与否取决于基本再生数R₀.当R₀<1时,无病平衡点全局渐近稳定即包虫病趋向灭绝;而当R₀> 1时,地方病平衡点全局渐近稳定即包虫病持久存在.依据彭阳县2011-2018年包虫病的监测指标及宁夏统计年鉴,得到彭阳县包虫病的基本再生数R₀=0.63 <1,说明彭阳县最终将消灭包虫病.最后,通过数值模拟及基本再生数的敏感性和不确定性分析,得到犬驱虫较羊免疫更能影响包虫病的传播,另外羊屠宰情况也是影响疾病传播的关键因素,这为彭阳县相关部门制定包虫病防控策略提供一定的理论依据.     

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.     

一类具有垂直传染的传染病模型的稳定性

基于动力系统的理论,讨论了一类具有垂直传染的传染病模型的稳定性.采用下一代矩阵法获得了基本再生数R₀.当R₀<1时,由Routh-Hurwitz判别法,得到了无病平衡点的局部渐近稳定性.通过构造Lyapunov函数,证明了系统在无病平衡点全局渐近稳定.当R₀> 1时,地方病平衡点存在且唯一,借助Routh判据,得出了系统在地方病平衡点局部渐近稳定的条件,并通过构造Lyapunov函数,证明了系统在地方病平衡点全局渐近稳定.最后,用数值模拟验证了结论的合理性.     

一类具有潜伏周期的空间异质反应扩散梅毒模型动力学分析

该文研究了一类具有潜伏周期的异质空间扩散的梅毒模型的阈值动力学行为.首先讨论了系统解的全局存在性以及系统全局吸引子的存在性.其次,根据传染病模型下一代再生算子定义推导出模型的动力学阈值-基本再生数R₀.具体地,当R₀ <1,无病平衡态是全局吸引的;根据耗散系统的持久性理论证明了当R₀> 1时疾病是一致持久的.最后,在空间同质情形下,推导出模型基本再生数R₀的显示表达式.此外,除了证明无病平衡点的全局稳定之外,还利用波动引理证明了系统正平衡点的全局稳定性.     

一类具有阶段结构的虫媒传播植物病模型的全局分析

为了研究化学控制和移除病树对虫媒植物病传播控制的影响,本文建立了一类具有阶段结构的虫媒传播植物病时滞模型.首先,利用再生矩阵法计算得到了基本再生数R₀.理论结果表明,在入侵强度不强的情况下,基本再生数是决定疾病是否流行的阈值条件,即当R₀<1时疾病灭绝,而当R₀>1时疾病爆发.进一步,如果不实施移除病树策略,利用振动逼近的方法我们得到了地方病平衡点全局吸引的充分条件.最后通过数值模拟验证了理论结果,并说明喷洒杀虫剂是一种非常有效的控制措施.     

带脉冲接种和垂直传染的时滞乙肝模型

研究一类具有脉冲预防接种和时滞的乙肝模型,考虑了疾病的垂直传染,获得了再生数R₁,R₂,证明了R₁<1时,系统存在无病周期解,且是全局渐近稳定的,当R2>1时,系统的疾病将持续并发展为地方病.     

具有潜伏期和免疫应答的时滞病毒感染模型的全局稳定性

研究了具有潜伏期和CTL免疫应答的时滞病毒感染模型的动力学行为.模型描述了病毒和两类靶细胞的相互作用:CD4+T淋巴细胞与巨噬细胞.通过构造适当的Lyapunov泛函,使用La Salle不变性原理,证明了CD4+T淋巴细胞和巨噬细胞的基本再生总数R0,CD4+T淋巴细胞和巨噬细胞的CTL免疫再生总数R*决定了模型的全局性态.若R0≤1,病毒在体内清除.若R01,正解在R*≤1时趋于无免疫平衡点,在R*1时趋于正平衡点.获得了无病平衡点、无免疫平衡点和正平衡点全局渐近稳定的充分条件.     

Dynamics of a Diffusion Malaria Model With Vector-Bias北大核心CSCD

为了探讨季节性、蚊子叮咬的偏好性和人类的扩散对疟疾传播的影响,该文提出了一个部分退化的周期反应扩散模型.利用动力系统的持续性理论,研究了模型关于基本再生数R₀的阈值动力学.即当R₀<1时,疾病灭绝;而当R₀>1时,疾病一致持续,且会发生季节性的流行.数值上发现了忽略空间异质性和蚊子叮咬的偏好性会低估疾病传染的风险.     

带有免疫反应的病毒动力学模型的全局稳定性

利用Lyapunov函数研究了带有免疫反应的病毒动力学模型的全局稳定性.当基本再生数R0≤1时.病毒在体内清除;当R0>1时,病毒在体内持续生存.并且模型的正解当免疫再生数R1≤1时,趋于无免疫平衡点,当R1>1.趋于地方病平衡点.     

Dynamical behavior of a virus dynamics model with CTL immune response

In this paper, the dynamical behavior of a virus dynamics model with CTL immune response is studied. Sufficient conditions for the asymptotical stability of a disease-free equilibrium, an immune-free equilibrium and an endemic equilibrium are obtained. We prove that there exists a threshold value of the infection rate b beyond which the endemic equilibrium bifurcates from the immune-free one. Still for increasing b values, the endemic equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bifurcation by applying Poore’s condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings.     

Global asymptotical properties for a diffused HBV infection model with CTL immune response and nonlinear incidence

This article proposes a diffused hepatitis B virus (HBV) model with CTL immune response and nonlinear incidence for the control of viral infections. By means of different Lyapunov functions, the global asymptotical properties of the viral-free equilibrium and immune-free equilibrium of the model are obtained. Global stability of the positive equilibrium of the model is also considered. The results show that the free diffusion of the virus has no effect on the global stability of such HBV infection problem with Neumann homogeneous boundary conditions.     

一类具有细胞免疫和吸收效应的时滞病毒动力学模型(英文)

本文主要研究一类具有细胞免疫和吸收效应的时滞病毒动力学模型.通过构造Lyapunov泛函,证明当R0≤1,R1 ≤1相似文献   

一类具免疫应答和非线性感染函数的时滞HIV-1感染模型的全局稳定性

考虑到HIV-1感染过程中免疫反应和非线性感染函数,建立了一类具有三个分布时滞的HIV-1感染动力学模型.得到了关于病毒感染的基本再生数R0和CTLs免疫反应的基本再生数R1 ＜R0.通过构造Lyapunov泛函证明了系统具有阈值动力学性质,即当R0≤1时,系统存在全局渐近稳定的无感染平衡点;当R1≤1＜R0时,系统出...     

Global stability of a virus dynamics model with intracellular delay and CTL immune response

In this paper, the global stability of a virus dynamics model with intracellular delay, Crowley–Martin functional response of the infection rate, and CTL immune response is studied. By constructing suitable Lyapunov functions and using LaSalles invariance principle, the global dynamics is established; it is proved that if the basic reproductive number, R₀, is less than or equal to one, the infection‐free equilibrium is globally asymptotically stable; if R₀ is more than one, and if immune response reproductive number, R⁰, is less than one, the immune‐free equilibrium is globally asymptotically stable, and if R⁰ is more than one, the endemic equilibrium is globally asymptotically stable. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamical behavior of a delay virus dynamics model with CTL immune response

In this paper, the dynamical behavior of a virus dynamics model with CTL immune response and time delay is studied. Time delay is used to describe the time between the infected cell and the emission of viral particles on a cellular level. The effect of time delay on stability of the equilibria of the CTL immune response model has been studied and sufficient criteria for local asymptotic stability of the disease-free equilibrium, immune-free equilibrium and endemic equilibrium and global asymptotic stability of the disease-free equilibrium are given. Some conditions for Hopf bifurcation around immune-free equilibrium and endemic equilibrium to occur are also obtained by using the time delay as a bifurcation parameter. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings.     

Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period

In this paper, we studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, R₀, is derived. If R₀  1, the disease-free equilibrium is globally stable and the disease always dies out. If R₀ > 1, there exists a unique endemic equilibrium which is locally stable. Furthermore, we proved the global stability of the unique endemic equilibrium when ₁ = ₂ = 0 and the disease persists at an endemic equilibrium state if it initially exists.     

Global dynamics of a cell mediated immunity in viral infection models with distributed delays

In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection R₀ and for CTL response R₁ such that R₁<R₀. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if R₀?1, an infected equilibrium without immune response is globally asymptotically stable if R₁?1<R₀ and an infected equilibrium with immune response is globally asymptotically stable if R₁>1. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if R₁>1.