一类具有Beddington-DeAngelis型功能反应函数的HIV病毒动力学系统模型的稳定性

基于Nowak等于1996年提出的一类经典的HIV病毒动力学模型,考虑了一类具有Beddington-DeAngelis功能反映函数的HIV病毒动力学模型,并研究了无病毒平衡点的全局稳定性与感染平衡点的局部稳定性等.     

一类抗体免疫下具有治愈率的HIV-1感染模型[英文]

本文主要研究一类抗体免疫下具有治愈率的HIV感染模型的动力学行为. 该模型不仅考虑潜伏阶段的感染细胞而且潜伏期的感染细胞可以治愈转化为健康的易感细胞. 通过构造Lyapunov函数, 证明了在一定条件下, 系统的无感染平衡点,无免疫平衡点以及感染平衡点的全局渐近稳定性.     

具有分布时滞的病毒感染模型动力学性质研究

本文研究具有分布时滞的病毒感染模型的动力学性质.构建该模型,基于Lyapunov泛函分析方法,研究该系统平衡点的全局稳定性.分别得到该系统无病平衡点和感染平衡点全局稳定的充分条件.     

一类具有抗体免疫反应和治愈率的HIV-1感染模型（英文）

本文主要研究一类抗体免疫下具有治愈率的HIV感染模型的动力学行为.该模型不仅考虑潜伏阶段的感染细胞而且潜伏期的感染细胞可以治愈转化为健康的易感细胞.通过构造Lyapunov函数,证明了在一定条件下,系统的无感染平衡点,无免疫平衡点以及感染平衡点的全局渐近稳定性.     

具有感染年龄结构的CD4+ T-细胞感染HIV病毒模型分析

本文建立和研究一类具有感染年龄结构的CD4+ T-细胞感染HIV病毒的动力学模型.得到决定该模型的未感染平衡点和感染平衡点的存在性和局部渐近稳定性条件,即当一个感染细胞在其整个感染期间产生病毒的总数不超过某-个阈值时,系统总存在局部渐近稳定的未感染平衡点;当-个感染细胞在其整个感染期间产生病毒的总数超过这一阈值时,未感染平衡点不稳定,此时存在局部渐近稳定的感染平衡点.     

乙肝病毒感染动力学的固有频率分析

诺瓦克模型作为研究乙肝感染动力学的基础模型,虽然被人熟知,其内部的信息与性质并没有充分被发掘.关注于其平衡点类型的分类,并用图呈现诺瓦克模型详细的动力学特征,得到了参数空间中分支曲线的解析表达式.尤其,当平衡点为焦点时,得到了系统固有频率与参数的依赖关系.     

传播动力学模型回顾与展望

传播动力学模型主要包括传染病动力学模型、计算机病毒传播模型以及谣言传播模型.首先从传染病动力学模型入手,分别介绍均匀混合传染病动力学模型和网络动力学模型;然后介绍计算机病毒传播模型以及谣言传播模型,并与传染病模型进行对比.最后作了总结与展望.     

广义网络上的计算机病毒传播模型

为了研究计算机病毒在广义网络中传播的机制,文章分别提出了计算机病毒传播的非线性和线性模型.理论分析表明,网络的最大特征值是决定计算机病毒传播的重要参数.其次,文章给出非线性和线性模型中的无病毒均衡点全局稳定的充分条件,同时也证明了线性模型的有病毒平衡点的全局吸引性.最后,通过一些数学模拟实验验证了理论分析的主要结论.     

一类具有双时滞的HIV感染模型的研究（英文）

本文主要研究具有时滞和毒性淋巴细胞(CTL)免疫反应的HIV感染模型的动力学行为.分别引入两类时滞:一类描述新感染的细胞开始产生病毒所需的时间,另一类是控制病毒复制的免疫反应出现所需的时间.通过分析时滞对平衡点稳定性的影响,建立了系统的无病平衡点P0,地方病平衡点P1的局部渐近稳定性.并且证明了在一定条件下,在地方病平衡点附近时滞可以诱导产生Hopf分支.     

一类HIV病毒动力学模型的全局稳定性与周期解

建立了一类较广泛的HIV感染CD4+T细胞病毒动力学模型,给出了一个感染细胞在其整个感染期内产生的病毒的平均数(基本再生数)R0的表达式,运用Lyapunov原理和Routh-Hurwitz判据得到了该模型的未感染平衡点与感染平衡点的存在性与稳定性条件.同时也得到了模型存在轨道渐近稳定周期解和系统持续生存的条件,并通过数值模拟验证了所得到的结果.     

A propagation model of computer virus with nonlinear vaccination probability

This paper is intended to examine the effect of vaccination on the spread of computer viruses. For that purpose, a novel computer virus propagation model, which incorporates a nonlinear vaccination probability, is proposed. A qualitative analysis of this model reveals that, depending on the value of the basic reproduction number, either the virus-free equilibrium or the viral equilibrium is globally asymptotically stable. The results of simulation experiments not only demonstrate the validity of our model, but also show the effectiveness of nonlinear vaccination strategies. Through parameter analysis, some effective strategies for eradicating viruses are suggested.     

Propagation of computer virus both across the Internet and external computers: A complex-network approach

Based on the assumption that external computers (particularly, infected external computers) are connected to the Internet, and by considering the influence of the Internet topology on computer virus spreading, this paper establishes a novel computer virus propagation model with a complex-network approach. This model possesses a unique (viral) equilibrium which is globally attractive. Some numerical simulations are also given to illustrate this result. Further study shows that the computers with higher node degrees are more susceptible to infection than those with lower node degrees. In this regard, some appropriate protective measures are suggested.     

Modeling and analysis of the spread of computer virus

Based on a set of reasonable assumptions, we propose a novel dynamical model describing the spread of computer virus. Through qualitative analysis, we give a threshold and prove that (1) the infection-free equilibrium is globally asymptotically stable if the threshold is less than one, implying that the virus would eventually die out, and (2) the infection equilibrium is globally asymptotically stable if the threshold is greater than one. Two numerical examples are presented to demonstrate the analytical results.     

The impact of patch forwarding on the prevalence of computer virus: A theoretical assessment approach

Virus patches can be disseminated rapidly through computer networks and take effect as soon as they have been installed, which significantly enhances their virus-containing capability. This paper aims to theoretically assess the impact of patch forwarding on the prevalence of computer virus. For that purpose, a new malware epidemic model, which takes into full account the influence of patch forwarding, is proposed. The dynamics of the model is revealed. Specifically, besides the permanent susceptible equilibrium, this model may admit an infected or a patched or a mixed equilibrium. Criteria for the global stability of the four equilibria are given, respectively, accompanied with numerical examples. The obtained results show that the spectral radii of the patch-forwarding network and the virus-spreading network both have a marked impact on the prevalence of computer virus. The influence of some key factors on the prevalence of virus is also revealed. Based on these findings, some strategies of containing electronic virus are recommended.     

一类时滞分数阶计算机病毒模型的稳定性研究

本文研究一类改进的时滞分数阶计算机病毒模型正平衡点的稳定性问题.利用线性化方法和拉普拉斯变换获得模型对应的线性化系统的特征方程,通过讨论特征方程的根以及横截条件研究时滞和正平衡点稳定性之间的关系,推导了Hopf分支出现时时滞临界值的计算公式,并选择恰当的系统参数进行数值模拟以验证理论分析的合理性.     

On global stability of a nonresident computer virus model

In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.     

具有非线性传染率和时滞的随机SIQR计算机病毒模型的渐近行为

研究了一类具有非线性发生率和时滞的随机SIQR计算机病毒模型.首先证明了该系统具有唯一的全局正解,然后通过构造适当的Lyapunov函数并利用伊藤公式,分析了该模型的解在无病平衡点附近及地方病平衡点附近的渐近行为,最后通过数值模拟对随机系统解的渐近行为做了进一步的分析并给出了结论.     

Dynamical behavior of computer virus on Internet

In this paper, we presented a computer virus model using an SIRS model and the threshold value R₀ determining whether the disease dies out is obtained. If R₀ is less than one, the disease-free equilibrium is globally asymptotically stable. By using the time delay as a bifurcation parameter, the local stability and Hopf bifurcation for the endemic state is investigated. Numerical results demonstrate that the system has periodic solution when time delay is larger than a critical values. The obtained results may provide some new insight to prevent the computer virus.     

ON GLOBAL STABILITY OF A NONRESIDENT COMPUTER VIRUS MODEL

In this paper, we establish new sufficient conditions for the infected equilibrium of a nonresident computer virus model to be globally asymptotically stable. Our results extend two kind of known results in recent literature.     

A new epidemic model of computer viruses

This paper addresses the epidemiological modeling of computer viruses. By incorporating the effect of removable storage media, considering the possibility of connecting infected computers to the Internet, and removing the conservative restriction on the total number of computers connected to the Internet, a new epidemic model is proposed. Unlike most previous models, the proposed model has no virus-free equilibrium and has a unique endemic equilibrium. With the aid of the theory of asymptotically autonomous systems as well as the generalized Poincare–Bendixson theorem, the endemic equilibrium is shown to be globally asymptotically stable. By analyzing the influence of different system parameters on the steady number of infected computers, a collection of policies is recommended to prohibit the virus prevalence.