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.     

A modified epidemiological model for computer viruses

Since the computer viruses pose a serious problem to individual and corporative computer systems, a lot of effort has been dedicated to study how to avoid their deleterious actions, trying to create anti-virus programs acting as vaccines in personal computers or in strategic network nodes. Another way to combat viruses propagation is to establish preventive policies based on the whole operation of a system that can be modeled with population models, similar to those that are used in epidemiological studies. Here, a modified version of the SIR (Susceptible-Infected-Removed) model is presented and how its parameters are related to network characteristics is explained. Then, disease-free and endemic equilibrium points are calculated, stability and bifurcation conditions are derived and some numerical simulations are shown. The relations among the model parameters in the several bifurcation conditions allow a network design minimizing viruses risks.     

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.     

考虑蠕虫传播风险的信任度更新模型

基于网络节点信任度的评估机制是一种有效防御蠕虫传播的方法。针对现有节点信任度计算模型对蠕虫攻击行为不敏感,对恶意节点识别不全面的问题,本文提出了一种考虑蠕虫传播风险的信任度更新模型。通过蠕虫传播模型中STIDR状态定义,对节点信任度和传播概率的关系进行了定量刻画;建立了直接风险、间接风险和传播性风险三种条件下的信任度更新模型。仿真结果表明,与基本信任模型相比,本文考虑蠕虫传播风险的信任度更新模型使网络中感染状态节点的信任度更低,感染状态节点数目更少,隔离状态节点数目更多,表明信任度的更新使节点对感染状态节点的识别更加有效,在一定程度上达到了抵御蠕虫攻击,抑制蠕虫在网络中传播的目的。     

基于复杂网络的邮件病毒的传播模型

本文以电子邮件病毒为例，通过构建改进的SEIR病毒传播模型，并结合更符合实际的复杂网络与人际关系对病毒的传播特性进行深入研究。从用户的主观与客观等多种角度研究了有效拉制病毒在网络中快速传播的方式．理论分析及仿真实验表明，通过对实际生活中某些参数的控制，能有效遏制邮件病毒在网络中的传播．‘     

Markovian traffic equilibrium

We analyze an equilibrium model for traffic networks based on stochastic dynamic programming. In this model passengers move towards their destinations by a sequential process of arc selection based on a discrete choice model at every intermediate node in their trip. Route selection is the outcome of this sequential process while network flows correspond to the invariant measures of the underlying Markov chains. The approach may handle different discrete choice models at every node, including the possibility of mixing deterministic and stochastic distribution rules. It can also be used over a multi-modal network in order to model the simultaneous selection of mode and route, as well as to treat the case of elastic demands. We establish the existence of a unique equilibrium, which is characterized as the solution of an unconstrained strictly convex minimization problem of low dimension. We report some numerical experiences comparing the performance of the method of successive averages (MSA) and Newton’s method on one small and one large network, providing a formal convergence proof for MSA. Dedicated to Clovis Gonzaga on the occassion of his 60th birthday.     

考虑攻击相关性的蠕虫传播模型

网络节点的感染概率直接对蠕虫的传播过程产生影响,而攻击行为的相关性会加大节点的感染概率。基于此,本文提出了考虑攻击相关性的STIR蠕虫传播模型。根据攻击相关性的特点,给出感染概率的更新计算方法,并利用状态转移概率法对传播过程进行数学描述,推导传播临界值的计算公式,最后在无标度网络中进行仿真分析。实验结果验证了数值推导出的传播临界值的正确性。与未考虑攻击相关性的蠕虫传播模型相比,STIR模型能够更好地模拟蠕虫的传播过程。同时在研究中还发现,感染概率初始值、感染变化率和传播概率的增加都会加大蠕虫的传播速度和传播规模。     

Global dynamics of a viral infection model with a latent period and Beddington-DeAngelis response

In this paper, we study the global dynamics of a viral infection model with a latent period. The model has a nonlinear function which denotes the incidence rate of the virus infection in vivo. The basic reproduction number of the virus is identified and it is shown that the uninfected equilibrium is globally asymptotically stable if the basic reproduction number is equal to or less than unity. Moreover, the virus and infected cells eventually persist and there exists a unique infected equilibrium which is globally asymptotically stable if the basic reproduction number is greater than unity. The basic reproduction number determines the equilibrium that is globally asymptotically stable, even if there is a time delay in the infection.     

Dynamical Analysis and Control Strategies of Rumor Spreading Models in Both Homogeneous and Heterogeneous Networks

In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the global stability of the equilibrium points are discussed by linearization approach of nonlinear systems and Lyapunov function. In the heterogeneous network model, we calculate the basic reproduction number through algebraic method. In addition, Lyapunov functional method and Lasalle invariance principle are applied to study the stability of equilibrium points in the complex network model. Further, we put forward some useful strategies to control the spreading of rumor based on the complex network theory. Finally, we take advantage of numerical simulations to verify the theory above and come up with necessary conclusions.

     

Dynamics of virus infection models with density‐dependent diffusion and Beddington–DeAngelis functional response

In this work, we integrate both density‐dependent diffusion process and Beddington–DeAngelis functional response into virus infection models to consider their combined effects on viral infection and its control. We perform global analysis by constructing Lyapunov functions and prove that the system is well posed. We investigated the viral dynamics for scenarios of single‐strain and multi‐strain viruses and find that, for the multi‐strain model, if the basic reproduction number for all viral strains is greater than 1, then each strain persists in the host. Our investigation indicates that treating a patient using only a single type of therapy may cause competitive exclusion, which is disadvantageous to the patient's health. For patients infected with several viral strains, the combination of several therapies is a better choice. Copyright © 2017 John Wiley & Sons, Ltd.     

考虑风险传导情形的供应风险评估方法

针对考虑风险传导情形的供应风险评估问题,提出了一种基于贝叶斯网络的供应风险评估方法。该方法中,通过识别引起供应链中各节点企业供应风险的关键风险因素,构建一个贝叶斯网络,并依据贝叶斯公式计算考虑风险传导情形下供应风险的发生概率,在此基础上,对考虑风险传导的供应风险进行评估。最后,通过一个算例说明了该方法的可行性和有效性。     

考虑直销的多期供应链网络均衡模型

研究了直销供应链网络动态均衡模型,分别对制造商、零售商和需求市场的决策者的多期独立决策行为及其相互作用进行了分析,利用变分不等式构建了各层均衡模型以及系统均衡模型,得到了系统达到均衡的条件,给出了具体算例并进行了求解.构建的供应链网络动态均衡模型具有更好的适用性及普遍性,为供应链的各层成员保持供应链的稳定和长期均衡提供决策依据和决策方法.     

Diffusion and growth in an evolving network

We study a simple model of a population of agents whose interaction network co-evolves with knowledge diffusion and accumulation. Diffusion takes place along the current network and, reciprocally, network formation depends on the knowledge profile. Diffusion makes neighboring agents tend to display similar knowledge levels. On the other hand, similarity in knowledge favors network formation. The cumulative nonlinear effects induced by this interplay produce sharp transitions, equilibrium co-existence, and hysteresis, which sheds some light on why multiplicity of outcomes and segmentation in performance may persist resiliently over time in knowledge-based processes.     

Models for network evolution

This paper describes mathematical models for network evolution when ties (edges) are directed and the node set is fixed. Each of these models implies a specific type of departure from the standard null binomial model. We provide statistical tests that, in keeping with these models, are sensitive to particular types of departures from the null. Each model (and associated test) discussed follows directly from one or more socio‐cognitive theories about how individuals alter the colleagues with whom they are likely to interact. The models include triad completion models, degree variance models, polarization and balkanization models, the Holland‐Leinhardt models, metric models, and the constructural model. We find that many of these models, in their basic form, tend asymptotically towards an equilibrium distribution centered at the completely connected network (i.e., all individuals are equally likely to interact with all other individuals); a fact that can inhibit the development of satisfactory tests.     

面向可靠性的网络级联失效分析

本文从可靠性角度定义了影响级联失效过程的关键指标,探讨网络不同类型节点在失效传播过程中的作用及其对可靠性的影响。通过节点聚合描述不同节点的失效传递,以及节点失效时的网络拓扑结构变化特征,从而构建网络级联失效模型,然后确定网络的关键失效路径。最后通过案例分析,发现交通网络在经过聚合变化后稳定性更强,流通性也有提高,验证了该模型的有效性。     

Minimum action method for the study of rare events

The least action principle from the Wentzell‐Freidlin theory of large deviations is exploited as a numerical tool for finding the optimal dynamical paths in spatially extended systems driven by a small noise. The action is discretized and a preconditioned BFGS method is used to optimize the discrete action. Applications are presented for thermally activated reversal in the Ginzburg‐Landau model in one and two dimensions, and for noise induced excursion events in the Brusselator taken as an example of non‐gradient system arising in chemistry. In the Ginzburg‐Landau model, the reversal proceeds via interesting nucleation events, followed by propagation of domain walls. The issue of nucleation versus propagation is discussed and the scaling for the number of nucleation events as a function of the reversal time and other material parameters is computed. Good agreement is found with the numerical results. In the Brusselator, whose deterministic dynamics has a single stable equilibrium state, the presence of noise is shown to induce large excursions by which the system cycles out of this equilibrium state. © 2004 Wiley Periodicals, Inc.     

Long term dynamics in a mathematical model of HIV-1 infection with delay in different variants of the basic drug therapy model

Infection with HIV-1, degrading the human immune system and recent advances of drug therapy to arrest HIV-1 infection, has generated considerable research interest in the area. Bonhoeffer et al. (1997) [1], introduced a population model representing long term dynamics of HIV infection in response to available drug therapies. We consider a similar type of approximate model incorporating time delay in the process of infection on the healthy T cells which, in turn, implies inclusion of a similar delay in the process of viral replication. The model is studied both analytically and numerically. We also include a similar delay in the killing rate of infected CD4⁺ T cells by Cytotoxic T-Lymphocyte (CTL) and in the stimulation of CTL and analyse two resulting models numerically.The models with no time delay present have two equilibria: one where there is no infection and a non-trivial equilibrium where the infection can persist. If there is no time delay then the non-trivial equilibrium is locally asymptotically stable. Both our analytical results (for the first model) and our numerical results (for all three models) indicate that introduction of a time delay can destabilize the non-trivial equilibrium. The numerical results indicate that such destabilization occurs at realistic time delays and that there is a threshold time delay beneath which the equilibrium with infection present is locally asymptotically stable and above which this equilibrium is unstable and exhibits oscillatory solutions of increasing amplitude.     

Stability analysis of VEISV propagation modeling for network worm attack

In this paper, we propose VEISV (vulnerable – exposed – infectious – secured – vulnerable) network worm attack model, which is appropriate for measuring the effects of security countermeasures on worm propagation. Contrary to existing models, our model takes into consideration accurate positions for dysfunctional hosts and their replacements in state transition. Using the reproduction rate, we derive global stability of a worm-free state and local stability of a unique worm-epidemic state. Furthermore, simulation results show the positive impact of increasing security countermeasures in the vulnerable state on worm-exposed and infectious propagation waves. Finally, equilibrium points are confirmed by phase plots.     

Global stability of delay-distributed viral infection model with two modes of viral transmission and B-cell impairment

This paper formulates a virus dynamics model with impairment of B-cell functions. The model incorporates two modes of viral transmission: cell-free and cell-to-cell. The cell-free and cell-cell incidence rates are modeled by general functions. The model incorporates both, latently and actively, infected cells as well as three distributed time delays. Nonnegativity and boundedness properties of the solutions are proven to show the well-posedness of the model. The model admits two equilibria that are determined by the basic reproduction number R₀. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions and time delays on the virus dynamics are studied. We have shown that if the functions of B-cell is impaired, then the concentration of viruses is increased in the plasma. Moreover, we have observed that increasing the time delay will suppress the viral replication.