Mathematical model on the transmission of worms in wireless sensor network

Wireless sensor networks (WSNs) have received extensive attention due to their great potential in civil and military applications. The sensor nodes have limited power and radio communication capabilities. As sensor nodes are resource constrained, they generally have weak defense capabilities and are attractive targets for software attacks. Cyber attack by worm presents one of the most dangerous threats to the security and integrity of the computer and WSN. In this paper, we study the attacking behavior of possible worms in WSN. Using compartmental epidemic model, we propose susceptible – exposed – infectious – recovered – susceptible with a vaccination compartment (SEIRS-V) to describe the dynamics of worm propagation with respect to time in WSN. The proposed model captures both the spatial and temporal dynamics of worms spread process. Reproduction number, equilibria, and their stability are also found. If reproduction number is less than one, the infected fraction of the sensor nodes disappears and if the reproduction number is greater than one, the infected fraction persists and the feasible region is asymptotically stable region for the endemic equilibrium state. Numerical methods are employed to solve and simulate the systems of equations developed and also to validate our model. A critical analysis of vaccination class with respect to susceptible class and infectious class has been made for a positive impact of increasing security measures on worm propagation in WSN.     

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。     

Dynamic model of worms with vertical transmission in computer network

An e-epidemic SEIRS model for the transmission of worms in computer network through vertical transmission is formulated. It has been observed that if the basic reproduction number is less than or equal to one, the infected part of the nodes disappear and the worm dies out, but if the basic reproduction number is greater than one, the infected nodes exists and the worms persist at an endemic equilibrium state. Numerical methods are employed to solve and simulate the system of equations developed. We have analyzed the behavior of the susceptible, exposed, infected and recovered nodes in the computer network with real parametric values.     

两类网络蠕虫的模型建立及动力学性态分析

网络蠕虫之间存在着复杂的关系,它们对蠕虫的传播和演化等动力学行为有着重要的影响,刻画这些关系有助于找到更好的控制和预防策略.本文建立了两类蠕虫(蠕虫I、蠕虫II)传播的数学模型,通过分析得到两个阈值条件R_1和R_2,当R_11和R_21,无病平衡点全局渐近稳定,意味着两类蠕虫最终均被清除;当R_21R1边界平衡点Q_1全局渐近稳定,也即蠕虫II灭绝,蠕虫I将持续存在;当R_11R2边界平衡点Q2全局渐近稳定,也即蠕虫I灭绝,蠕虫II将持续存在;当R_11和R21时,存在惟一正平衡点且全局渐近稳定,即两类蠕虫(蠕虫I与蠕虫II)同时持续存在.通过理论分析可以得到要控制蠕虫病毒可以通过控制参数来实现,进一步给出控制蠕虫病毒相对应的措施.最后通过数值模拟验证了理论分析结果.     

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.     

Conficker蠕虫传播模型

"飞客"(conficker)蠕虫病毒是近期在全球爆发的以微软的windows操作系统为攻击目标的计算机蠕虫病毒,从爆发至今,感染数量巨大,形成了巨大规模的僵尸网络,对互联网安全形成了巨大的威胁.采用域名重定向技术监测conficker蠕虫的扩散传播,针对其查杀率低,传播周期长的特点,考虑地域、连通性等因素所导致的感染主机传播能力的差异,建立conficker蠕虫传播模型,最后通过真实的conficker蠕虫监测数据验证了模型的有效性.     

Fuzzy epidemic model for the transmission of worms in computer network

An e-epidemic SIRS (susceptible–infectious–recovered–susceptible) model for the fuzzy transmission of worms in computer network is formulated. We have analyzed the comparison between classical basic reproduction number and fuzzy basic reproduction number, that is, when both coincide and when both differ. The three cases of epidemic control strategies of worms in the computer network–low, medium, and, high–are analyzed, which may help us to understand the attacking behavior and also may lead to control of worms. Numerical methods are employed to solve and simulate the system of equations developed.     

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。     

复杂网络上的病毒免疫策略研究

为了给预防病毒传播提供指导意见并且更好地对病毒传播行为进行预测和控制,主要研究了几种经典复杂网络中病毒传播的模型,并对几种复杂网络病毒免疫的模型特点进行了分析,通过对这些病毒免疫模型在多局域加权网络中应用不足的分析,对多局域加权网络的病毒免疫策略进行了相应的研究.     

群体行为的异质节点复杂网络传播

当遭遇突发的公共社会安全事件时,具有负面影响的应激行为可能迅速在社会范围内传播扩散,形成群体行为.虽然一些复杂网络的传染模型能够对此进行刻画,但更为符合实际的是行为群体根据一些特性可能划分为不同的亚群体,为此将建立异质节点SIS复杂网络模型.此后,依据亚群体的有效传播率与度分布无关、正相关和负相关三种情形,分别研究了群体行为在异质节点的小世界网络传播特性,及异质节点的无标度网络传播特性.无论是异质节点的小世界网络模型还是异质节点的无标度网络模型,平均场动力学分析和计算机模拟结果显示,当亚群体的传播率与度分布呈正相关时,群体行为的传播会出现放大相应;反之,当亚群体的传播率与度分布成负相关时,群体行为的传播会出现抑制效应.但以上的两种效应在离散性更强的无标度网络上更为明显.     

Two time-delay dynamic model on the transmission of malicious signals in wireless sensor network

Deployed in a hostile environment, motes of a Wireless sensor network (WSN) could be easily compromised by the attackers because of several constraints such as limited processing capabilities, memory space, and limited battery life time etc. While transmitting the data to their neighbour motes within the network, motes are easily compromised due to resource constraints. Here time delay can play an efficient role to reduce the adversary effect on motes. In this paper, we propose an epidemic model SEIR (Susceptible–Exposed–Infectious–Recovered) with two time delays to describe the transmission dynamics of malicious signals in wireless sensor network. The first delay accounts for an exposed (latent) period while the second delay is for the temporary immunity period due to multiple worm outbreaks. The dynamical behaviour of worm-free equilibrium and endemic equilibrium is shown from the point of stability which switches under some threshold condition specified by the basic reproduction number. Our results show that the global properties of equilibria also depends on the threshold condition and that latent and temporary immunity period in a mote does not affect the stability, but they play a positive role to control malicious attack. Moreover, numerical simulations are given to support the theoretical analysis.     

Equilibrium,pseudoequilibrium and sliding-mode heteroclinic orbit in a Filippov-type plant disease model

Plant diseases have caused tremendous crop losses and have massive impacts on food security and environment. Modeling the spread of plant diseases and understanding the dynamics of the resulting plant disease models may provide practical insights on designing effective control measures. In this paper, by incorporating cultural strategies and economic threshold policy, we present a Filippov-type plant disease model. The resulting model has state dependent discontinuous right-hand side and thus non-smooth analysis and generalized Lyapunov approach are employed for model analysis. We show that the model exhibits the phenomena of stable equilibrium, unstable pseudoequilibrium as well as sliding-mode heteroclinic orbit. Biological implications of our results in implementing control strategies for plant diseases are also discussed.     

Analysis of the binge drinking models with demographics and nonlinear infectivity on networks

Two new binge drinking models incorporating demographics on different weighted networks are investigated. First, the dynamics of the drinking model with the linear infectivity $\varphi(k)=k$ on the unweighted network is investigated. The basic reproduction number $R_0$ and the uniqueness and stability of all the equilibria are derived. Second, the model with the nonlinear infectivity $\varphi(k)=k^a(0相似文献   

基于Chebyshev多项式的神经网络中长期负荷预测研究

高精度负荷预测在提高电力系统的安全性和经济性方面有着极其重要的意义,而现有的负荷预测方法因参数有限,难以完全反映其内在规律,因而导致预测结果不够准确.为此提出了一种基于Chebyshev多项式神经网络模型的预测方法.该方法使用递推最小二乘法训练神经网络权值系数,以获得高精度的参数估计,从而实现Chebyshev多项式神经网络模型对负荷量的最优拟合,再利用训练好的Chebyshev多项式神经网络模型实现中长期负荷预测.研究结果表明,该方法能较好模拟负荷变化规律,有效提高了负荷预测精度,在电力系统负荷预测中有较大的应用价值.     

The dynamics of spreading and immune strategies of sexually transmitted diseases on scale-free network

We examine epidemic threshold and dynamics for sexually transmitted diseases (STDs) spread using a multiple susceptible-infected-removed-susceptible ODE model on scale-free networks. We derive the threshold for the epidemic to be zero in infinite scale-free network. For a hard cut off scale-free network, we also prove the stability of disease-free equilibrium and the persistence of STDs infection. The effects of two immunization schemes, including proportional scheme and targeted vaccination, are studied and compared. We find that targeted strategy compare favorably to a proportional scheme in terms of effectiveness. Theory and simulations both prove that an appropriate condom using has prominent effect to control STDs spread on scale-free networks.     

基于韧性度的低轨卫星通信网络抗毁性度量及优化

低轨卫星通信网络的抗毁性是描述网络安全可靠的有效工具,在网络体系结构设计和路由策略等领域得到了广泛的应用。根据低轨卫星通信网络中卫星在轨道平面内移动,需要不断进行切换的特点,从建立抗毁性测度模型以及网络抗毁性优化两个角度来评估和提高网络抗毁性,提出一种基于韧性度的低轨卫星通信网络抗毁性度量方法。通过对移动模型以及切换模型的结构分析,对每种结构以一定概率出现的低轨卫星通信网络,应用韧性度函数,求得网络在某个时刻及某一段时间段内的抗毁性,并针对切换模型的不足之处进行优化,用赋权韧性度来体现优化的效果,得到了优化后的网络抗毁性。以铱星系统为应用实例进行仿真,结果表明:任意时刻网络的抗毁性跟拓扑结构的韧性度值有关,并且是一种线性关系,即随着韧性度的增加,其抗毁性也增加。通过对铱星通信系统切换模型的优化,网络的抗毁性与平均抗毁性都得到了提升,说明本文所构建模型的有效性和实用性。     

网络安全漏洞信息披露中多元参与主体行为策略演化博弈分析

全球网络威胁日趋严峻,作为网络安全事件产生的根源之一,网络安全漏洞越来越被重视,对漏洞的披露已是国家网络安全应急体系建设的重要内容之一。本文构建了网络安全漏洞共享平台、软件厂商及黑客之间的三方博弈模型,并从演化博弈角度对模型进行了分析和数值模拟,确立了稳定均衡点存在的条件。研究结果表明:不同参数初始值对三方博弈结果存在显著差异,软件质量越差,平台越倾向于“封闭披露”策略;对漏洞发现者的支付积极影响软件厂商“注册会员”倾向,对黑客的“努力攻击”倾向产生负面影响;随披露成本的上升,平台更倾向于采纳“封闭披露”策略;预期损失过大,软件厂商倾向于“注册会员”策略。     

Deadlock free buffer allocation in closed queueing networks

Blocking queueing networks are of much interest in performance analysis due to their realistic modeling capability. One important feature of such networks is that they may have deadlocks which can occur if the node capacities are not sufficiently large. A necessary and sufficient condition for the node capacities is presented such that the network is deadlock free. An algorithm is given for buffer allocation in blocking queueing networks such that no deadlocks will occur assuming that the network has the special structure called cacti-graph. Additional algorithm which takes linear time in the number of nodes, is presented to find cycles in cacti networks.Akyildiz's work was supported in part by School of Information and Computer Science, ICS, of Georgia Tech and by the Air Force Office of the Scientific Research (AFOSR) under Grant AFOSR-88-0028.     

基于攻击传播性的分布式网络信任模型

根据分布式网络的特点及现有网络节点信任模型的不足,提出了基于攻击传播性的分布式网络信任模型。根据恶意节点攻击行为及其攻击传播性的特点,给出了在攻击具有传播性条件下的信任度更新计算方法,结合直接信任度和间接信任度计算出总体信任度,最后给出模型的计算协议及仿真实验。实验结果表明,该模型更逼近真实网络运行情况,并有效地避免恶意节点的攻击,提高文件成功传输的比率。该模型对于分布式网络环境下提高网络节点信任度评价的准确性,建立可信网络传输路径具有重要意义。     

Common cold outbreaks: A network theory approach

In this study, at first we evaluated the network structure in social encounters by which respiratory diseases can spread. We considered common-cold and recorded a sample of human population and actual encounters between them. Our results show that the database structure presents a great value of clustering. In the second step, we evaluated dynamics of disease spread with SIR model by assigning a function to each node of the structural network. The rate of disease spread in networks was observed to be inversely correlated with characteristic path length. Therefore, the shortcuts have a significant role in increasing spread rate. We conclude that the dynamics of social encounters’ network stands between the random and the lattice in network spectrum. Although in this study we considered the period of common-cold disease for network dynamics, it seems that similar approaches may be useful for other airborne diseases such as SARS.