在二部无标度网上的两性疾病传播

利用易感-感染-易感(SIS)传播模型研究人类性接触网上的病毒传播.当仅仅考虑异性性接触时,该网络是一个二部的无标度网.对这个网络上的SIS传播模型,通过率方程的方法分析了男性感染率和女性感染率与传染阈值之间的关系,发现女性感染者与男性感染者之比由网络的拓扑和男女感染率之比所确定.这一结果表明性接触网的拓扑对性传染病传播的重要性.最后给出了支持理论结果的数值模拟. 关键词： 性传染病 两性性接触网 无标度网络 二部图     

考虑网络流量的无标度网络病毒免疫策略研究

考虑网络交通流量对病毒传播行为的影响,基于平均场理论研究无标度网络上的病毒免疫策略,提出一种改进的熟人免疫机理.理论分析表明,在考虑网络交通流量影响的情况下,当免疫节点密度较小时,随机免疫几乎不能降低病毒的传播速率,而对网络实施目标免疫则能够有效抑制病毒的传播,并且选择度最大的节点进行免疫与选择介数最大的节点进行免疫的效果基本相同.研究还发现,对于网络全局信息未知的情况,与经典熟人免疫策略相比,所提出的免疫策略能够获得更好的免疫效果.通过数值仿真对理论分析进行了验证. 关键词： 无标度网络 病毒传播 交通流量 免疫策略     

同时考虑传染媒介和传播延迟的复杂网络病毒传播行为研究

提出一种新的流行病传播模型,基于平均场理论,研究传染媒介和传播延迟同时存在对网络中流行病传播行为的影响.理论分析和仿真结果表明,传染媒介和传播延迟同时存在显著增强了网络中流行病爆发的危险性,并加速了流行病的传播.研究还发现,对于给定的有效传播率,均匀网络中流行病的感染程度分别与传染媒介的传染概率和传播延迟呈对数关系,无标度网络中流行病的感染程度与传染媒介的传染概率呈幂率关系,而与传播延迟之间则存在线性关系。     

复杂网络上的意见动力学对谣言传播的影响

通过在SIR(susceptible-infected-recovered)模型中引入抑制者对谣言的辟谣机制研究了在线社交网络上的意见动力学对谣言传播的影响.在这一模型中,节点可以与自身的邻居组成1个群,传播者可以通过该群传播信息,抑制者也可以在此群中对信息发表意见进行辟谣.辟谣机制在降低未知者对于谣言的接受概率的同时也可以促使传播者向抑制者转变.本文采用ER(Erd?s-Rényi)随机网络、无标度网络以及真实的社交网络研究了抑制者的沉默概率对于谣言传播范围的影响.首先发现,谣言传播的过程以传播者的峰值为界可以分为两个阶段,即谣言自由传播的前期以及抑制者和传播者互相制衡的后期;其次,谣言的传播会随着抑制者的沉默概率的增大而突然暴发.在谣言暴发阈值之下,沉默概率的增大不会导致谣言传播范围显著增大,这是由于未知者在感知到谣言并转变为传播者后又迅速转变为抑制者;而当沉默概率达到谣言暴发阈值时,抑制者将不能控制传播者对谣言的传播从而导致抑制者的降低和谣言的暴发;最后,无标度上的谣言自由传播的前期阶段比随机网络持续的时间更短,从而使无标度上的谣言更难以暴发.本文的模型综合考虑了意见动力学和谣言传播的相互作用,更加真实地模拟了真实世界社交网络中的谣言传播过程.为谣言传播的控制和干预提供了一些有用的思路和见解.     

基于元胞自动机考虑传播延迟的复杂网络病毒传播研究

基于元胞自动机,研究传播延迟对复杂网络病毒传播动力学行为的影响,提出一种新的易染状态-感染状态-易染状态(SIS)传播模型.研究表明,传播延迟的存在显著降低了网络的传播临界值,增强了网络中病毒爆发的危险性.研究还发现,随着传播延迟的增大,病毒的感染程度以及传播速率都明显增大.此外,SIS传播模型不仅能够反映病毒的平均传播趋势,而且可以描述病毒随时间的动态演化过程以及病毒的爆发和消亡等概率事件,从而有效地克服了利用平均场方法构建的微分方程模型只能反映病毒平均传播趋势的局限性.同时,还给出有效控制网络中病毒传 关键词： 复杂网络 病毒传播 元胞自动机 传播延迟     

具有非均匀传输和抗攻击差异的网络病毒传播模型

针对实际网络中节点存在抗攻击差异以及边的非均匀传输等情况,基于平均场理论,提出具有抗攻击差异和非均匀传输特性的网络病毒传播平均场SIR模型.该模型中,通过引入脆弱性函数和传输函数,分别描述节点的抗攻击差异以及边的非均匀传输能力.通过对所提模型的分析,得到传播阈值的理论结果.理论分析和仿真表明,节点的抗攻击差异以及边的非均匀传输,都可导致出现正的传播阈值,使得病毒传播风险有效降低.     

复杂网络中考虑不完全免疫的病毒传播研究

复杂网络中不完全免疫包括免疫失败和免疫失效两种情况,本文研究两者同时存在对网络病毒传播行为的影响,基于平均场理论,提出一种新的传播模型.理论分析表明,免疫失败和免疫失效同时存在显著降低了网络的传播临界值,增强了病毒的感染程度.根据传播临界值与免疫节点密度、免疫成功率以及免疫失效率之间的关系,给出有效控制网络病毒传播的策略.通过数值仿真进行验证。     

自适应网络中病毒传播的稳定性和分岔行为研究

自适应复杂网络是以节点状态与拓扑结构之间存在反馈回路为特征的网络. 针对自适应网络病毒传播模型, 利用非线性微分动力学系统研究病毒传播行为; 通过分析非线性系统对应雅可比矩阵的特征方程, 研究其平衡点的局部稳定性和分岔行为, 并推导出各种分岔点的计算公式. 研究表明, 当病毒传播阈值小于病毒存在阈值, 即R₀0^c时, 网络中病毒逐渐消除, 系统的无病毒平衡点是局部渐近稳定的; R₀^c0<1时, 网络出现滞后分岔, 产生双稳态现象, 系统存在稳定的无病毒平衡点、较大稳定的地方病平衡点和较小不稳定的地方病平衡点; R₀>1时, 网络中病毒持续存在, 系统唯一的地方病平衡点是局部渐近稳定的. 研究发现, 系统先后出现了鞍结分岔、跨临界分岔、霍普夫分岔等分岔行为. 最后通过数值仿真验证所得结论的正确性. 关键词： 自适应网络 稳定性 分岔 基本再生数     

基于有向网络的Email病毒传播模型及其震荡吸引子研究

基于有向Email网络和Email病毒传播特点,运用平均场方法建立Email病毒传播的时滞微分方程模型,研究Email病毒在有向网络中的震荡传播行为.理论上给出了震荡解的全局吸引子存在的充要条件,数值实验验证了吸引子的存在性和控制.研究表明,子图之间的传播概率决定吸引子的存在性,而有效传播率影响吸引子的振幅,因此这两个参数对于有效预测和控制Email病毒在网络上的传播规模具有重要意义.     

一种基于元胞自动机的自适应网络病毒传播模型

自适应网络是节点动力学和网络动力学相互作用和反馈的演化网络. 基于元胞自动机建立自适应网络中易感-感染-易感(susceptible-infected-susceptible)的病毒传播模型,研究节点为了规避病毒传播所采取的多种网络重连规则对病毒传播及网络统计特征的影响. 结果表明:自适应网络中的重连规则可以有效减缓病毒传播速度,降低病毒传播规模;随机重连规则使得网络统计特征趋于随机网络;基于元胞自动机建立的传播模型清晰地表达了病毒在传播过程中的双稳态现象. 关键词： 自适应网络 传播动力学 网络动力学 元胞自动机     

Contagion dynamics on adaptive multiplex networks with awareness-dependent rewiring

Over the last few years, the interplay between contagion dynamics of social influences (e.g., human awareness, risk perception, and information dissemination) and biological infections has been extensively investigated within the framework of multiplex networks. The vast majority of existing multiplex network spreading models typically resort to heterogeneous mean-field approximation and microscopic Markov chain approaches. Such approaches usually manifest richer dynamical properties on multiplex networks than those on simplex networks; however, they fall short of a subtle analysis of the variations in connections between nodes of the network and fail to account for the adaptive behavioral changes among individuals in response to epidemic outbreaks. To transcend these limitations, in this paper we develop a highly integrated effective degree approach to modeling epidemic and awareness spreading processes on multiplex networks coupled with awareness-dependent adaptive rewiring. This approach keeps track of the number of nearest neighbors in each state of an individual; consequently, it allows for the integration of changes in local contacts into the multiplex network model. We derive a formula for the threshold condition of contagion outbreak. Also, we provide a lower bound for the threshold parameter to indicate the effect of adaptive rewiring. The threshold analysis is confirmed by extensive simulations. Our results show that awareness-dependent link rewiring plays an important role in enhancing the transmission threshold as well as lowering the epidemic prevalence. Moreover, it is revealed that intensified awareness diffusion in conjunction with enhanced link rewiring makes a greater contribution to disease prevention and control. In addition, the critical phenomenon is observed in the dependence of the epidemic threshold on the awareness diffusion rate, supporting the metacritical point previously reported in literature. This work may shed light on understanding of the interplay between epidemic dynamics and social contagion on adaptive networks.     

Modelling of discrete-time SIS models with awareness interactions on degree-uncorrelated networks

Many epidemic models ignored the impact of awareness on epidemics in a population, though it is not the case from the real viewpoints. In this paper, a discrete-time SIS model with awareness interactions on degree-uncorrelated networks is considered. We study three kinds of awareness, including local awareness and global awareness which are originated from the epidemic-dependent information, and individual awareness which is epidemic-independent and determined by the individual information. We demonstrate analytically that awareness of the epidemic-dependent information cannot change the epidemic threshold regardless of the global or local spreading information. In contrast, epidemic-independent awareness to individual information increases the epidemic threshold in finite scale-free networks, but cannot halt the absence of epidemic threshold in an infinite scale-free network. By numerical simulations, we find that local awareness has a stronger impact on epidemic prevalence than global awareness. Our findings explore the effects of various types of awareness on epidemic spreading and address their roles in the epidemic control.     

Theory of rumour spreading in complex social networks

We introduce a general stochastic model for the spread of rumours, and derive mean-field equations that describe the dynamics of the model on complex social networks (in particular, those mediated by the Internet). We use analytical and numerical solutions of these equations to examine the threshold behaviour and dynamics of the model on several models of such networks: random graphs, uncorrelated scale-free networks and scale-free networks with assortative degree correlations. We show that in both homogeneous networks and random graphs the model exhibits a critical threshold in the rumour spreading rate below which a rumour cannot propagate in the system. In the case of scale-free networks, on the other hand, this threshold becomes vanishingly small in the limit of infinite system size. We find that the initial rate at which a rumour spreads is much higher in scale-free networks than in random graphs, and that the rate at which the spreading proceeds on scale-free networks is further increased when assortative degree correlations are introduced. The impact of degree correlations on the final fraction of nodes that ever hears a rumour, however, depends on the interplay between network topology and the rumour spreading rate. Our results show that scale-free social networks are prone to the spreading of rumours, just as they are to the spreading of infections. They are relevant to the spreading dynamics of chain emails, viral advertising and large-scale information dissemination algorithms on the Internet.     

Thresholds for epidemic spreading in networks

We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible model the activity threshold λ(c) vanishes in the large size limit on any network whose maximum degree k(max) diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has nothing to do with the scale-free nature of the network but stems instead from the largest hub in the system being active for any spreading rate λ>1/√k(max) and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.     

Statistical model for the effects of phase and momentum randomization on electron transport

In this paper, the study of epidemic spreading of mobile individuals on networks focuses on the system in which each node of the network may be occupied by either one individual or a void, and each individual could move to a neighbour void node. It is found that for the susceptible-infected-susceptible (SIS) model, the diffusion increases the epidemic threshold for arbitrary heterogeneous networks having the degree fluctuations, and the diffusion doesn??t affect the epidemic threshold for regular random networks. In the SI model, the diffusion suppresses the epidemic spread at the early outbreak stage, which indicates that the growth time scale of outbreaks is monotonically increasing with diffusion rate d. The heterogeneous mean-field analysis is in good agreement with the numerical simulations on annealed networks.     

Multiple routes transmitted epidemics on multiplex networks

This letter investigates the multiple routes transmitted epidemic process on multiplex networks. We propose detailed theoretical analysis that allows us to accurately calculate the epidemic threshold and outbreak size. It is found that the epidemic can spread across the multiplex network even if all the network layers are well below their respective epidemic thresholds. Strong positive degree–degree correlation of nodes in multiplex network could lead to a much lower epidemic threshold and a relatively smaller outbreak size. However, the average similarity of neighbors from different layers of nodes has no obvious effect on the epidemic threshold and outbreak size.     

Epidemic outbreaks in complex heterogeneous networks

We present a detailed analytical and numerical study for the spreading of infections with acquired immunity in complex population networks. We show that the large connectivity fluctuations usually found in these networks strengthen considerably the incidence of epidemic outbreaks. Scale-free networks, which are characterized by diverging connectivity fluctuations in the limit of a very large number of nodes, exhibit the lack of an epidemic threshold and always show a finite fraction of infected individuals. This particular weakness, observed also in models without immunity, defines a new epidemiological framework characterized by a highly heterogeneous response of the system to the introduction of infected individuals with different connectivity. The understanding of epidemics in complex networks might deliver new insights in the spread of information and diseases in biological and technological networks that often appear to be characterized by complex heterogeneous architectures. Received 20 September 2001 and Received in final form 4 February 2002     

Epidemic thresholds in a heterogenous population with competing strains

Among many epidemic models,one epidemic disease may transmit with the existence of other pathogens or other strains from the same pathogen. In this paper,we consider the case where all of the strains obey the susceptible-infected-susceptible mechanism and compete with each other at the expense of common susceptible individuals. By using the heterogenous mean-field approach,we discuss the epidemic threshold for one of two strains. We confirm the existence of epidemic threshold in both finite and infinite populations subject to underlying epidemic transmission. Simulations in the Barabasi-Albert (BA) scale-free networks are in good agreement with the analytical results.     

基于节点度信息的自愿免疫模型研究

疾病的广泛传播给人类带来了巨大的损失, 因此抑制疾病的传播非常重要. 本文考虑了个体接种疫苗意愿的差异性, 并结合博弈理论建立了一个基于节点度信息的自愿免疫模型. 理论解析结果证明当感染率超过某个阈值时, 该模型与忽略个体接种意愿差异性的经典模型(Zhang et al 2010 New J. Phys. 12 023015) 传播效果(感染节点数)一样. 继而考虑疫苗永久有效和有效期有限两种情况, 在Barabási-Albert网络中利用SIS传播模型对疾病的传播进程进行了数值模拟, 发现数值模拟结果与理论解析结果非常符合. 实验证明, 当感染耗费和接种疫苗耗费相同时, 该模型比忽略个体接种意愿差异性的经典模型能够更好的抑制疾病的传播, 且感染人数下降比例超过65%, 更重要的是,疫苗有效期越长本文的模型 (与忽略个体接种意愿差异性的经典模型相比)抑制疾病传播效果越好. 关键词： 疾病传播 自愿免疫 接种疫苗倾向 节点度     

Epidemic spreading on weighted complex networks

Nowadays, the emergence of online services provides various multi-relation information to support the comprehensive understanding of the epidemic spreading process. In this Letter, we consider the edge weights to represent such multi-role relations. In addition, we perform detailed analysis of two representative metrics, outbreak threshold and epidemic prevalence, on SIS and SIR models. Both theoretical and simulation results find good agreements with each other. Furthermore, experiments show that, on fully mixed networks, the weight distribution on edges would not affect the epidemic results once the average weight of whole network is fixed. This work may shed some light on the in-depth understanding of epidemic spreading on multi-relation and weighted networks.