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     

Disease spreading in structured scale-free networks

We study the spreading of a disease on top of structured scale-free networks recently introduced. By means of numerical simulations we analyze the SIS and the SIR models. Our results show that when the connectivity fluctuations of the network are unbounded whether the epidemic threshold exists strongly depends on the initial density of infected individuals and the type of epidemiological model considered. Analytical arguments are provided in order to account for the observed behavior. We conclude that the peculiar topological features of this network and the absence of small-world properties determine the dynamics of epidemic spreading. Received 16 October 2002 Published online 4 February 2003 RID="a" ID="a"e-mail: yamir@ictp.trieste.it     

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。     

A modified SIS model with an infective medium on complex networks and its global stability

In this paper, we propose a modified susceptible-infected-susceptible model with an infective medium, which describes epidemics transmitted through an infective medium on complex networks. We examine epidemic thresholds for disease spreading by using this new model and compare it with the standard SIS model and another SIS model having an infective medium. We also study and compare the effects of the uniform immunization scheme on different models. We finally give some necessary and sufficient conditions for the global stability of the new model.     

Epidemic prevalence on random mobile dynamical networks: individual heterogeneity and correlation

In this paper, we extend the susceptible-infected-susceptible (SIS) epidemiological model on a random dynamical network composed of mobile individuals, in which the infection is caused by the collisions between susceptible and infected individuals at the spreading rate proportional to their susceptibilities and infectivities. We analytically study the criticality of spreading dynamics under different distributions of individual susceptibility and infectivity, and numerically verify the cases of power-law and (or) Gaussian distributions. Our findings show that the heterogeneity of individual susceptibility and infectivity increases the epidemic threshold, and the positive correlation of individual susceptibility and infectivity avails to the epidemic prevalence.     

无标度网络上的传播动力学

介绍了无标度网络上的传播动力学,在susceptible-infected-susceptible（SIS）模型的基础上考察了一般情况下无标度网络中疾病爆发的临界点问题,得出了关于临界点一般性的表达式.得到的结果在特殊情况下分别退化为已有的一些经典结论.同时分别讨论了这些情况的建模意义和可靠性. 关键词： 无标度网络 传播动力学 susceptible-infected-susceptible模型 临界点     

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.     

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.     

基于交通流量的病毒扩散动力学研究

不同于经典扩散模型中节点传染力等同于节点度k的假定, 基于交通流量的病毒扩散模型中, 各个节点的传染力可以等同于节点实际介数b_k. 利用平均场近似方法, 提出基于交通流量SIS病毒修正扩散模型. 根据修正SIS模型, 以最小搜索信息路由为例, 重新研究病毒传播率β, 平均发包率λ同传播阈值β_c, 平稳状态病毒密度ρ之间的关系. 理论分析与实验结果均表明, 当网络拓扑和路由策略一定时, 传播阈值β_c为实际介数b_k的均值<b_k>与其平方的均值<b_k²>的比值. 而稳定状态时感染密度ρ同感染同病毒传播率β, 平均发包率λ 以及λ =1时节点实际介数的均值<b_λ=1> 的乘积倒数存在幂率关系.     

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     

Effect of local rewiring in adaptive epidemic networks

We investigate the dynamics of a susceptible-infected-susceptible (SIS) epidemic model on adaptive (co-evolutionary) networks. In most of these models, the rewiring mechanism is based on information known globally. Here, we propose local rewiring where rewiring decision is based on local information around a given node. Our results show that there are phase overlaps between local and global rewirings. The results suggest that under a certain circumstance, even with limited local information, outcomes from both rewirings are statistically similar. Furthermore, we found that the epidemic threshold does not depend on the amount of information. This could be useful for planned intervention of an epidemic spreading using minimal information.     

Epidemic dynamics behavior in some bus transport networks

We abstract bus transport networks (BTNs) to complex networks using the Space P approach. First, we select three actual BTNs in three major cities in China, namely, Beijing, Shanghai and Hangzhou. Using the SIS model, we simulate and study the epidemic spreading in the three BTNs. We obtain the density of infected vertices varying with time and the stationary density of infected vertices varying with infection rate. Second, we simulate and study the epidemic spreading in a recently introduced BTN evolution model, the network properties of which correspond well with those of actual BTNs. Third, we use mean-field theory to analyze the epidemic dynamics behavior of the BTN evolution model and obtain the theoretical epidemic threshold of this model. The theoretical value agrees well with the simulation results. Based on the work in this paper, we provide the following possible forecasts for epidemic dynamics in actual BTNs. An actual BTN should have a finite positive epidemic threshold. If the effective infection rate is above this threshold, the epidemic spread in the network and the density of infected vertices finally stabilizes in a balanced state. Below this threshold, the number of infected vertices decays exponentially fast and the epidemic cannot spread on a large scale.     

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     

Epidemic spreading on networks with vaccination

In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.     

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.     

Modular Epidemic Spreading in Small-World Networks

We study the epidemic spreading of the susceptible-infected-susceptible model on small-world networks with modular structure. It is found that the epidemic threshold increases linearly with the modular strength. Furthermore, the modular structure may influence the infected density in the steady state and the spreading velocity at the beginning of propagation. Practically, the propagation can be hindered by strengthening the modular structure in the view of network topology. In addition, to reduce the probability of reconnection between modules may also help to control the propagation.     

Epidemic spreading on networks with overlapping community structure

Many real networks are characterized by overlapping community structures in which vertices may belong to more than one community. In this paper, we propose a network model with overlapping community structure. The analytical and numerical results show that the connectivity distribution of this network follows a power law. We employ this network to investigate the impact of overlapping community structure on susceptible-infected-susceptible (SIS) epidemic spreading process. The simulation results indicate that significant overlapping community structure results in a major infection prevalence and leads to a peak of the spread velocity in the early stages of the emerging infection.     

A Class of Rumor Spreading Models with Population Dynamics

Based on the characteristics of rumor spreading in online social networks, this paper proposes a new rumor spreading model. This is an improved SIS rumor spreading model in online social networks that combines the transmission dynamics and population dynamics with consideration of the impact of both of the changing number of online social network users and different levels of user activity. We numerically simulate the rumor spreading process. The results of numerical simulation show that the improved SIS model can successfully characterize the rumor spreading behavior in online social networks. We also give the effective strategies of curbing the rumor spreading in online social networks.     

具有局部结构的增长无标度网络中传染病传播机制研究

为了研究人群中的一些基本的社会关系结构,如家庭、室友、同事等,对传染病传播过程的影响机制,本文建立了一个具有局部结构的增长无标度网络模型.研究表明,局部结构的引入使得该网络模型能够同时再现社会网络的两个重要特征：节点度分布的不均匀性以及节点度之间的相关性.首先,该网络的节点度和局部结构度均服从幂律分布,且度分布指数依赖于局部结构的大小.此外,局部结构的存在还导致网络节点度之间具有正相关特性,而这种正相关正是社会网络所特有的一个重要特性.接着,通过理论分析和数值模拟,我们进一步研究了该网络结构对易感者-感染 关键词： 复杂网络 无标度网络 局部结构 传染病建模