Magnetic and quantum entanglement properties of the distorted diamond chain model for azurite

On the basis of experimental data on interactions between humans we have investigated the process of epidemic spreading in a social network. We found that the distribution of the number of contacts maintained in one day is exponential. Data on frequency and duration of interpersonal interactions are presented. They allow us to simulate the spread of droplet-/-air-borne infections and to investigate the influence of human dynamics on the epidemic spread. Specifically, we investigated the influence of the distribution of frequency and duration of those contacts on magnitude, epidemic threshold and peak timing of epidemics propagating in respective networks. It turns out that a large increase in the magnitude of an epidemic and a decrease in epidemic threshold are visible if and only if both are taken into account. We have found that correlation between contact frequency and duration strongly influences the effectiveness of control measures like mass immunization campaigns.     

Epidemic spreading on random surfer networks with infected avoidance strategy

In this paper, we study epidemic spreading on random surfer networks with infected avoidance(IA) strategy. In particular, we consider that susceptible individuals' moving direction angles are affected by the current location information received from infected individuals through a directed information network. The model is mainly analyzed by discrete-time numerical simulations. The results indicate that the IA strategy can restrain epidemic spreading effectively. However,when long-distance jumps of individuals exist, the IA strategy's effectiveness on restraining epidemic spreading is heavily reduced. Finally, it is found that the influence of the noises from information transferring process on epidemic spreading is indistinctive.     

Roles of different update strategies in the vaccination behavior on two-layered networks

Epidemic spreading has been widely investigated over the past decades. And voluntary vaccination has been often utilized to explore dynamical process in epidemics where vaccines are available. In this letter, we establish a framework considering conformity motivated update as well as myopic best response motivated update on a family network which is demonstrated by a two-layered network. Extensive numerical simulations are conducted to study the dynamics of epidemic spreading under the aforementioned update rules, from which we discover the oscillation phenomenon under the pure myopic best response condition and the amplitude diversification phenomenon under the mixing of conformity and myopic best response motivated conditions. Moreover, we find that smaller overlapping fraction of links on two-layered network shall promote the epidemic propagation. The current findings can shed some lights on the evolution of epidemic spreading process in the real-world scenarios.     

Epidemic spreading in scale-free networks including the effect of individual vigilance

In this paper, we study the epidemic spreading in scale-free networks and propose a new susceptible-infected- recovered (SIR) model that includes the effect of individual vigilance. In our model, the effective spreading rate is dynamically adjusted with the time evolution at the vigilance period. Using the mean-field theory, an analytical result is derived. It shows that individual vigilance has no effect on the epidemic threshold. The numerical simulations agree well with the analytical result. Furthermore, we investigate the effect of individual vigilance on the epidemic spreading speed. It is shown that individual vigilance can slow the epidemic spreading speed effectively and delay the arrival of peak epidemic infection.     

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     

Phase diagram of epidemic spreading — unimodal vs. bimodal probability distributions

Disease spreading on complex networks is studied in SIR model. Simulations on empirical complex networks reveal two specific regimes of disease spreading: local containment and epidemic outbreak. The variables measuring the extent of disease spreading are in general characterized by a bimodal probability distribution. Phase diagrams of disease spreading for empirical complex networks are introduced. A theoretical model of disease spreading on m-ary tree is investigated both analytically and in simulations. It is shown that the model reproduces qualitative features of phase diagrams of disease spreading observed in empirical complex networks. The role of tree-like structure of complex networks in disease spreading is discussed.     

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     

异质自适应网络中的核心-边缘结构及其对疾病传播的抑制作用

节点属性异质自适应网络中疾病传播的研究表明节点属性异质性可以很大程度上增大传播阈值, 并且自组织形成一个更鲁棒的度异质网络结构. 本文从数值模拟方面研究鲁棒的度分布异质结构的自组织形成过程, 分析发现核心-边缘结构的形成才是导致传播阈值增大的根本原因. 鉴于此, 提出一种重连策略, 能够促进核心-边缘结构的形成, 从而达到增大传播阈值的目的. 这不仅有助于深入认识节点属性异质自适应网络中的流行病传播过程, 而且为疾病传播控制策略的提出提供了新思路.     

Finite size effects in epidemic spreading: the problem of overpopulated systems

In this paper we analyze the impact of network size on the dynamics of epidemic spreading. In particular, we investigate the pace of infection in overpopulated systems. In order to do that, we design a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step, which can serve as a model for sexually transmitted diseases spreading in some student communes. Because of the highly discrete character of the process, the analysis cannot use the continuous approximation widely exploited for most models. Using a discrete approach, we investigate the epidemic threshold and the quasi-stationary distribution. The main results are two theorems about the mixing time for the process: it scales like the logarithm of the network size and it is proportional to the inverse of the distance from the epidemic threshold.     

移动环境下网络病毒传播模型及其稳定性研究

考虑网络节点的随机移动, 基于平均场理论 提出一个移动环境下网络病毒传播的数学模型, 利用微分动力学系统理论研究了病毒传播行为. 研究表明, 当病毒基本再生数R₀ ≤ 1时, 网络中病毒逐渐消除, 系统的无病毒平衡点全局渐进稳定; 当R₀ > 1时, 网络中病毒持续存在, 系统的地方病平衡点全局渐进稳定.通过仿真验证了所得结论的正确性.     

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     

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     

Epidemic centrality — is there an underestimated epidemic impact of network peripheral nodes?

In the study of disease spreading on empirical complex networks in SIR model, initially infected nodes can be ranked according to some measure of their epidemic impact. The highest ranked nodes, also referred to as “superspreaders”, are associated to dominant epidemic risks and therefore deserve special attention. In simulations on studied empirical complex networks, it is shown that the ranking depends on the dynamical regime of the disease spreading. A possible mechanism leading to this dependence is illustrated in an analytically tractable example. In systems where the allocation of resources to counter disease spreading to individual nodes is based on their ranking, the dynamical regime of disease spreading is frequently not known before the outbreak of the disease. Therefore, we introduce a quantity called epidemic centrality as an average over all relevant regimes of disease spreading as a basis of the ranking. A recently introduced concept of phase diagram of epidemic spreading is used as a framework in which several types of averaging are studied. The epidemic centrality is compared to structural properties of nodes such as node degree, k-cores and betweenness. There is a growing trend of epidemic centrality with degree and k-cores values, but the variation of epidemic centrality is much smaller than the variation of degree or k-cores value. It is found that the epidemic centrality of the structurally peripheral nodes is of the same order of magnitude as the epidemic centrality of the structurally central nodes. The implications of these findings for the distributions of resources to counter disease spreading are discussed.     

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.     

Periodic Wave of Epidemic Spreading in Community Networks

It was reported by Cummings ef al. [Nature 427 （2004） 344] that there are periodic waves in the spatiotemporal data of epidemics. For understanding the mechanism, we study the epidemic spreading on community networks by both the SIS model and the SIRS model. We find that with the increase of infection rate, the number of total infected nodes may be stabilized at a fixed point, oscillatory waves, and periodic cycles. Moreover, the epidemic spreading in the SIS model can be explained by an analytic map.     

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。     

Variability of contact process in complex networks

We study numerically how the structures of distinct networks influence the epidemic dynamics in contact process. We first find that the variability difference between homogeneous and heterogeneous networks is very narrow, although the heterogeneous structures can induce the lighter prevalence. Contrary to non-community networks, strong community structures can cause the secondary outbreak of prevalence and two peaks of variability appeared. Especially in the local community, the extraordinarily large variability in early stage of the outbreak makes the prediction of epidemic spreading hard. Importantly, the bridgeness plays a significant role in the predictability, meaning the further distance of the initial seed to the bridgeness, the less accurate the predictability is. Also, we investigate the effect of different disease reaction mechanisms on variability, and find that the different reaction mechanisms will result in the distinct variabilities at the end of epidemic spreading.     

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.     

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。     

多关系网络上的流行病传播动力学研究

多关系网络已经吸引了许多人的注意, 目前的研究主要涉及其拓扑结构及其演化的分析、 不同类型关系的挖掘、重叠社区的检测、级联失效动力学等. 然而,多关系网络上流行病传播的研究还相对较少. 由此提出一种双关系网络模型(工作-朋友关系网), 研究多关系对于流行病传播动力学行为的影响. 在全接触模式下, 多关系的存在会显著降低网络中的爆发阈值, 使得疾病更容易流行而难以控制. 对比ER (Erdös-Rènyi), WS (Watts-Strogatz), BA (Barabási-Albert)三种网络, 由于结构异质性的差异, WS网络受到的影响最大, ER网络次之, BA网络最小. 有趣的是, 其爆发阈值的相对变化大小与网络结构无关. 在单点接触模式下, 增加强关系的权重将显著提升爆发阈值, 降低感染密度; 随着强关系的比例变化将出现最优值现象: 极大的爆发阈值和极小的感染密度. 随着强关系的边权增加, 达到最优值的边比例将减少. 更为有趣的是, 三个网络中优值出现的位置几乎一致, 独立于网络结构. 这一研究不但有助于理解多关系网络上的病毒传播过程, 也为多关系网络研究提供了一个新的视角. 关键词： 多关系网络 流行病传播 接触模式 爆发阈值