Dynamic properties of epidemic spreading on finite size complex networks

The Internet presents a complex topological structure, on which computer viruses can easily spread. By using theoretical analysis and computer simulation methods, the dynamic process of disease spreading on finite size networks with complex topological structure is investigated. On the finite size networks, the spreading process of SIS （susceptibleinfected-susceptible） model is a finite Markov chain with an absorbing state. Two parameters, the survival probability and the conditional infecting probability, are introduced to describe the dynamic properties of disease spreading on finite size networks. Our results can help understanding computer virus epidemics and other spreading phenomena on communication and social networks. Also, knowledge about the dynamic character of virus spreading is helpful for adopting immunity policy.

Effect of incubation period on epidemic spreading in complex networks

We study the effect of incubation period on epidemic spreading in the Barabasi-Albert scale-free network and the Watts-Strogatz small world network by using a Suspectable-Incubated-Infected-Suspectable model. Our analytical investigations show that the epidemic threshold is independent of incubation period in both networks, which is verified by our large-scale simulation results. We also investigate the effect of incubation period on the epidemic dynamics in a supercritical regime. It is found that with the increase of incubation period Ω, a damped oscillation evolution of ρT （the ratio of persons in incubated state） appears and the time needed to reach a saturation value increases. Moreover, the steady value of ρT increases and approaches to an asymptotic constant with the value of Ω increasing. As a result, the infected ratio ρI decreases with the increase of Ω according to a power law.

Reverse-feeding effect of epidemic by propagators in two-layered networks

Epidemic spreading has been studied for a long time and is currently focused on the spreading of multiple pathogens,especially in multiplex networks. However, little attention has been paid to the case where the mutual influence between different pathogens comes from a fraction of epidemic propagators, such as bisexual people in two separated groups of heterosexual and homosexual people. We here study this topic by presenting a network model of two layers connected by impulsive links, in contrast to the persistent links in each layer. We let each layer have a distinct pathogen and their interactive infection is implemented by a fraction of propagators jumping between the corresponding pairs of nodes in the two layers. By this model we show that（i） the propagators take the key role to transmit pathogens from one layer to the other,which significantly influences the stabilized epidemics;（ii） the epidemic thresholds will be changed by the propagators;and（iii） a reverse-feeding effect can be expected when the infective rate is smaller than its threshold of isolated spreading.A theoretical analysis is presented to explain the numerical results.

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.

Spreading behavior of SIS epidemic model on networks with dynamical topology

Based on the two-dimensional regular lattice,a modified SIS(Susceptible-Infected-Susceptible)epidemic model with motion rules is presented to study the spreading behavior on networks with dynamical topology.The mean-field theory is utilized to analyze the critical threshold(λc)of epidemic spreading under the randomly mixing conditions.It is found that λc is only related with the population density within the lattice.Large-scale numerical simulations are carried out to verify the mean-field results,and it is observed that the long-range probability p largely affects the epidemic spreading behavior.In addition,the effect of the dual time scales on epidemic spreading is also investigated by the simulations,and it is shown that the dual time scales accelerate the dynamic spreading behavior.The results indicate that the model with motion can help us to further understand the real epidemics.

交通驱动型异质恢复概率的病毒传播

当前复杂网络上对交通驱动型病毒传播的研究均假设网络中所有节点具有相同的恢复概率,而节点间异质恢复概率对病毒传播的影响依然不清楚。文章研究异质恢复概率对交通驱动型病毒传播阈值的影响,得出网络结构、交通流量、恢复概率分配策略和路由策略等可以调整病毒传播的阈值。研究结果表明:当节点传输能力无限、网络中交通处于自由流时,合适的恢复概率分配策略可以提高传播阈值,并且恢复概率分配策略与路由策略耦合可以进一步提高传播阈值,有效抑制网络中病毒的传播;当节点传输能力有限、网络中存在交通拥挤时,病毒传播阈值增大,说明交通拥挤的存在会抑制病毒的爆发。

Epidemic spreading behavior with time delay on local-world evolving networks

An improved susceptible-infected-susceptible(SIS)model in the local-world evolving network model is presented to study the epidemic spreading behavior with time delay,which is added into the infected phase.The local-world evolving model displays a transition from the exponential network to the scale-free network with respect to the degree distribution.Two typical delay regimes,i.e.,uniform and degree-dependent delays are incorporated into the SIS epidemic model to investigate the epidemic infection processes in the local-world net-work model.The results indicate that the infection delay will promote the epidemic outbreaks,increase the prevalence and reduce the critical threshold of epidemic spreading.It is also found that local-world size M will considerably influence the epidemic spreading behavior with time delay in the local-world network through large-scale numerical simulations.Simulation results are also of relevance to fight epidemic outbreaks.

基于复杂网络的闭环供应链风险传播模型构建及仿真

根据闭环供应链的结构特征,设计闭环供应链演化网络,并从风险对抗能力出发改进灾害蔓延动力学模型,以构建闭环供应链风险传播模型。仿真结果表明:闭环供应链网络中的风险传播范围与初始风险值、初始攻击节点数量成正相关;网络对抗风险能力与节点企业风险阈值和风险恢复能力分布的平均程度成正相关,且只有当风险阈值系数超过关键风险阈值系数时才能有效控制和预防风险的传播;度大蓄意攻击与随机攻击比度小蓄意攻击对网络风险传播的影响大,且制造商作为闭环供应链网络的中心节点,当其受到风险攻击时对网络造成的影响较大。

复杂网络上流行病传播动力学的爆发阈值解析综述

对流行病传播爆发阈值的理论解析方法进行总结,主要介绍平均场、点对近似、主方程、边渗流、空穴理论、边划分以及谱分析这7种常用的动力学解析方法的前提假设、具体思路、步骤及其应用局限,并且梳理总结了SIS与SIR模型爆发阈值的异同。

复杂网络上的传播动力学及其新进展

深刻理解传染病在社会群体中的传播规律、计算机病毒在因特网上的扩散过程是复杂系统和传染病动力学领域研究的一个热点问题.主要从复杂网络的拓扑结构和流行病的感染机制2个方面综述了当前国内外传播动力学研究的现状和最新进展,探讨了传播动力学在疾病预防与免疫中的应用,最后指出值得进一步研究的问题.例如带社区、层次结构的加权演化模型,动态网络结构下的疾病传播行为和微观感染机制等.

复杂网络上疫情与舆情的传播及其基于免疫的控制策略

较为全面的综述复杂网络的免疫问题,包括:真实疫情和舆情传播场景的抽象与建模、疾病传播模型、全局免疫策略和局域免疫策略等。在若干真实网络和模型网络上模拟免疫控制的结果表明,基于中心性、图划分、熟人免疫等策略的免疫效果比随机免疫好,这说明免疫策略的选择对传播控制具有实际指导意义。在选择免疫策略时,应考虑网络的拓扑结构特性和信息的完整程度,才能达到较佳控制效果。

复杂网络模型及其在疫情传播和控制中的应用研究

复杂网络已成为一个热点研究问题,它在工程技术、社会、政治、医药、经济、管理等领域都有着广泛的应用。越来越多的科学家开始关注基于复杂网络拓扑结构的动力学研究。其中,关于疾病传播的研究是一个重要方面。分析和研究了小世界网络模型和BA无标度网络模型两种经典的复杂网络模型,并模拟了传染病按照SIR传播模型在两种网络中的传播情况,讨论了其上的传播阈值以及随机免疫和目标免疫策略对传播阈值的影响。最后对H1N1病毒的传播情况进行了仿真模拟,包括H1N1病毒在自由传播和采取随机及目标免疫两种免疫策略时的传播情况。仿真结果表明,目标免疫策略可以有效抑制疾病的传播。

自适应网络中的流行病传播动力学研究综述

从自适应模型和自适应网络上的疾病控制措施两个方面总结了近年来自适应网络上传播动力学研究的主要成果,特别关注自适应行为带来的网络结构变化和许多有趣的动力学现象。

基于局域信息的社交网络信息传播模型

针对传统传播模型更适用于均匀网络而无法有效应用于现实非均匀无标度社交网络的问题,提出一种基于用户局域信息的社交网络信息传播模型。模型中考虑了无标度网络中用户间拓扑特征差异和用户影响力不同对信息传播的影响,根据节点周边邻居节点的感染情况和权威性计算感染概率,模拟现实社交网络中的信息传播情况。通过在采集的真实微博网络数据上进行仿真实验,结果表明该模型较传统的SIR模型更能体现社交网络中信息传播的快速性与范围的广泛性;同时,通过调整模型中的相关参数,验证了相关管控措施对传播效果的影响。

传感器网络病毒感染传播局域控制研究

从传感器网络节点重要性的角度来研究病毒传播的局域控制,研究表明,通过对少量的重要节点进行免疫,可以抑制病毒的大范围扩散,提高网络的抗蓄意攻击能力.随着免疫效率的提高,使感染传播率临界值增加,同时使病毒感染局域范围控制的效果得到加强.

新个体的加入及初始条件对疾病传播的影响

用复杂网络理论构建人群关系网,采用随机差分方程组等价描述SIS模型与SIR模型的疾病传播过程,通过方程组,理论上得到了某些一般性结论。然后讨论了由于新个体加入使网络变复杂的传播情况,通过仿真发现,新加个体的重要度及人群关系网的拓扑结构对疾病传播过程有影响。此外,研究了SIR模型中不同初始感染个体对疾病传播的影响,当初始个体是随机选取或来自不同k-center时,传播过程有明显的不同。而且对个体数目及平均度相同的网络,在相同条件下,网络的深度越小,感染的人数越多。

基于空穴理论的复杂网络传染病传播控制

针对传染病的传播与控制问题,应用复杂网络进行建模,模型支持非指数形式的传播和康复概率函数,具有准确的预测精度,控制措施考虑边移除和节点移除对传染病发展的影响,控制参数可自由调节。文中利用空穴理论对模型进行了数学解析,得到了可以进行数值计算的解析结果,仿真实验证实了解析结果的准确性。对控制措施的实验表明加强重点人群防控对防治传染病具有重要意义。

复杂网络上具有分布式传染速率的流行病传播行为(英文)

提出一个改进的SI模型来研究分布式传染速率对复杂网络上的流行病传播的影响.与标准的SI模型不同,假定传播速率为几种典型的分布参数,如二值分布、均匀分布和指数分布.这种分布式的速率可以表示个体在传染性上的差异,这种差异可在很多真实的传染病中观察到.大量的数值仿真表明,这种分布式的传染速率能大大减小被感染结点的密度,减缓其动态传播过程,并且允许有更长的时间来采取相应的控制措施.因而,当前的研究结果对进一步理解网络上真实流行病的传播特性具有重要意义.

复杂网络中初始节点对传染病传播的影响分析

长期以来,传染病对人类造成持续不断的威胁。研究工作者在传染病传播上投入了大量的精力进行研究,比如:传播模型、传播阈值以及影响传播的因素等方面。主要研究复杂网络中初始染病节点如何影响传染病的传播,对5种初始染病节点选择方法进行了深入分析并在两个大规模无向网络上进行了仿真实验。结果表明,传播速度以及传染病影响规模不仅与初始染病节点的选择有关,而且与网络结构有关。本研究成果对传染病控制可提供有价值的借鉴与参考作用。

基于复杂网络的疾病传播

疾病传播问题的研究,一直是科学家所关注的焦点。近几年兴起研究的复杂网络,真实地反映出现实中系统的某些重要特性,成为研究现实网络的有效手段。在介绍复杂网络的基础上,着重阐述了复杂网络描述疾病传播的研究工作及成果,特别指出其应用于SARS病毒传播研究得到的一些有意义的结论,从而为控制病毒的传播提供了一种重要的参考依据。