基于反向感染的复合种群网络传播溯源算法

流行病的传播会对整个人类社会构成巨大威胁,因此迅速识别传播源并及时采取控制措施至关重要。然而,由于流行病传播过程具有多样性、信息不确定性等因素,使得快速准确识别传播源成为一项挑战。结合反向感染算法、复合种群网络模型以及马尔可夫链理论,提出了一个在复合种群网络中识别传播源的新算法。该算法首先利用马尔可夫链来初步估计子种群被感染的时间,被感染子种群根据感染时间获得自己的身份信息,然后遍历所有获得感染子种群身份信息的子种群,将收集到的感染子种群身份信息传播给其所有邻居,最后根据获得所有感染子种群身份信息的时间顺序推断出复合种群网络的传播源。在真实的航空网和人造复合种群网络上进行大量仿真实验,发现无论在已知全部感染快照还是部分感染快照的情况下,该算法与其他传播溯源算法相比,识别传播源的准确性都有显著提升。该算法非常适合用于航空网这类复合种群网络,对现实世界中的流行病传播溯源和控制也具有参考意义。     

考虑个体警觉行为的双层网络流行病传播模型

流行病传播过程中常伴随个体意识信息的扩散,然而目前关于流行病与意识信息关系的研究大部分未考虑意识信息在传播过程中对个体接触行为的影响。提出一种基于个体警觉状态的双层网络流行病传播模型。建立下层物理接触网络描述流行病的传播,构建上层信息扩散网络描述流行病传播中信息扩散,根据个体的行为偏好和警觉性设计警觉个体避免与非警觉个体接触、警觉个体避免与警觉个体接触两种接触行为策略,并在BA-BA、BA-WS和WS-WS 3种双层网络中模拟两种行为策略对流行病传播的影响。仿真结果表明,该模型中两种个体警觉行为策略通过调节警觉性参数均能有效降低流行病感染规模并提高流行病爆发阈值,从而抑制流行病在人群中传播。     

流行病防控策略的多主体仿真研究

为有效应对流行病应急管理活动中的复杂性问题,引入多主体仿真的方法和技术,以甲型(H1N1)流感输入性病例引发的疫情蔓延为例,构建了流行病传播的多主体仿真模型,并对其"围堵式"防控策略的执行效果进行了仿真实现。结果表明:多主体仿真可以作为流行病研究的一种十分有效的方法和技术工具,通过借助于计算机手段来构建流行病研究的"人工实验室",基于仿真进行实验研究可以为流行病应急管理活动的组织与实施提供必要的策略和决策依据。     

流行病在空间分布人群中的传播模型

研究流行病传播规律,考虑了流行病在空间分布人群中的随机传播过程。目前,人们通常应用复杂网络来模拟人群中的流行病传播过程,但是,复杂网络模型中没有空间、距离等概念,在现实中,人群通常是空间分布,即空间关系是流行病传播的重要影响因素。针对上述问题,提出一种流行病传播的新模型,使人群分布在一个有界区域内,并创新性地引入了距离的概念,改善了复杂网络模型忽视空间因素的缺陷。利用模型建构,通过编写Matlab程序对整个传播过程进行仿真,分析了个体针对病毒所产生的暂时性免疫力对流行病传播过程的影响。表明仿真结果与实际现象吻合。结果证明将空间因素纳入模型更为合理。     

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．     

基于传染病模型的社交网络舆情话题传播

针对传统模型难以真实地描述社交网络舆情话题传播过程,提出一种基于传染病模型的社交网络舆情话题传播模型。分析了社交网络舆情话题的传播特点,根据传染病动力学机制,将内部感染概率、外部感染概率、免疫概率以及直接免疫概率引入舆情话题传播过程中,构建了社交网络舆情话题传播模型,在Matlab 2012平台下采用Facebook数据集进行仿真测试。仿真实验结果表明,该模型可以准确描述社交网络中的话题传播行为特征,研究结果可以为社交网络舆论管理者提供有价值的参考意见。     

云南-东南亚航空网络影响下的甲型H1N1的时空传播模拟研究

针对航空旅行影响传染性疾病时空传播过程的问题,提出了以航空交通网络为切入点,融合智能体(Agent)技术,构建一个基于航空网络的疾病时空传播Agent模型,并模拟2009-2010年甲型H1N1流感在云南和东南亚区域的传播。其中模型由城市间与城市内模型组成,Agent代表一个城市人类种群,在城市内采用不考虑空间差异的SEIR模型;在城市间根据航空网络构建Agent模型来模拟不同人群空间上的流动,从而模拟疾病在城市间的传播。实验结果表明：航空交通运输方式加速了流行病的扩散,假设不设任何控制的机制,流感只需40d左右就蔓延整个研究区域;而在整个完整的航空网络下,新加坡只需要55d左右的时间就可迎来疫情的高峰期。     

复杂网络上同时考虑感染延迟和非均匀传播的SIR模型

为了能更有效地分析和理解传染性疾病的传播,提出了一个新颖的SIR模型,在这个传播模型里同时考虑了影响疾病传播行为的2个因素:感染延迟和非均匀传播.基于平均场理论和大量的数值仿真,给出了疾病传播临界值的解析公式,并发现感染延迟和非均匀传播对临界值影响截然不同:感染延迟能够在很大程度上减小传播阈值,促进疾病在人群中的传播;而非均匀传播能够增大传播临界值,阻碍疾病的大规模传播.当前的研究结果有助于深入理解真实复杂系统中的疾病传播行为,充分考虑感染延迟、传播机制和实际人群的拓扑结构等因素在疾病传播中的作用,从而为制定有效的传染病预防和控制措施提供理论依据.     

谣言传播过程中官方媒体影响模型

随着互联网的迅猛发展,网络谣言正如“病毒”一样在我们的生活中散播。如何有效地消除谣言在人们接收健康信息时带去的阻碍以及混淆作用,在现今的信息时代显得尤为重要。本文借鉴了经典的SIS疾病传播模型和种群竞争模型,探讨了官方媒体在谣言传播过程中的影响作用,构建非线性微分方程模型来刻画谣言传播过程,并对方程的平衡点、解的有界性以及稳定性进行了分析。最后,赋予相关参数一定的数值,利用MATLAB进行模拟仿真,讨论不同情境下的演化机理,得出了相关结论与建议,为应急管理者制定谣言传播控制策略提供支持。     

一类SIQR传染病模型在无尺度网络上的传播行为分析

研究了无尺度网络中的具有隔离项的SIQR传染病模型,利用平均场理论对疾病的传播进行了研究分析,经过计算得到了疾病传播的临界条件R0,证明了最终疾病的消失或者爆发是由临界值来决定的。然后,通过计算机仿真表明降低感染状态的感染率和提高染病节点的隔离率可以有效地控制该类传染病的传播。     

An alternative approach to characterize the topology of complex networks and its application in epidemic spreading

Based on the mean-field approach, epidemic spreading has been well studied. However, the mean-field approach cannot show the detailed contagion process, which is important in the control of epidemic. To fill this gap, we present a novel approach to study how the topological structure of complex network influences the concrete process of epidemic spreading. After transforming the network structure into hierarchical layers, we introduce a set of new parameters, i.e., the average fractions of degree for outgoing, ingoing, and remaining in the same layer, to describe the infection process. We find that this set of parameters are closely related to the degree distribution and the clustering coefficient but are more convenient than them in describing the process of epidemic spreading. Moreover, we find that the networks with exponential distribution have slower spreading speed than the networks with power-law degree distribution. Numerical simulations have confirmed the theoretical predictions.     

An alternative approach to characterize the topology of complex networks and its application in epidemic spreading

Based on the mean-field approach, epidemic spreading has been well studied. However, the mean-field approach cannot show the detailed contagion process, which is important in the control of epidemic. To fill this gap, we present a novel approach to study how the topological structure of complex network influences the concrete process of epidemic spreading. After transforming the network structure into hierarchical layers, we introduce a set of new parameters, i.e., the average fractions of degree for outgoing, ingoing, and remaining in the same layer, to describe the infection process. We find that this set of parameters are closely related to the degree distribution and the clustering coefficient but are more convenient than them in describing the process of epidemic spreading. Moreover, we find that the networks with exponential distribution have slower spreading speed than the networks with power-law degree distribution. Numerical simulations have confirmed the theoretical predictions.     

无标度网络上分片线性传染力与免疫作用下的流行病动力学

本文研究了含有免疫作用的易感染者-感染者-移出者传染病模型（即SIR模型）在复杂网络上的动力学行为,讨论了免疫作用对疾病传播的影响．当接种比例大于零时,传染率需要跨越更大的传染临界值疾病才能流行,且随着时间的增大传染临界值也增大．所以通过接种疫苗确实可以起到预防和控制疾病在复杂网络上传播的作用．具体讨论了具有分片线性传染力的SIR模型在无标度网络上的流行病传播阈值,并运用分片线性传染力得到了传播阈值为正的条件．接着分析了各种免疫策略的SIR模型,得出各类免疫后的传播阈值,并进行了数值模拟和比较．在相同的免疫概率下,目标免疫比随机免疫、近邻免疫、主动免疫更为有效．     

Structure optimization based on memetic algorithm for adjusting epidemic threshold on complex networks

Many social spreading phenomena can be modeled as epidemic spreading models over networks, and the studies of these phenomena are important to avoid epidemic outbreaks. Epidemic threshold of the network, which fundamentally depends on the network structure itself, is a critical measure to judge whether the epidemic dies out or results in an epidemic breakout. In this study, epidemic threshold is regarded as the objective function to control the spreading process. In addition, an efficient structure optimization strategy based on memetic algorithm is proposed to adjust the spreading threshold without changing the degree of each node. Lowering the threshold can promote the spreading process whereas heightening the threshold can prevent the spreading process. In the proposed algorithm, genetic algorithm is adopted as the global search strategy and a modified simulated annealing algorithm combined with the properties of networks is proposed as the local search strategy. Experiments on computer-generated and real-world networks demonstrate that the proposed algorithm has superior performances for both the threshold minimization and maximization problems.     

疫情沿交通工具跨区域扩散建模及最优控制

交通运输系统在服务民众的同时也为疫情沿跨区域传播扩散提供了载体.鉴于此,研究疫情沿多种交通工具跨区域扩散模型及最优控制问题.考虑人口空间状态、迁徙过程、疫情状态和交通工具特征,构建多区域迁徙-疫情扩散耦合动力学方程,并分析其扩散性质.综合考虑应急资源的有限性,进一步建立基于本地与迁徙隔离政策的动态最优控制模型.数值计算对比分析不同管控策略组合下疫情的扩散速度与范围,验证疫情扩散模型和最优控制策略的有效性.结果表明:疫情可以借助交通工具快速扩散;仅对单一交通工具实施管控措施可以快速降低疫情跨区域扩散的速度,但对均衡状态的扩散范围影响小.     

Epidemic spreading model of complex dynamical network with the heterogeneity of nodes

In this paper, we model epidemic spreading by considering the mobility of nodes in complex dynamical network based on mean field theory using differential equations. Moreover, a resistance factor which can characterise the impact of individual's difference on the propagation dynamics in complex dynamical network is proposed by considering the influence of total number of connections and the continuous time to remain in contact. The effect of heterogeneity on the evolution process of propagation dynamics is explored by simulation. Extensive simulations are conducted to study the key influence parameters and the influence of them on the spreading dynamics, which are helpful to the understanding of epidemic spreading mechanism and the designing of effective control strategies.     

复杂网络中的弱化免疫策略分析

针对免疫策略在病毒免疫时会删除网络结构级联边从而出现削弱网络连通效率的问题,提出一种含权网络特定的病毒弱化免疫策略方法。该方法通过构建SI病毒传播模型,给出该模型的病毒感染密度演化公式。理论分析表明:病毒传播率与网络结构的异化性有密切关系,节点度的大小会影响病毒传播的效果,同时弱化免疫策略能衰减连边权值降低传播率,达到遏制病毒传播保留网络连通效率的目的。计算机仿真结果验证了理论模型的可行性和弱化免疫的合理性。最后,将弱化免疫策略应用到局域世界以及目标免疫策略中,更进一步说明了弱化免疫策略能有效控制病毒传播速度。     

Inferring Contagion Patterns in Social Contact Networks with Limited Infection Data

The spread of infectious disease is an inherently stochastic process. As such, real time control and prediction methods present a significant challenge. For diseases which spread through direct human interaction, (e.g., transferred from infected to susceptible individuals) the contagion process can be modeled on a social-contact network where individuals are represented as nodes, and contacts between individuals are represented as links. The model presented in this paper seeks to identify the infection pattern which depicts the current state of an ongoing outbreak. This is accomplished by inferring the most likely paths of infection through a contact network under the assumption of partially available infection data. The problem is formulated as a bi-linear integer program, and heuristic solution methods are developed based on sub-problems which can be solved much more efficiently. The heuristic performance is presented for a range of randomly generated networks and different levels of information. The model results, which include the most likely set of infection spreading contacts, can be used to provide insight into future epidemic outbreak patterns, and aid in the development of intervention strategies.