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基于SEIR模型的复杂网络上的动态隔离措施研究
信息技术与网络安全
汪 意,刘润然,贾春晓
(杭州师范大学 复杂科学研究中心,浙江 杭州311121)
摘要:在尚未研发出有效疫苗前,对潜在感染者和易感者的隔离对于流行病控制而言具有十分重要的意义。研究采用潜伏者具有传染性的SEIR(Susceptible-Exposed-Infected-Recovered)模型,并提出两种动态隔离方法:一是在掌握网络全局信息时,计算候选隔离对象一阶邻居的有效度、介数、距离确诊者节点的路径长度之和,把三者乘积作为其权重;二是在仅有节点局域信息时,将候选隔离对象的有效边数和相邻感染节点数的同趋化之和作为其权重。仿真实验表明,隔离容量为1%~10%时,优先隔离借助全局信息识别出的高权重节点可使90%以上节点免受感染,优先隔离借助局域信息识别出的高权重节点可使70%以上节点免受感染,从而达到抑制疾病传播的目的。
中图分类号:TP301
文献标识码:A
DOI:10.19358/j.issn.2096-5133.2021.06.013
引用格式: 汪意,刘润然,贾春晓. 基于SEIR模型的复杂网络上的动态隔离措施研究[J].信息技术与网络安全,2021,40(6):75-82.
Dynamic isolation measures on complex networks based on SEIR model
Wang Yi,Liu Runran,Jia Chunxiao
(Research Center for Complexity Sciences,Hangzhou Normal University,Hangzhou 311121,China)
Abstract:Before the vaccine is developed, the isolation of potential infected and susceptible is of great importance for epidemiological control. By using the Susceptible-Exposed-Infected-Recovered(SEIR) model with infectious exposed individuals, this paper has proposed two dynamic isolation measures to suppress the epidemic, where each node is assigned a weight according to the local or the global information of the network and the nodes with the highest weights are considered as the isolation priorities. The first one considers the situation where the global information of the network is available, and the sum of the effective degrees of the first order neighbors, the sum of the effective betweenness of the first order neighbors, and the sum of effective path lengths to all infected nodes are taking into account as the weight of an isolation candidate. The second one is for the condition if there is only local information of the infected nodes, and the effective degrees and the numbers of adjacent infected nodes are taking into account as the weights of the isolation candidates. The simulation results show that,when the isolation capacity is set to 1% to 10% of the total number of nodes, the first isolation measure can prevent more than 90% of nodes from infection when the global information of the network is available, and the second one can prevent more than 70% of nodes from infection when the local information of the infected nodes is available, i.e., the spreading of disease can be suppressed effectively.
Key words :complex networks;the spread of disease;dynamic isolation measures;SEIR model

0 引言

为了研究和预测传染病的传播规律、趋势及范围,学者们基于疾病发展过程,将人群分成若干类:易感者(Susceptible)、潜伏者(Exposed)、感染者(Infected)、移除者(Recovered)[1]。根据这些人群分类并结合流行病的不同特征,人们建立了SIR(Suscep-tible-Infected-Recovered)[2]、SEIR(Susceptible-Exposed-Infected-Recovered)[3]等模型来研究疾病传播趋势和动态过程。在此基础上,人们发现感染者在传播时的特征对疾病在人群中的扩散过程有着重要影响,如在SEIR模型中的超级传播者[4]、无症状传播者[5]以及具有传染滞后性的传播者[6];此外,感染者传播能力的分布特性也对疾病传播过程有较强的影响,如在SEIR模型中潜伏者传染性服从Coxian分布[7]、指数及伽马分布[8]等;有的学者还研究了网络对传播模型的影响,包含网络规模的变化[9-10],网络度分布的异质性,如ER网络和无标度网络[11]。这些研究揭示了具有不同传播特征的疾病在人群中的发展和演化规律[12],对于传染病的传播和控制提供了十分有价值的认识[13]。





本文详细内容请下载:http://www.chinaaet.com/resource/share/2000003604




作者信息:

汪 意,刘润然,贾春晓

(杭州师范大学 复杂科学研究中心,浙江 杭州311121)


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