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基于SEIR模型的復(fù)雜網(wǎng)絡(luò)上的動態(tài)隔離措施研究
信息技術(shù)與網(wǎng)絡(luò)安全
汪 意,,劉潤然,,賈春曉
(杭州師范大學(xué) 復(fù)雜科學(xué)研究中心,浙江 杭州311121)
摘要: 在尚未研發(fā)出有效疫苗前,對潛在感染者和易感者的隔離對于流行病控制而言具有十分重要的意義,。研究采用潛伏者具有傳染性的SEIR(Susceptible-Exposed-Infected-Recovered)模型,,并提出兩種動態(tài)隔離方法:一是在掌握網(wǎng)絡(luò)全局信息時,計算候選隔離對象一階鄰居的有效度,、介數(shù),、距離確診者節(jié)點(diǎn)的路徑長度之和,把三者乘積作為其權(quán)重,;二是在僅有節(jié)點(diǎn)局域信息時,,將候選隔離對象的有效邊數(shù)和相鄰感染節(jié)點(diǎn)數(shù)的同趨化之和作為其權(quán)重。仿真實(shí)驗(yàn)表明,,隔離容量為1%~10%時,,優(yōu)先隔離借助全局信息識別出的高權(quán)重節(jié)點(diǎn)可使90%以上節(jié)點(diǎn)免受感染,優(yōu)先隔離借助局域信息識別出的高權(quán)重節(jié)點(diǎn)可使70%以上節(jié)點(diǎn)免受感染,,從而達(dá)到抑制疾病傳播的目的,。
中圖分類號: TP301
文獻(xiàn)標(biāo)識碼: A
DOI: 10.19358/j.issn.2096-5133.2021.06.013
引用格式: 汪意,劉潤然,,賈春曉. 基于SEIR模型的復(fù)雜網(wǎng)絡(luò)上的動態(tài)隔離措施研究[J].信息技術(shù)與網(wǎng)絡(luò)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

為了研究和預(yù)測傳染病的傳播規(guī)律,、趨勢及范圍,,學(xué)者們基于疾病發(fā)展過程,將人群分成若干類:易感者(Susceptible),、潛伏者(Exposed),、感染者(Infected)、移除者(Recovered)[1],。根據(jù)這些人群分類并結(jié)合流行病的不同特征,,人們建立了SIR(Suscep-tible-Infected-Recovered)[2]、SEIR(Susceptible-Exposed-Infected-Recovered)[3]等模型來研究疾病傳播趨勢和動態(tài)過程,。在此基礎(chǔ)上,,人們發(fā)現(xiàn)感染者在傳播時的特征對疾病在人群中的擴(kuò)散過程有著重要影響,,如在SEIR模型中的超級傳播者[4]、無癥狀傳播者[5]以及具有傳染滯后性的傳播者[6],;此外,,感染者傳播能力的分布特性也對疾病傳播過程有較強(qiáng)的影響,如在SEIR模型中潛伏者傳染性服從Coxian分布[7],、指數(shù)及伽馬分布[8]等,;有的學(xué)者還研究了網(wǎng)絡(luò)對傳播模型的影響,,包含網(wǎng)絡(luò)規(guī)模的變化[9-10],,網(wǎng)絡(luò)度分布的異質(zhì)性,如ER網(wǎng)絡(luò)和無標(biāo)度網(wǎng)絡(luò)[11],。這些研究揭示了具有不同傳播特征的疾病在人群中的發(fā)展和演化規(guī)律[12],,對于傳染病的傳播和控制提供了十分有價值的認(rèn)識[13]。





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作者信息:

汪  意,,劉潤然,,賈春曉

(杭州師范大學(xué) 復(fù)雜科學(xué)研究中心,浙江 杭州311121)


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