重叠网络上疾病与意识传播模型:非同步的影响
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摘要
针对Granell等人所建立的重叠网络上疾病与信息传播模型中信息更新早于疾病传播的非同步现象,研究了疾病传播先于信息更新的另一种非同步传播模型,发现这种非同步次序在传染率较大时对各状态节点,特别是对易感者的数量影响较大,而对离散时间模型的疾病暴发阈值以及连续时间模型的稳定性结论均无影响.
In this paper,a susceptible-infected-susceptible(SIS) epidemic model coupled with an unaware-aware-unaware(UAU) information diffusion model on multiplex networks was studied.In contrast with the scenario considered by Granell where the awareness information is updated prior to disease spread,the other scenario where the disease spread is prior to information transmission is focused on.It is found that the order of asynchronous update of disease and information has an important impact on the evolution of the number of nodes of various states especially the susceptible nodes(either aware or unaware) as the transmission rate is relatively large.However,the order of asynchronous updating has no effect on the epidemic threshold of the discrete-time model as well as the stability conclusion of the continuous-time model.
In this paper,a susceptible-infected-susceptible(SIS) epidemic model coupled with an unaware-aware-unaware(UAU) information diffusion model on multiplex networks was studied.In contrast with the scenario considered by Granell where the awareness information is updated prior to disease spread,the other scenario where the disease spread is prior to information transmission is focused on.It is found that the order of asynchronous update of disease and information has an important impact on the evolution of the number of nodes of various states especially the susceptible nodes(either aware or unaware) as the transmission rate is relatively large.However,the order of asynchronous updating has no effect on the epidemic threshold of the discrete-time model as well as the stability conclusion of the continuous-time model.
引文
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[5] ZHANG X G,SHAN C H,JIN Z,ZHU H P.Complex dynamics of epidemic models on adaptive networks[J].Journal of Differential Equations,2019,266(1):803-832.
[6] 王璐,张娟.基于百度指数的H7N9传播动力学模型研究[J].云南师范大学学报:自然科学版,2018,38(2):49-55.
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[9] GRANELL C,GOMEZ S,ARENAS A.Competing spreading processes on multiplex networks:awareness and epidemics[J].Physical Review E,2014,90(1):012 808.
[10] HUANG Y J,JUANG J,LIANG Y H,et al.Global stability for epidemic models on multiplex networks[J].Journal of Mathematical Biology,2018,76(6):1 339-1 356.
[2] NEWMAN M.Networks:an introduction [M].New York:Oxford University Press,2010.
[3] 靳祯,孙桂全,刘茂省.网络传染病动力学建模与分析[M].北京:科学出版社,2014.
[4] 张泽琼,彭小龙.个体具有异质易感性的动态网络SIS传染病模型[J].云南师范大学学报:自然科学版,2017,37(6):26-31.
[5] ZHANG X G,SHAN C H,JIN Z,ZHU H P.Complex dynamics of epidemic models on adaptive networks[J].Journal of Differential Equations,2019,266(1):803-832.
[6] 王璐,张娟.基于百度指数的H7N9传播动力学模型研究[J].云南师范大学学报:自然科学版,2018,38(2):49-55.
[7] LIU G R,LIU Z M,JIN Z.Dynamics analysis of epidemic and information spreading in overlay networks[J].Journal of Theoretical Biology,2018,444:28-37.
[8] GRANELL C,GOMEZ S,ARENAS A.Dynamical interplay between awareness and epidemic spreading in multiplex networks[J].Physical Review Letters,2013,111(12):128 701.
[9] GRANELL C,GOMEZ S,ARENAS A.Competing spreading processes on multiplex networks:awareness and epidemics[J].Physical Review E,2014,90(1):012 808.
[10] HUANG Y J,JUANG J,LIANG Y H,et al.Global stability for epidemic models on multiplex networks[J].Journal of Mathematical Biology,2018,76(6):1 339-1 356.