融入迁移限制与双层集合种群网络的传染病模型  

An epidemic model integrated with migration restriction and bilayer metapopulation network

作　　者：顾秋阳 琚春华 张双竹 GU Qiu-yang;JU Chun-hua;ZHANG Shuang-zhu(School of Management,Zhejiang University of Technology,Hangzhou Zhejiang 310023,China;China Institute for Small and Medium Enterprises,Zhejiang University of Technology,Hangzhou Zhejiang 310023,China;School of Management Science&Engineering,Zhejiang Gongshang University,Hangzhou Zhejiang 310018,China)

机构地区：[1]浙江工业大学管理学院,浙江杭州310023 [2]浙江工业大学中国中小企业研究院,浙江杭州310023 [3]浙江工商大学管理工程与电子商务学院,浙江杭州310018

出　　处：《控制理论与应用》2021年第1期121-129,共9页Control Theory & Applications

基　　金：国家自然科学基金项目(71571162);国家社科基金应急管理体系建设研究专项项目(20VYJ073);浙江省社科规划重点课题项目(20YSXK02ZD,20NDJC10Z)资助。

摘　　要：本文在斑块环境下基于易感–感染–易感模型(SIS模型)研究了感染者迁移限制对传染病传播的影响,其中迁移限制用双层网络进行表示,并提出了双层集合种群动态网络.子种群(即斑块)用双层网络上的节点表示,双层网络上的链接分别代表易感节点斑块和感染节点斑块间的迁移路径,易感染和感染节点分别通过双层网络上的链接随机游走.并提出了两种反应扩散方程分别作为易感染与感染节点的微分方程,分别计算其数值解,以评估每个斑块(节点)的感染风险.研究表明:在双层网络中,迁移限制会降低感染节点密度,将感染节点限制在中心节点(度值最高的子种群)中.感染节点密度高度依赖于双层网络结构.Under the patch environment,this paper conducts research on the effect of migration limitation of the infected person on the transmission of infectious disease based on the susceptible-infected-susceptible(SIS)model,where the migration limitation is presented by multilayer network.In addition,the multilayer integrated population dynamic network is put forward.The sub-population(patch)is represented by the node on the multilayer network,and the links on the multilayer network represent the migration path between the susceptible nodes patch and the infected nodes patch.The susceptible nodes and infected nodes walk randomly on the links of the multilayer network.Also,two reaction diffusion equations are raised as the differential equation of the susceptible nodes and the infected nodes.Their numerical solutions are calculated,for assessing the infection risk of each patch(node).The research indicates that in a multilayer network,the migration limitation will lower then density of nodes and contain the infected nodes within the central nodes(sub-population with the highest value).The density of infected nodes highly relies on the multilayer network structure.

关 键 词：传染病模型 迁移限制 集合种群 SIS模型 多层网络图 

分 类 号：O157.5[理学—数学] R51[理学—基础数学]