基于个体异质传染率及状态转移的SIR模型分析  

Analysis of SIR Model Based on Individual Heterogeneous Infectivity and State Transition

作　　者：瞿倩倩 韩华[1] QU Qian-qian;HAN Hua(School of Science,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学理学院

出　　处：《计算机科学》2019年第12期327-333,共7页Computer Science

基　　金：国家自然科学基金项目(71140015,71372135);国家自然科学基金青年科学基金项目(61303028);中央高校基本科研业务费专项基金项目(2015-zy-115)资助

摘　　要：针对染病个体具有不同传染率的现象,基于复杂网络中的基本SIR传染病模型,提出了一种具有两种传染率且存在转移概率的传染病模型。根据地方病平衡点的存在性,求出了基本再生数R 0。在此模型上,分析了随机免疫和目标免疫两种常见免疫策略。通过仿真模拟发现:在同等条件下,R 0>1时,疾病在异质网络中比在同质网络中传播速度更快,范围更广;R 0<1时,网络结构对疾病传播的影响不大。进一步研究得出:网络中初始染病节点度的越大,疾病传播速度越快且感染峰值越大;初始染病节点的接近度中心性越大,疾病传播速度越快且范围更广;点集聚系数对传播过程的影响不大;基本再生数R 0随转移概率的增大而减小,增大转移概率能有效减少疾病的传播;在平均免疫率相同的情况下,目标免疫比随机免疫更有效。To explore the phenomenon of infected individuals with different infectious rates,based on the basic SIR epidemic model in complex networks,this paper proposed an epidemic model with two types of infections and probability of metastasis.Based on the existence of the equilibrium point of endemic diseases,it obtaines the basic reproduction number R 0.It analyzes two common immunization strategies:random immunization and target immunization.Simulation experiments show that under the same conditions,diseases spread faster and wider in heterogeneous networks than in homogeneous networks when R 0>1,and network structure has little influence on the spread of diseases when R 0<1.Further researches show that the greater the degree of initial infection nodes in the network,the faster the disease transmission speed and the greater the peak value;the greater the centrality of the proximity of the initial infected nodes,the faster and wider the disease spreads;the point aggregation coefficient has little effect on the transmission process;the basic reproduction number decreases with the increase of the transfer probability,and the increase of the transfer probability can effectively reduce the spread of disease;in the case of the same average immunity rate,the target immunity is more effective than random immunity.

关 键 词：复杂网络 异质传染率 状态转移 基本再生数 免疫策略 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]