复杂网络上同时考虑感染延迟和非均匀传播的SIR模型  

A novel SIR model with infection delay and nonuniform transmission in complex networks

作　　者：赵敬[1,2] 夏承遗[1,2] 孙世温[1,2] 王莉[1,2] 

机构地区：[1]天津理工大学天津市智能计算与软件新技术重点实验室,天津300384 [2]天津理工大学省部共建教育部计算机视觉与系统重点实验室,天津300384

出　　处：《智能系统学报》2013年第2期128-134,共7页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金资助项目(60904063;61203138);天津市应用基础及前沿技术研究计划资助项目(11JCYBJC06600);天津市高等学校科技发展基金资助项目(20090813)

摘　　要：为了能更有效地分析和理解传染性疾病的传播,提出了一个新颖的SIR模型,在这个传播模型里同时考虑了影响疾病传播行为的2个因素:感染延迟和非均匀传播.基于平均场理论和大量的数值仿真,给出了疾病传播临界值的解析公式,并发现感染延迟和非均匀传播对临界值影响截然不同:感染延迟能够在很大程度上减小传播阈值,促进疾病在人群中的传播;而非均匀传播能够增大传播临界值,阻碍疾病的大规模传播.当前的研究结果有助于深入理解真实复杂系统中的疾病传播行为,充分考虑感染延迟、传播机制和实际人群的拓扑结构等因素在疾病传播中的作用,从而为制定有效的传染病预防和控制措施提供理论依据.In order to analyze and understand the spreading behavior of infectious diseases, the authors propose to examine susceptible-infected-removed （SIR） model. The researchers simultaneously introduce into the epidemic model the two factors： influencing disease spreading behavior, and infection delay and nonuniform transmission, utilizing the SIR model. Based on the mean-field approximation and large-scale numerical simulations, the analytical results of critical thresholds of disease spreading were derived, along with the infection delay and the nonuniform transmission having a distinct impact on the critical threshold. The infection delay can greatly decrease the critical threshold and facilitate the spread of epidemics, while the nonuniform transmission can augment the critical threshold and hinder the epidemic spreading in complex networks. Current results are conducive to further understand the epidemic spreading inside the complex real systems, as well as to fully consider the roles of infection delay, transmission factors and topological structure of population in the spreading of diseases. The results also provide a number of theoretical evidence to design more effective epidemic prevention and containment measures.

关 键 词：感染延迟 非均匀传播 临界值 复杂网络 SIR模型 

分 类 号：O157.5[理学—数学]