传染病在小世界网络中传播的相变  

The Transition of Epidemic Spreading in Small World

作　　者：孟锰[1] 李晟[1] 马红孺[1] 

机构地区：[1]上海交通大学物理系,上海200240

出　　处：《上海交通大学学报》2006年第5期869-872,共4页Journal of Shanghai Jiaotong University

基　　金：国家自然科学基金资助项目(10105007;10334020;90103035)

摘　　要：为了研究传染病在小世界网络中传播的动力学特性,数值模拟了小世界网络中传染病的传播行为,观察到了相变现象.使用Watts等提出的小世界网络模型以及传统的SIR模型作为传染病模型,分别模拟了在固定传染概率Pi、改变构建小世界网络的无序参数Ps以及固定无序参数Ps、改变传染概率Pi两种情况下的传染病动力学行为.研究了以Pi和Ps为变量的传染病在小世界网络中传播的三维相变行为,并讨论了传染病传播过程中出现的这种相变行为与传染速度之间的关系.结果表明,在上述两种情况下,传染病的传播动力学行为都会有明显的相变发生,可以观测到在传染病稳定期传染人数从收敛态向振荡态的相变.In order to study the dynamics of epidemic spreading in a small world network, an epidemic spreading was simulated and phase transitions were observed. By making use of the small world network model proposed by Watts and Strogatz and the traditional SIR model as the epidemic model, the behavior of an infection dynamics was simulated when infection probability was fixed and disorder parameter was varied, and contrariwise. The three-dimensional transitional behavior of epidemic spreading in small world network was also studied with infection probability and disorder parameter as variables. Transitions from convergent states to oscillation states are found respectively when varying the disorder parameter and the infection probability. The relation between the transitional behavior during the epidemic spreading process and the epidemic spreading speed was discussed.

关 键 词：传染病 小世界网络 相变 传播 

分 类 号：O414.3[理学—理论物理]