一种小世界网络上L-SIRS类疾病传播模型

Analyze of L-SIRS Model in the Small-world Network

提出了一种感染节点可能随机感染与其不存在边连接的陌生节点的L-SIRS模型,利用平均场理论对疾病传播行为进行分析,求出该类型疾病传播的临界阈值,并与不具有远程感染的传统SIRS类疾病传播模型进行比较,该文所研究的模型具有更小的临界值。利用计算机对其进行数值模拟及仿真,结果表明,远程感染的概率对疾病的传播具有重要的影响,随着感染节点随机感染陌生节点概率的增大,网络的传播阈值会逐渐减小直至消失。

In the model with the long-distance in the small-world network, The infected nodes not only infect their neigh- bors but also infect other nodes with the certain probability. Base on this , the L-SIRS model which the infected nodes may con- nect with the nodes which is not their neighbors, With the mean-field theory analyzes the spread of the disease, it is easy to get the critical threshold of immunization. Then compare it with the traditional SIRS model, and simulate it with computer, the re- sults show that the probability of long-distance spread is very important to the spread of the disease, with the increasing of the probability of the infected nodes infect their strangers, the critical threshold will decrease until die away.