中文摘要：

将远程随机感染引入到经典的SIRS模型来研究复杂网络上疾病传播行为,考虑到感染节点在以一定概率把疾病感染到其邻接节点的同时,随机选取网络中一个不存在边连接的非邻接节点,并以一定的远程感染概率进行感染。针对小世界网络和无标度网络,分别采用重连概率相关和度相关的远程感染概率,利用平均场的方法求得改进的SIRS模型在这两种网络上的传播阈值以及稳态感染密度。数值仿真结果表明：对于小世界网络,有效传播率在一定范围内,重连概率对稳态感染密度和传播速度有明显的影响,超过这个范围,重连概率对稳态感染密度的影响可以忽略;而对于无标度网络,感染节点的度数对稳态感染密度和传播速度均有显著的影响。

英文摘要：

This paper proposed an epidemic model with the long-distance spreading.In this model,the infected nodes could propagate the virus to the non-adjacent nodes with a certain probability while infecting the adjacent nodes.It focused our attention on the SIRS model.For small-world networks and scale-free networks,integrated the long-distance infecting rate with rewiring probability-dependent and degree-dependent into the improved SIRS model respectively and got the accurately value of the epidemic threshold and the stationary infected density of the improved model in above two kinds of networks by the mean-field theory.Theoretical analysis and simulated results show that：for small-world networks,the rewiring probability has evident effect on stationary infected density and epidemic spreading velocity while the effective spreading rate changing in a range,however,the effect on the stationary infected density can be neglected once beyond the range,for scale-free networks,infected nodes＇degree plays an significant role in altering stationary infected density and epidemic spreading velocity.