复杂网络上带传播媒介SIS模型的全局稳定性

Global stability of SIS epidemic model with infective medium on complex networks

研究非齐次复杂网络上带传播媒介的易感者-感染者-易感者(SIS)模型的全局稳定性.首先根据经典的SIS模型建立带有传播媒介的SIS模型,接着求出该模型的流行病阈值,然后证明当感染率大于该流行病阈值时,只要模型存在初始感染节点,模型就总存在惟一的正不动点,从而证明了该模型的传染过程的全局稳定性.

This paper studies the global stability of the SIS epidemic model with infective medium on complex heterogeneous networks.Firstly,the dynamical mean-field reaction rate equations for the SIS model with infective medium on complex heterogeneous networks are established based on the well-known classical SIS model.Secondly,the epidemic threshold for the model is figured out.Finally,it is proved that if infection rate is above the epidemic threshold,the infection spreads and approaches the unique positive steady state of the model as long as there exist initial infected nodes on the complex heterogeneous networks,in other words,the infection process is globally stable.