中文摘要：

在无权网络标准SIRS模型的基础上,提出了具有加权传播率和非线性传染能力的SIRS模型和带有直接免疫的SIRS模型.利用平均场理论,分析得到在加权无标度网络中,这2个模型都可以通过调整相应的参数得到非零的传播阈值,其中SIRS模型的传播阈值主要与网络的拓扑结构和节点的传染能力有关;而带有直接免疫的SIRS模型的传播阈值除与上述2点有关外,还与直接免疫速率和免疫丧失速率有关,且直接免疫可以增大疾病传播的阈值,降低传播范围,从而可以较好的控制疾病传播.

英文摘要：

In the paper,SIRS epidemic model and SIRS epidemic model with direct immunization,which have weighted transmission rate and the nonlinear infectivity,are proposed based on unweighted networks standard SIRS model.By using the mean-field theory,the non-zero epidemic threshold of the two models can be obtained by adjusting the corresponding parameters in the weighted scale-free networks.The propagation threshold of SIRS model is mainly related to the topology of the network and the transmission ability of the node.The propagation threshold of SIRS model with direct immunization is not only related to the above two points but also related to direct immunization rate and immune loss rate.Direct immunization can increase the threshold of disease transmission and reduce transmission range,which can be used to control the epidemic of disease.