复杂网络上带有非线性感染率的SIRS模型分析

针对实际人群的接触情况,在已有SIRS模型的基础上提出一种带有非线性传染率的SIRS改进模型.利用平均场理论及李亚普诺夫稳定性分析方法,分析得到该传播模型的传播阈值以及拓扑结构与传播阈值的相关性;当传播过程中系统满足阈值条件时,疾病最终消失;用假设的方法证明了系统不满足阈值条件时地方病平衡点的存在并通过推导得出满足地方病平衡点稳定的限制条件.对比仿真试验结果验证上述的理论结果成立,并且表明带有非线性感染率的SIRS模型比已有的SIRS模型更加逼近现实的疾病传播过程.

Analysis of a SIRS Model with Nonlinear Incidence Rate on Complex Networks

An improved SIRS(susceptible-infected-removed-susceptible) model with nonlinear incidence rate was proposed according to the actual exposure of people.The conclusion that the existence of the threshold and how the threshold of this model is concerned with the topology of networks was deduced by the mean-field theory and the approach in Lyapunov stability theory;The diseases will extinguish when the system satisfied the threshold condition;The existence of threshold is proved by the hypothesis theory and the system must reach the trivial steady state under some conditions,which was another conclusion.The numerical simulation results indicated that the theoretical conclusions are valid,and the SIRS model with nonlinear incidence rate approaches the actual epidemic more accurately.