具有媒体效应时滞的SEIRS-M传染病模型的动力学分析

Dynamic Analysis of SEIRS-M Epidemic Mod-el with Media Effect Delay

摘要: 为了研究在突发疫情中媒体信息对病毒传播的影响，本文建立了包含正负面信息影响的SEIRS-M模型，并且在模型中加入了一个媒体效应时滞。理论部分证明了模型解的非负性，得到了基本再生数和平衡点的表达式，分析了模型的稳定性以及Hopf分叉的存在性。最后通过数值模拟验证了理论结果，参数敏感性分析表明时滞越小疫情传播规模就越小，不同的信息贯彻率对疫情传播速度也有很大影响。因此，媒体应该在及时发布疫情相关信息的同时保障信息的质量，为群众提供有价值的信息从而增强人们的疾病预防意识，减少疫情传播规模。

Abstract: In order to study the influence of media information on virus transmission in an outbreak, a SEIRS- M model containing positive and negative information is established in this paper, and a media ef-fect delay is added to the model. In the theoretical part, the non-negative solution of the model is proved, the expressions of the basic regeneration number and the equilibrium point are obtained, and the stability of the model and the existence of Hopf bifurcation are analyzed. Finally, the theo-retical results were verified by numerical simulation. The parameter sensitivity analysis showed that the smaller the time delay, the smaller the epidemic transmission scale, and different infor-mation implementation rates also had a great impact on the epidemic transmission speed. There-fore, the media should release epidemy-related information in a timely manner and ensure the quality of information, so as to provide valuable information for the masses, so as to enhance peo-ple’s awareness of disease prevention and reduce the scale of epidemic transmission.