具有饱和发生率和媒体报道的双时滞传染病模型研究  

Analysis on A Two-delay Epidemic Model with Saturation Incidence Rate and Media Impact

作　　者：张瑜 胡志兴[1] Zhang Yu;Hu Zhixing(School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China)

机构地区：[1]北京科技大学数理学院,北京100083

出　　处：《宁夏大学学报（自然科学版）》2020年第3期220-229,共10页Journal of Ningxia University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11471034)。

摘　　要：研究了一类具有饱和发生率和媒体报道的双时滞传染病模型.两个时滞分别为易感者接受信息后进行自我保护和媒体报道信息的时间延迟.首先,计算得到基本再生数R0,讨论了无病平衡点E0和地方病平衡点E^*存在的条件,通过分析特征方程讨论了平衡点的局部渐近稳定性.然后,研究了在不同情形下,两个时滞对地方病平衡点E^*的稳定性所产生的影响,分析了系统在E^*处Hopf分支的存在性.最后,通过MATLAB数值模拟对理论结果进行了验证.The two-delay epidemic model with saturation incidence rate and media impact is studied.The two time lags are the time delays for self-protection and media coverage information after receiving the information.First,the basic reproductive number is calculated,and the existence conditions of the disease-free equilibrium E0 and the endemic disease equilibrium E^*are discussed.Through the analysis of the characteristic equation,the locally asymptotic stability of the disease-free and endemic equilibrium is considered.Then,the stability of the two-time delay to the endemic equilibrium E^*is studied under different conditions.And the existence of Hopf bifurcations at equilibrium E^*in the system is analyzed.Finally,the theoretical results are verified by MATLAB numerical simulation.

关 键 词：基本再生数 无病平衡点 地方病平衡点 稳定性 HOPF分支 

分 类 号：O175[理学—数学]