考虑媒体影响的一类时滞传染病模型的分岔周期解  

The bifurcating periodic solutions of a delayed epidemic model considering media influence

作　　者：张子振[1] 张怡雪 张伟诗 宋志强[2] ZHANG Zizhen;ZHANG Yixue;ZHANG Weishi;SONG Zhiqiang(School of Management Science and Engineering,Anhui University of Finance and Economics,Bengbu 233030,China;College of Engineering,Hulunbuir University,Hulunbuir 021008,China)

机构地区：[1]安徽财经大学管理科学与工程学院,安徽蚌埠233030 [2]呼伦贝尔学院工学院,内蒙古呼伦贝尔021008

出　　处：《延边大学学报（自然科学版）》2023年第4期333-340,共8页Journal of Yanbian University（Natural Science Edition）

基　　金：国家自然科学基金(12061033)。

摘　　要：为了研究媒体报道和时滞对传染病的影响,提出了一类考虑媒体影响的时滞传染病模型.首先,以媒体对疾病进行宣传报道的滞后时间为分岔参数,利用特征值法讨论了模型的局部渐近稳定性和Hopf分岔的存在性.其次,利用中心流形法研究了模型分岔周期解的稳定性.最后,通过数值模拟验证了所得结果的正确性.In order to explore the impact of media coverage and time delay on infectious diseases,a delayed epidemic model considering influence of media was proposed.Firstly,the local asymptotic stability and the exhibition of Hopf bifurcation were discussed by using the eigenvalue method and regarding the time delay of the media coverage of infectious disease as bifurcation parameter.Secondly,the stability of the bifurcating periodic solutions were studied with the aid of the central manifold method.Finally,the correctness of the obtained results were verified by computer numerical simulations.

关 键 词：媒体影响 时滞 传染病模型 局部渐近稳定性 HOPF分岔 周期解 

分 类 号：O175.12[理学—数学]