带有饱和治疗函数的SIS模型的几类分支分析  

Several bifurcation analyses of the SIS model with saturated treatment functions

作　　者：张加男 张伟鹏 ZHANG Jia-nan;ZHANG Wei-peng(School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China;Department of Mathematics,Jinan University,Guangzhou 510632,China)

机构地区：[1]东北师范大学数学与统计学院,吉林长春130024 [2]暨南大学数学系,广东广州510632

出　　处：《东北师大学报（自然科学版）》2024年第2期17-26,共10页Journal of Northeast Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11971096);吉林省自然科学基金资助项目(YDZJ202101ZYTS154).

摘　　要：研究了具有标准发生率和饱和治疗函数的SIS传染病模型的几类分支.该模型中使用的饱和治疗函数是一个连续且可微的函数,用以说明当治愈率较低以及感染人数较多时延迟治疗所产生的影响.讨论了系统无病平衡点和地方病平衡点的存在性,证明了该系统存在倒向分支,分析了系统平衡点的局部和全局稳定性,讨论了该系统Hopf分支和Bogdanov-Takens分支的存在情况,得出了相应结论并且给出了系统的分支相图,以及针对研究得出的数学结果提出了一些合理化建议.Several bifurcations of the SIS epidemic model with standard incidence and saturation treatment functions are studied.The saturation treatment function used in this model is a continuous and differentiable function that accounts for the effect of delayed treatment when the cure rate is low and the number of infections is large.The existence of disease-free and endemic equilibrium is discussed and it is shown that the system has a backward bifurcation.The local and global stability of the equilibrium of the system are analysed separately.The existence of Hopf and Bogdanov-Takens bifurcations is shown.The corresponding conclusions are drawn,the bifurcation phase diagram of the system is given,and some reasonable suggestions are made for the mathematical results obtained from the study.

关 键 词：传染病模型 饱和治疗 稳定性 分支 

分 类 号：O175[理学—数学]