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

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.