摘要
推广了一类具有双线性发生率函数和饱和治疗函数的SIR传染病模型,研究了其地方性平衡点的存在性、稳定性及后向分支现象。研究表明:当基本再生数小于1时,若饱和治疗率较小,则系统发生后向分支。同时证明了系统至多存在4个平衡点。
This paper generalizes an SIR epidemic model with bilinear incidence rate function and saturation therapy function.The existence,stability and backward bifurcation of the local equilibrium point were studied.The results showed that when the basic reproduction number is less than 1 and the saturation treatment rate is small,backward bifurcation will happen to the system.Meanwhile,the results proved that four equilibrium points exist at most.
出处
《浙江理工大学学报（自然科学版）》
2017年第6期874-880,共7页
Journal of Zhejiang Sci-Tech University(Natural Sciences)
基金
国家自然科学基金项目(11101370)
浙江理工大学"521"人才培养计划(11430132521304)
关键词
治疗函数
SIR传染病模型
后向分支
基本再生数
therapy function
SIRepidemic model
backward bifurcation
the basic reproduction number
