具有饱和治疗函数与密度制约的SIS传染病模型的后向分支  

Backward Bifurcation of a SiS Epidemic Model with Density Dependent Birth and Death Rates and Saturated Treatment Function

作　　者：唐晓明[1] 薛亚奎[1] 

机构地区：[1]中北大学数学系,山西太原030051

出　　处：《数学的实践与认识》2010年第24期241-246,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10471040);山西省自然科学基金(2009011005-1)

摘　　要：讨论了一个具有饱和治疗函数以及出生率和死亡率均具有密度制约的SIS传染病模型,其中总人口的变化满足Logistic方程,治疗项采用一个连续可微的函数,描述在医疗条件有限的情况下患病者的治疗被耽误的影响.研究发现当患病者的治疗被耽误的影响较强时,模型将出现后向分支,因此基本再生数R_0=1不再是疾病是否消亡的阈值.另外还得到无病平衡点和地方平衡点全局稳定的充分条件.In this paper,an epidemic model with saturated treatment function and density dependent birth and death rates is studied.Here,the total number of the population is governed by Logistic equation and the treatment function adopts a continuous and differentiable function which can describe the effect of delayed treatment when the medical condition is limited.However,it is shown that a backward bifurcation will take place when this delayed effect for treatment is strong.Therefore,the basic reproduction number below the unity is not enough to eradicate the disease.Some sufficient conditions for the disease-free equilibrium and the endemic equilibrium being globally asymptotically stable are also obtained.

关 键 词：饱和治疗函数 后向分支 全局稳定 双稳定 

分 类 号：O175[理学—数学]