一类具logistic出生率的SIS传染病模型的全局稳定性  

The dynamical analysis of an SIS epidemic model with the logistic birth rate

作　　者：杜鹏[1] 段彩霞[1] 廖新元[1] 

机构地区：[1]南华大学数理学院,湖南衡阳421001

出　　处：《陕西科技大学学报（自然科学版）》2014年第4期167-171,共5页Journal of Shaanxi University of Science & Technology

基　　金：国家自然科学基金项目(10771139);南华大学研究生科研创新项目(2013XCX10)

摘　　要：许多传染病流行时间远超过物种的生命周期,基于此我们建立和研究了一类具logistic出生率的SIS传染病模型.利用微分方程稳定性理论,研究了平衡点的存在性及其稳定性的条件,并用Dulac函数证明了闭轨线和奇异闭轨线的不存在性,证明了各平衡点稳定的条件.The transmission time of many infectious diseases is longer than the lifetime of species. In this paper, we consider an SIS epidemic model with the logistic birth rate. By using the qualitative theory of ordinary differential equations and Dulac functions, we obtain the existence of equilibrium and stability conditions and the nonexistence of closed trajectory and singular closed trajectory. In addition,we prove the conditional factors for the stability of equilibrium.

关 键 词：传染病模型 LOGISTIC DULAC函数 动力性 

分 类 号：O193[理学—数学]