一类SARS传染病模型的稳定性分析  

Analysis on the Stability for a Class of SARS Epidemic Model

作　　者：普昭年[1] 

机构地区：[1]河西学院数学系,甘肃张掖734000

出　　处：《兰州工业高等专科学校学报》2009年第3期42-46,共5页Journal of Lanzhou Higher Polytechnical College

基　　金：甘肃省教育厅科研项目(0709-03)

摘　　要：在现有模型的基础上,进一步将人群分为六个仓室并考虑易感人群的密度制约以及患病者类的死亡率与治愈率等因素,建立了描述SARS传染病的一个新的动力学模型.证明了该模型的疾病消除平衡点在一定条件下是全局渐近稳定的,而地方病平衡点不是渐近稳定的,同时得到了该模型在适当的条件下为永久持续生存的结果.By partitioning population into six compartmemts and considering the density constraint of sus- ceptible population and the cure and death rate of patients, a new and extended dynamic model for SARS epidemic is established based on the present model. It is shown that the infection--free equilibrium is globally asymptotically stable and the endemic equilibrium is not asymptotically stable under certain con- ditions. It comes to the conclusion that the epidemic system is permanent under appropriate conditions.

关 键 词：传染病模型 SARS传染病 平衡点 渐近稳定性 持续生存 

分 类 号：O175.13[理学—数学]