一类具有垂直传染和预防接种的传染病模型的稳定性  

Global Stability of an Epidemic Model with Vertical Transmission and Vaccination

作　　者：王俊峰 薛亚奎[1] 

机构地区：[1]中北大学数学系,山西太原030051

出　　处：《生物数学学报》2011年第1期169-174,共6页Journal of Biomathematics

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

摘　　要：考虑了垂直传染和预防接种因素对传染病流行影响的SEIRS模型,主要研究了系统的平衡点及其稳定性,得出当预防接种水平超过某一个阈值时疾病可以根除,若接种水平低于阈值时疾病将流行.In this paper,the SEIRS epidemic model with vertical transmission and vaccination is studied.It is proved that the global dynamics are completely determined by the basic reproduction number R_0.IfR_01,the disease-free equilibrium is global asymptotically stable and the disease always dies out.If R_01,a unique endemic equilibrium exists and is globally stable in the interior of the feasible region,and the disease persists at the endemic equilibrium state if it initially exits.At the same time,using global stability analysis of the model,it is shown that the disease can be eradicated from the population if the vaccination coverage level exceeds a certain threshold value.It is also shown that the disease will persist within the population if the coverage level is below this threshold.

关 键 词：垂直传染 预防接种 全局稳定性 阈值 

分 类 号：O175.13[理学—数学]