具有饱和传染率、免疫接种和垂直传染的SIR传染病模型的稳定性  

Stability of a SIR Epidemic Model with Saturating Infect Rate,Vaccination and Vertical Transmission

作　　者：朱春娟[1] 原三领[2] 

机构地区：[1]韶关学院数学与统计学院,广东韶关512005 [2]上海理工大学理学院,上海200093

出　　处：《数学的实践与认识》2015年第13期286-292,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11271260)

摘　　要：研究了一类具有饱和传染率、免疫接种和垂直传染的SIR传染病模型,确定了疾病的基本再生数,得出当疾病的基本再生数小于1时,无病平衡点是全局指数渐近稳定的,当疾病基本再生数大于1时.地方病平衡点是全局渐近稳定的,讨论了其生物意义.In this paper, the SIR epidemic model with saturating infect rate, vaccination and vertical transmission is studied; the basic reproduction number for the existence of infective disease is established. If , the disease-free equilibrium is global exponential asymptotically stable. If , a unique endemic equilibrium exists and is globally stable iu the interior of the feasible region .We discuss the biological significance at the end.

关 键 词：饱和传染率 免疫接种 垂直传染 基本再生数 稳定性 

分 类 号：O175[理学—数学]