终身免疫和疫苗接种对梅毒清除的影响  

Effects of Lifelong Immunization and Vaccination on Syphilis Clearance

作　　者：石月莲[1] 赵东霞[2] SHI Yue-lian;ZHAO Dong-xia(School of Mathematics,Jinzhong University,Jinzhong 030619,China;School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]晋中学院数学学院,山西晋中030619 [2]中北大学理学院,山西太原030051

出　　处：《数学的实践与认识》2020年第21期59-64,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(61603351);晋中学院博士基金资助项目(bsjj2016202)。

摘　　要：在假设梅毒疫苗已经成功研制而且获得的免疫是终身免疫的情况下建立数学模型,用下一代矩阵方法求得基本再生数,通过构造Lyapunov函数证明了无病平衡点以及地方病平衡点的全局渐进稳定性.In this paper,a mathematical model is established on the assumption that syphilis vaccine has been successfully developed and the immunization obtained is permanent immunization,and the basic regeneration number is obtained by the next generation matrix method,the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium is proved by constructing Lyapunov function.

关 键 词：梅毒 疫苗 终身免疫 全局稳定性 

分 类 号：R186[医药卫生—流行病学]