一类具有垂直传染率的SIS模型的稳定性分析  

Stability Analysis of a Class of Sis Model with Vertical Infection Rate

作　　者：豆中丽[1] 王锐[2] DOU Zhong-li;WANG Rui(Rongzhi College of Chongqing Technology and Business University,Chongqing 400055,China;School of Mathematics Science,Chongqing University,Chongqing 401331,China)

机构地区：[1]重庆工商大学融智学院,重庆400055 [2]重庆大学社会科学学院,重庆401331

出　　处：《数学的实践与认识》2020年第1期324-328,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11304403);重庆市教委科技项目(KJQN201902105).

摘　　要：研究了一类具有垂直传染率的SIS模型,首先计算出该模型的基本再生数和平衡点,其次分析了该模型在无病平衡点处的局部渐近稳定性和全局稳定性;然后构造Lyapunov函数证明了地方病平衡点的全局稳定性;最后得到当基本再生数小于1时,传染病会逐渐消失;基本再生数大于1时,传染病将会流行并最终形成一种地方病.This article studies an SIS model with vertical infection rate.It firstly calculates the basic reproduction number and equilibrium of the model,analyzes local asymptotic stability and global stability of the model at the disease-free equilibrium,builds Lyapunov function to prove global stability of the endemic equilibrium;and finally concludes that the infectious disease may disappear when the basic reproduction number is less than 1;while the infectious disease may be epidemic and finally develop into an endemic disease when the basic reproduction number is greater than 1.

关 键 词：基本再生数 局部渐近稳定性 全局稳定性 

分 类 号：R51[医药卫生—内科学] O175[医药卫生—临床医学]