数学杂志2016，Vol.36Issue(6)：1283-1290,8.
具有垂直传染和接触传染的传染病模型的稳定性研究
ON THE STABILITY PROPERTY OF A EPIDEMIC MODEL WITH VERTICAL TRANSMISSION AND CONTACT TRANSMISSION
摘要
Abstract
In this paper, a class of epidemic model with vertical transmission and contact transmission is established. By means of qualitative method and stability method of ordinary differential equations, the model and the existence of nonnegative equilibrium point are analyzed. And by constructing proper Lyapunov function and LaSalle invariance principle, sufficient conditions of the global asymptotic stability of the trivial equilibrium point, disease-free equilib-rium point and endemic equilibrium point are obtained. The results show that when the basic reproduction number is less than or equal to 1, all populations tend to be extinct; when the basic reproduction number is greater than 1 and virus dominant reproduction number is less than 1, the viruses was quickly cleared; when the basic reproduction number is greater than 1 and virus dominant reproduction number is greater than 1 and satisfy certain conditis, the viruses continue to prevail and will become a local disease.关键词
传染病模型/非负平衡点/全局渐近稳定性Key words
epidemic model/nonnegative equilibrium point/global asymptotic stability分类
数理科学引用本文复制引用
傅金波,陈兰荪..具有垂直传染和接触传染的传染病模型的稳定性研究[J].数学杂志,2016,36(6):1283-1290,8.基金项目
国家自然科学基金(11371306) （11371306）
福建省教育厅自然科学基金(JA13370 （）
JAT160676) （）
福建师范大学闽南科技学院青年骨干教师重点培养对象(mkq201006) （mkq201006）
