摘要
研究了一类具有接种仓室和潜伏仓室的结核病模型,得到了结核病灭绝与否的阈值——基本再生数R0,并运用Liapunov函数,中心流行理论、La Salle不变集原理证明了当R0≤1时,此模型存在唯一的无病平衡点E0,且无病平衡点全局渐近稳定;当R0>1且无限接近于1时,地方病平衡点E*局部渐近稳定;当R0>1时,地方病平衡点E*全局渐近稳定.且用数值模拟进一步证明了无病平衡点和地方病平衡点稳定性.
A tuberculosis model with vaccination and latent chamber is studied, and the threshold of tuberculosis extinction was obtained. The existence and global stabilities of the disease- free equilibrium and the endemic equilibrium were proved by used the Liapunov function, the center manifold theory and LaSalle invariance principle. The stability of the dis- ease -free equilibrium and the endemic equilibrium point were further proved by numerical simulation.
作者
杨高艳
胡新利
YANG Gao-yan, HU Xin-li(School of Science, Xi' an Polyteehnie University, Xi' an 710048, Chin)
出处
《哈尔滨商业大学学报(自然科学版)》
CAS
2018年第1期101-106,123,共7页
Journal of Harbin University of Commerce:Natural Sciences Edition
基金
陕西省教育厅自然科学专项基金(15JK1295)
陕西省自然科学基础研究计划资助项目(2016JQ1029)
关键词
接种
治疗
全局稳定性
结核病
模型
vaccination
treatment
global stability
tuberculosis
model