摘要
首先,针对水源性传染病具有多种传播途径的特点,考虑疾病在易感者体内要潜伏一段时间,建立带时滞的传染病模型,并得出该模型的基本再生数和平衡点;其次,通过分析相应的特征方程来研究该模型的两个平衡点(无病平衡点和地方病平衡点)的局部渐近稳定性;最后,通过构造两个合适的Lyapunov函数来研究两个平衡点的全局渐近稳定性.
Firstly,to address the characteristics of waterborne infectious diseases with multiple transmission routes and considering that the disease has to be latent in susceptible individuals for a period of time,an infectious disease model with time delay is established and the basic regeneration number and equilibrium points of the model are derived;secondly,the local asymptotic stability of the two equilibrium points(disease-free equilibrium point and endemic equilibrium point) of the model is studied by analyzing the corresponding characteristic equations;finally,the full stability of the two equilibrium points is studied by constructing Finally,the global asymptotic stability of the two equilibrium points was investigated by constructing two appropriate Lyapunov functions.
作者
廖书
方章英
LIAO Shu;FANG Zhangying(School of Mathematics and Statistics,Chongqing University of Technology and Business,Chongqing 400067,China)
出处
《西南师范大学学报(自然科学版)》
CAS
2023年第3期47-51,共5页
Journal of Southwest China Normal University(Natural Science Edition)
基金
重庆市基础研究与前沿探索项目(cstc2020jcyj-msxmX0394)
重庆市教委科学技术研究项目(KJQN201900806)。