一类带时滞的霍乱传染病模型的稳定性分析

Stability Analysis of a Class of Cholera Epidemic Models with Time Delay

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.