摘要
研究了具有非线性发生率的离散SIQ模型的稳定性.通过非标准差分方法得到了离散的SIQ模型,利用迭代法得到了模型解的正性和有界性、基于定义的基本再生数、无病平衡点和地方病平衡点的唯一存在性;通过线性化方法和构造离散Lyapunov函数方法得到了无病平衡点的稳定性;利用数值例子说明了地方病平衡点的稳定性结果.
The stability of a discrete SIQ epidemic model with nonlinear incidence is studied.We get the discrete SIQ epidemic model by Micken non-standard finite difference scheme(NSFD).The positive and bounded solution is given by the induction,and based on the defined basic reproduction number R 0,we prove the existence of infection-free equilibrium and endemic equilibrium.The stability of the infection-free equilibrium is obtained by the linearzation method and constructing the discrete Lyapunov function method.The stability result of the endemic equilibrium is explained through the examples.
作者
王建鹏
王蕾
张学良
王凯
Wang Jianpeng;Wang Lei;Zhang Xueliang;Wang Kai(Department of Medical Engineering and Technology,Xinjiang Medical University,Urumqi 830011,China)
出处
《北华大学学报（自然科学版）》
CAS
2018年第4期430-435,共6页
Journal of Beihua University（Natural Science）
基金
新疆维吾尔自治区自然科学基金项目(2014211C014
2015211C024
2015211C031)
关键词
非标准差分
非线性发生率
基本再生数
稳定性
non-standard finite difference
nonlinear incidence rate
basic reproductive number
stability
