北华大学学报（自然科学版）2018，Vol.19Issue(4)：430-435,6.DOI:10.11713/j.issn.1009-4822.2018.04.003
具有非线性发生率的离散SIQ模型的稳定性分析
Stability Analysis for a Discrete SIQ Epidemic Model with Nonlinear Incidence
摘要
Abstract
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 R0, 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.关键词
非标准差分/非线性发生率/基本再生数/稳定性Key words
non-standard finite difference/nonlinear incidence rate/basic reproductive number/stability分类
数理科学引用本文复制引用
王建鹏,王蕾,张学良,王凯..具有非线性发生率的离散SIQ模型的稳定性分析[J].北华大学学报（自然科学版）,2018,19(4):430-435,6.基金项目
新疆维吾尔自治区自然科学基金项目(2014211C014,2015211C024,2015211C031). （2014211C014,2015211C024,2015211C031）
