摘要
研究了一类具有非线性发生率的时滞SIR传染病模型.确定了决定计算机病毒消失或继续存在的基本再生数,通过分析系统对应的特征方程,得到无病平衡点与地方平衡点的局部稳定性。通过构造适当的Lyapunov函数,利用La Salle不变原理,证明当基本再生数小于1时,无病平衡点是全局渐近稳定的;最后,通过MATLAB进行数值模拟验证了所得理论分析结果的正确性。
In this paper, A delayed SIR epidemic model with nonlinear incidence rate is investigated, the basic reproduction number is determining whether the disease dies is found, and the existence of the model is discussed. By analyzing the corresponding characteristic equation.the local stability of a disease-free equilibrium and endemic equilibrium are discussed. According to the suitable Lyapunov function and LaSalle invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable as the basic reproduction number for viral infection is less than unity, Finally,the theoretical results obtained are verified by numerical simulations for the numerical model with a specific incidence by MATLAB.
出处
《科技视界》
2017年第5期46-47,共2页
Science & Technology Vision
基金
贵州省联合基金项目
黔教合KY字[2016]306
黔东南科合J字[2016]001
凯里学院校级重点建设项目(数学:KZD2014004)
