具有非单调传染率的SIQR传染病模型的稳定性分析  

Stability of a SIQR Model with with Nonmonotone Incidence Rate

作　　者：叶志勇[1] 刘原[1] 吴用[1] 

机构地区：[1]重庆理工大学数学与统计学院,重庆40054

出　　处：《生物数学学报》2014年第1期105-112,共8页Journal of Biomathematics

基　　金：重庆市教委资助项目(KJ080622);重庆理工大学博士单位建设工程项目(CQ010040)

摘　　要：该文研究了一类具有非单调传染率的SIQR传染病模型,讨论了平衡点的存在性,运用特征值法、Hurwit判据和极限方程理论证明了当阈值R_0<1时无病平衡点是全局渐近稳定的;当R_0>1时,无病平衡点是不稳定的.并采用Lipunov函数法和Lasalle不变性原理证明了地方性平衡点是全局渐近稳定的.最后进行了数值模拟,验证了理论结果的有效性.In this paper,a SIQR epidemic model with nonmonotone incidence rate is investigated.The existence of the equilibriums is discussed,and we have proved that if the threshold R_0< 1,then the disease-free equiUbrium is globally stable by means of eigenvalue method,Hurwit criterion and limit equation theory;If R_0 > 1,then the disease-free equilibrium is not stable.Based on the Liapunov function method and Lasalle invariance principle,global stability of the endemic equilibrium is obtained.Finally numerical simulations are provided to illustrate the effectiveness of the results.

关 键 词：非单调传染率 SIQR模型 平衡点 稳定性 

分 类 号：O175.13[理学—数学]