离散SCIRS模型在我国流脑中的应用（英文）  

A Discrete SCIRS Model with Application to Meningococcal Meningitis in China

作　　者：马霞 周义仓[2] 

机构地区：[1]太原工业学院理学系,山西太原030008 [2]西安交通大学数学与统计学院,陕西西安710049

出　　处：《应用数学》2017年第4期715-725,共11页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11171267);IDRC of Canada grant 104519-010;Technology Department of Taiyuan Institute of Technology2015LQ19

摘　　要：本文研究一类离散SCIRS模型的动力学性态,利用再生矩阵的方法得到模型的基本再生数,证明模型无病平衡点的全局渐近稳定性,以及模型地方病平衡点的存在性与一致持续性.数值模拟显示地方病平衡点可能是全局渐近稳定的.最后,把模型应用到我国流脑的传播中,通过数值模拟的结果和法定传染病报告的结果对比,表明该模型在一定程度上可以用来预测流脑在我国的传播.In this paper, we considered a SCIRS model in discrete-time, and obtained the basic reproduction number by using the next generation matrix method. We also examined the global stability of disease-free equilibrium, the existence and persistence of the endemic equilibrium by using theoretical techniques. Numerical simulations demonstrate that the endemic equilibrium may be globally asymptotically stable. The model was applied to describe the transmission of Meningococcal meningitis. The comparison between the model simulation and notifiable disease data demonstrates that our model can give a good prediction for infection diseases.

关 键 词：离散SCIRS模型 流脑 基本再生数 稳定性 持续性 

分 类 号：O175[理学—数学]