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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (6): 597-612.doi: 10.3969/j.issn.1005-3085.2016.06.004

• • 上一篇    下一篇

具有年龄阶段的离散SCIRS 模型在我国流脑中的应用

马 霞1, 周义仓2   

  1. 1. 太原工业学院理学系，太原 030008
    2. 西安交通大学数学与统计学院，西安 710049
  • 收稿日期:2015-09-18 接受日期:2016-07-29 出版日期:2016-12-15 发布日期:2017-02-15
  • 基金资助:
    国家自然科学基金 (11171267)；太原工业学院科技处基金 (2015LQ19)；加拿大国际发展研究中心基金 (104519-010).

Age Structures of Discrete SCIRS Model with Application to Meningococcal Meningitis in China

MA Xia1, ZHOU Yi-cang2   

  1. 1. Department of Science, Taiyuan Institute of Technology, Taiyuan 030008
    2. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049
  • Received:2015-09-18 Accepted:2016-07-29 Online:2016-12-15 Published:2017-02-15
  • Supported by:
    The National Natural Science Foundation of China (11171267); the Technology Depar-tment Fund of Taiyuan Institute of Technology (2015LQ19); the International Development Research Center, Ottawa, Canada (104519-010).

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摘要： 本文主要研究了具有三个年龄阶段的离散SCIRS模型的动力学性态．首先，利用再生矩阵的方法定义了模型的基本再生数$\widetilde{R_0}$，证明了当$\widetilde{R_0}<1$时，模型存在唯一的无病平衡点并且是全局渐近稳定的，当$\widetilde{R_0}>1$时，除了无病平衡点，模型还存在唯一的地方病平衡点．其次，利用法定传染病报告的流脑数据，把模型应用到我国流脑的流行传播中．针对模型中很多参数的不确定性，对基本再生数中的参数进行了敏感性分析．最后，在模型的基础上考虑流脑发病的季节因素对模型加以改进，预测分析了我国流脑的发病情况，数值模拟的结果显示季节因素对疾病进展率的影响程度大于对疾病传染率的影响，为控制流脑在我国的流行传播提供建议．

关键词: 离散模型, 年龄结构, 流脑, 基本再生数, 敏感性

Abstract: The dynamic characteristic of meningococcal meningitis SCIRS model with three age structures is studied. First, the basic reproduction number $\widetilde{R_0}$ is defined by using the regeneration matrix. It is proved that the disease-free equilibrium is globally asymptotically stable when $\widetilde{R_0}<1$. The disease-free equilibrium is unstable, there exists an endemic equilibrium and the system is uniformly persistent when $\widetilde{R_0}>1$. Second, using the data from the report of notifiable infectious diseases in China, the model is applied to describe the spread of meningococcal meningitis in China. For the uncertainty of many parameters in the model, we make sensitivity analysis about the parameters of the basic reproductive number. Finally, we consider the influence of seasonal factors to the incidence of meningococcal meningitis to modify the model, and predict the meningococcal meningitis in population development trend of China. The numerical simulation results show that the impact of seasonal factors on the rate of disease progression of meningococcal meningitis is greater than the effect on infection rate, this also provides advice to control the spread of meningococcal meningitis in our country.

Key words: discrete model, age structure, meningococcal meningitis, basic reproduction number, sensitivity analysis

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