数学物理学报 ›› 2019, Vol. 39 ›› Issue (5): 1260-1271.

• 论文 • 上一篇    

人口总数变化的比例进入潜伏或染病群体的年龄结构传染病模型及稳定性

王改霞1, 刘纪轩2, 李学志3   

  1. 1 信阳学院数学与信息学院 河南信阳 464000;
    2 空军工程大学航空机务士官学校基础部 河南信阳 464000;
    3 河南师范大学数学与信息科学学院 河南新乡 453007
  • 收稿日期:2017-06-09 修回日期:2018-07-23 发布日期:2019-11-08
  • 作者简介:王改霞,E-mail:wwgx8@126.com;刘纪轩,E-mail:lljx8@126.com
  • 基金资助:
    国家自然科学基金(11271314)、河南省高等学校重点科研项目(17A110030)和河南省高等学校青年骨干教师培养计划(2018GGJS198)

Stability of Age-Structured with Proportion of Infected Groups or Enter the Latent Epidemiological Model with Varying Population Size

Wang Gaixia1, Liu Jixuan2, Li Xuezhi3   

  1. 1 College of Mathematics and Information, Xinyang University, Henan Xinyang 464000;
    2 Basic Department, Aeronautic Sergeant College of Air Force Engingeering University, Henan Xinyang 464000;
    3 College of Mathematics and Information Science, Henan Normal University, Henan Xinxiang 453007
  • Received:2017-06-09 Revised:2018-07-23 Published:2019-11-08
  • Supported by:
    Supported by the NSFC (11271314), the Key Scientific Research Projects in Colleges and Universities of Henan Province (17A110030) and the Training Program for Young Key Teachers in Institutions of Higher Learning of Henan Province (2018GGJS198)

摘要: 由于受到年龄或体质的影响,导致有些易感者被感染后进入潜伏期,有些直接变成患者,因而需要对比例进入潜伏或染病群体的传染病模型进行研究,但是这类数学模型很少考虑到年龄的影响,该文对人口总数变化的比例进入潜伏或染病群体的年龄结构传染病模型进行研究,得出了与人口增长指数有关的阈值参数的表达式,并根据此参数讨论了无病平衡态和地方病平衡态的存在性及局部渐近稳定性,这些条件对于控制疾病的传播具有重要的理论及实际意义.

关键词: 比例, 人口变化,

Abstract: Due to the influence of age or physical fitness, resulting in a number of susceptible to infection into the latent, some directly into patients, study of epidemic model so it is necessary to enter a latent or infected population proportion, but this kind of model is rarely taken into account the influence of age, study on the age structure of the infectious disease model of this change on the proportion of the total population in infected groups or latent, the expressions of the threshold parameters related to the population growth index are obtained, the existence and the local asymptotic stability conditions of the disease-free equilibrium and endemic equilibrium are discussed, then, the use of these conditions to control the spread of disease has important theoretical and practical significance.

Key words: Proportion, Varying population size, Spectrum

中图分类号: 

  • O175.12