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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 ›› 2019, Vol. 36 ›› Issue (3): 333-343.doi: 10.3969/j.issn.1005-3085.2019.03.009

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一类具有阶段结构的传染病模型的全局分析

张凤琴1,   赵  甜1,2,   刘汉武1   

  1. 1- 运城学院数学与信息技术学院，运城  044000 
    2- 山西师范大学数学与计算机科学学院，临汾  041004
  • 收稿日期:2017-05-18 接受日期:2017-11-07 出版日期:2019-06-15 发布日期:2019-08-15
  • 基金资助:
    国家自然科学基金(11371313; 11241005; 11501498)；运城学院生物数学重点实验室项目(swsx201502; swsx201602).

Global Analysis of an Epidemic Model with Stage-structure

ZHANG Feng-qin1,   ZHAO Tian1,2,   LIU Han-wu1   

  1. 1- School of Mathematics and Information Technology, Yuncheng University, Yuncheng 044000 
    2- School of Mathematical and Computer Science, Shanxi Normal University, Linfen 041004
  • Received:2017-05-18 Accepted:2017-11-07 Online:2019-06-15 Published:2019-08-15
  • Supported by:
    The National Natural Science Foundation of China (11371313; 11241005; 11501498); the Yuncheng University Key Laboratory of Biomathematics (swsx201502; swsx201602).

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摘要： 考虑疾病仅在成年个体间传播，并且成年个体的增长受到密度制约，本文建立了一类具有双线性发生率和阶段结构的传染病模型．文中得到了种群增长的基本再生数和疾病传播的基本再生数，通过构造Lyapunov函数证明了平衡点的全局稳定性，通过数值模拟验证了所获得的结果．结果显示，两类基本再生数完全确定了模型的动力学性态，通过降低传染率和增大染病者移除率可以降低疾病基本再生数．

关键词: 传染病模型, 阶段结构, 基本再生数, 平衡点, 全局稳定性

Abstract: An epidemic model with bilinear incidence and stage structure is established by assuming that the infection can transmit only among adult individuals and that the growth of adult individuals is density-dependent. The basic reproduction numbers of the population growth and the infection transmission are both obtained, the global stability of equilibriums is established by constructing Lyapunov functions, and the theoretical results are verified through numerical simulation. In conclusion, the dynamic behaviors of this model is completely determined by its two basic reproduction numbers, and the basic reproduction numbers of infection transmission can be depressed through decreasing the incidence or increasing the remove rate.

Key words: epidemic model, stage structure, the basic reproduction number, equilibrium, global stability

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