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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 ›› 2017, Vol. 34 ›› Issue (4): 409-423.doi: 10.3969/j.issn.1005-3085.2017.04.008

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具有时滞和旅途过程中有传染的两斑块SIS模型的全局动力学（英）

刘俊利1,   贾   滢1,   张太雷2   

  1. 1- 西安工程大学理学院，西安  710048
    2- 长安大学理学院，西安  710064
  • 收稿日期:2015-12-23 接受日期:2016-11-02 出版日期:2017-08-15 发布日期:2017-10-15
  • 基金资助:
    国家自然科学基金(11101323)；中央高校基础研究经费(310812152002)；陕西省自然科学基金(11101323)；陕西省自然科学基础研究计划(2014JQ1038;2014JQ1018)；陕西省教育厅科研项目(16JK1331).

Global Dynamics for a Two-patch SIS Model with Time Delay and Transport-related Infection

LIU Jun-li1,   JIA Ying1,   ZHANG Tai-lei2   

  1. 1- School of Science, Xi'an Polytechnic University, Xi'an 710048
    2- School of Science, Chang'an University, Xi'an 710064
  • Received:2015-12-23 Accepted:2016-11-02 Online:2017-08-15 Published:2017-10-15
  • Supported by:
    The National Natural Science Foundation of China (11101323); the Fundamental Research Funds for the Central Universities (310812152002); the Natural Science Foundation of Shaanxi Province (11101323); the Natural Science Basic Research Plan in Shaanxi Province (2014JQ1038; 2014JQ1018); the Scientific Research Program Funded by Shaanxi Provincial Education Department (16JK1331).

PDF (PC)

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摘要： 本文建立了一个具有时滞的SIS模型，研究了旅途过程中疾病的传染．得到了基本再生数．通过线性化方法和比较原理，证明了当基本再生数小于1时无病平衡点是全局渐近稳定的，疾病绝灭．当基本再生数大于1时，系统存在唯一的全局吸引的地方病平衡点，且疾病持续生存．数值模拟验证了扩散率对疾病传播的影响．分析了基本再生数对扩散率的依赖性．

关键词: 旅途过程中的传染, 基本再生数, 一直持续, 全局动力学, 时滞

Abstract: We formulate a delayed SIS model to describe the effect of transport-related infec-tion. The basic reproduction number is obtained. By the linearization method and comparison principle, it is proved that the disease-free equilibrium is globally asymptotically stable and the disease always dies out if the basic reproduction number is less than unity. While there exists a unique endemic equilibrium which is globally attractive and the disease persists if the basic reproduction number is greater than unity. The simulation results show the influence of travel rates on the disease spread. The dependence of the basic reproduction number on the travel rates during travel is also analyzed.

Key words: transport-related infection, basic reproduction number, uniform persistence, global dynamics, time delay

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