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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 ›› 2020, Vol. 37 ›› Issue (4): 495-510.doi: 10.3969/j.issn.1005-3085.2020.04.010

• • 上一篇    下一篇

具有吸毒年龄和治疗年龄的海洛因模型的全局稳定性（英）

刘俊利   

  1. 西安工程大学理学院，西安  710048
  • 收稿日期:2018-01-29 接受日期:2018-06-22 出版日期:2020-08-15 发布日期:2020-10-15
  • 基金资助:
    陕西省自然科学基础研究计划(2018JM1011)；陕西省教育厅专项科研计划(16JK1331).

Global Stability for a Heroin Model with Infection Age and Treat Age

LIU Jun-li   

  1. School of Science, Xi'an Polytechnic University, Xi'an 710048
  • Received:2018-01-29 Accepted:2018-06-22 Online:2020-08-15 Published:2020-10-15
  • Supported by:
    The Natural Science Basic Research Plan in Shaanxi Province of China (2018JM1011);  the Scientific Research Program Funded by Shaanxi Provincial Education Department (16JK1331).

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摘要： 本文建立了一个吸毒人群具有吸毒年龄，治疗人群具有治疗年龄的海洛因传播模型．得到了基本再生数．通过波动引理和李雅普诺夫泛函，证明了当基本再生数小于1时无海洛因吸食平衡点是全局渐近稳定的，当基本再生数大于1时，海洛因传播平衡点是全局渐近稳定的．

关键词: 吸毒年龄, 治疗年龄, 基本再生数, 李雅普诺夫泛函, 全局稳定性

Abstract: In this paper, a new model for the dynamics of heroin is formulated that incorporates both the infection age of drug users not in treatment and the treat age of drug users in treatment. We derive the basic reproduction number. By using the fluctuation lemma and Lyapunov functional, we show that if the basic reproduction number is less than unity, the disease-free steady state is globally asymptotically stable, whereas if the basic reproduction number is greater than unity, the endemic steady state is globally asymptotically stable.

Key words: infection age, treat age, basic reproduction number, Lyapunov functional, global stability

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