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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 ›› 2021, Vol. 38 ›› Issue (4): 573-585.doi: 10.3969/j.issn.1005-3085.2021.04.011

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人类行为在戒烟动力学模型中的影响（英）

李志民,   高建忠,   张太雷,   方   舒,   宋学力   

  1. 长安大学理学院，西安  710064
  • 收稿日期:2019-03-11 接受日期:2019-09-10 出版日期:2021-08-15 发布日期:2021-10-15
  • 通讯作者: 张太雷 E-mail: t.l.zhang@126.com
  • 基金资助:
    国家自然科学基金 (11701041)；陕西省自然科学基础研究计划 (2018JM1011)；长安大学卓越青年基金 (310812163504).

Influence of Human Behavior on Quitting Smoking Dynamics

LI Zhi-min,   GAO Jian-zhong,   ZHANG Tai-lei,   FANG Shu,   SONG Xue-li   

  1. School of Science, Chang'an University, Xi'an 710064
  • Received:2019-03-11 Accepted:2019-09-10 Online:2021-08-15 Published:2021-10-15
  • Contact: T. Zhang. E-mail address: t.l.zhang@126.com
  • Supported by:
    The National Natural Science Foundation of China (11701041); the Natural Science Basic Research Plan in Shaanxi Province (2018JM1011); the Special Fund for Basic Scientific Research of Central Colleges in Chang'an University (310812163504).

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摘要： 本文通过一类PLSQ数学模型，讨论人类行为在戒烟动力学模型中的影响．首先建立一类戒烟常微分方程模型，该模型具有人类行为影响的非线性发生率．通过建立基本再生矩阵，得到模型的基本再生数．利用Routh-Hurwitz准则、Lyapunov泛函、LaSalle不变集原理和第二加性复合矩阵，分析模型的局部稳定性和全局稳定性．通过偏置相关系数（PRCC），分析基本再生数中不同参数对吸烟者传播的影响．特别地，通过理论推导得到人类行为对吸烟者传播的影响．最后，通过数值模拟验证理论推导的正确性．研究结果表明，人类行为可以减少吸烟者的数量．

关键词: 非线性发生率, 戒烟模型, 人类行为, 局部稳定性, 全局稳定性

Abstract: This paper studies the impact of human behavior on quitting smoking dynamics by a PLSQ mathematical model. We start with a quitting smoking ordinary differential equation (ODE) model with nonlinear incidence and human behavior impacts. The basic reproduction number of the model is obtained by establishing the basic reproduction matrix. Using the Routh-Hurwitz criterion and Lyapunov functionals and LaSalle's invariant principle and the second additive compound matrix, local and global dynamics of the model are analysed. Based on the partial rank correlation coefficients (PRCCs), the influence of various parameters in the basic reproduction number on the transmission of smokers is analysed. Particularly, the influence of human behavior on the transmission of smokers is obtained through theoretical deduction. Finally, the theoretical derivation is verified by numerical simulation. Our results show that human behavior can reduce the number of smokers.

Key words: nonlinear incidence, quitting smoking model, human behavior, local stability, global stability

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