一类具有非线性接触率的戒烟模型  

A Giving up Smoking Model with General Nonlinear Incidence Rate

作　　者：王霞 李保林 葛情 WANG Xia;LI Baolin;GE Qing(College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范学院数学与统计学院

出　　处：《信阳师范学院学报（自然科学版）》2019年第3期362-366,共5页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11771374);河南省高校科技创新人才支持计划(17HASTIT011)

摘　　要：研究了一类带有非线性接触率和戒烟不完全成功的戒烟模型.定义了模型的基本再生数,得到了系统平衡点的存在性以及局部稳定性,并通过构造Lyapunov函数,证明了当基本再生数R0<1时,无烟平衡点是全局渐近稳定的;当R0>1时,吸烟平衡点是全局渐近稳定的.A giving up smoking model with general nonlinear incidence rate was proposed.The existence and local stability of equilibria are completely determined by the basic reproduction number.The threshold dynamics was established by employing the approach of Lyapunov functional.When the basic reproduction number is less than one,the smoking-free equilibrium is globally asymptotically stable;otherwise,the smoking-present equilibrium is globally asymptotically stable.

关 键 词：基本再生数 无烟平衡点 吸烟平衡点 非线性接触率 LYAPUNOV泛函 全局渐近稳定 

分 类 号：O175.1[理学—数学]