一类具有心理效应的海洛因毒品传播模型的全局稳定性  

Global stability of a heroin epidemic model with psychological effect

作　　者：王诗雪 刘俊利[1] WANG Shixue;LIU Junli(School of Science,Xi′an Polytechnic University,Xi′an 710048,China)

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纺织高校基础科学学报》2018年第3期329-334,共6页Basic Sciences Journal of Textile Universities

基　　金：陕西省自然科学基础研究计划项目(2014JQ1038);陕西省教育厅专项科研计划项目(16JK1331)

摘　　要：建立和分析了一类具有心理效应的海洛因毒品传播模型,给出模型的基本再生数R0.当R0≤1时,无海洛因滥用平衡点全局渐近稳定;当R0>1时,无海洛因滥用平衡点不稳定,且模型存在唯一的海洛因滥用平衡点.并利用Routh-Hurwitz判据,Lyapunov函数和LaSalle不变集原理,证明模型平衡点的全局渐近稳定性.A heroin epidemic model is constructed and analyzed, considering that the psychological effect, and the basic reproduction number R 0 of the model is given. When R 0≤1 , the drug-free equilibrium is globally asymptotical stable. When R 0〉1 , the drug use-free equilibrium is unstable, and there exists unique drug spread equilibrium. By using the Routh-Hurwitz criterion, Lyapunov function and LaSalle invariant set principle, the global asymptotical stability of the drug-free equilibrium and the drug spread equilibrium is obtained.

关 键 词：海洛因模型 基本再生数 平衡点 全局稳定性 

分 类 号：O175.1[理学—数学]