具有年龄结构的网络游戏成瘾数学模型的动力学分析  

Dynamic Analysis on a Kind of Mathematical Model Incorporating Online Game Addiction Model and Age-Structure

作　　者：王晓静[1] 史洋洋[1] 王丹[1] 许传青[1] 

机构地区：[1]北京建筑大学理学院,北京100044

出　　处：《北京建筑大学学报》2017年第2期54-58,共5页Journal of Beijing University of Civil Engineering and Architecture

基　　金：国家自然科学基金项目(11371048);北京市教育委员会项目(KM201610016018);中央支持的地方项目(21147515602)

摘　　要：在现代社会,网络游戏成瘾越来越困扰一部分人的正常生活.针对网络游戏的特点,我们应用传染病动力学来模拟网络游戏成瘾的传播过程以得到有效的控制策略.首先,建立了一类具有年龄结构的网络游戏成瘾的数学模型,给出了系统的基本再生数和有效再生数,并利用特征方程理论和阈值理论,证明了无病平衡点的全局稳定性.结果表明加强宣传教育能够有效控制网络成瘾.In modern life, online game addiction is more and more troubling some peoples＇ normal life. According to the characteristics of online game addiction, the infectious disease dynamics are applied to describe the spread of it so as to obtain effective control strategy. In this paper, a mathematical model is established for the online game addiction with age-structure, and then the calculation formulas are provided for the basic reproduction number and the effective reproduction number, respectively. The global stability of the disease-free equilibrium has been proved based on the theory of the characteristic equation and the threshold. The results show that strengthening publicity and education is a good way to prevent and control online game addiction.

关 键 词：网络游戏成瘾 数学模型 再生数 稳定性 宣传教育 

分 类 号：O175.14[理学—数学]