一类具有优化控制策略的计算机病毒传播模型分析  

A epidemic model of computer viruses with optimal control

作　　者：谭宏武 白云霄 乔蓉蓉 TAN Hong-wu;BAI Yun-xiao;QIAO Rong-rong(School of Arts and Sciences, Shaanxi University of Science & Technology, Xi′an 710021, China)

机构地区：[1]陕西科技大学文理学院

出　　处：《陕西科技大学学报》2019年第4期144-148,154,共6页Journal of Shaanxi University of Science & Technology

基　　金：国家自然科学基金项目(11301314,11501443);陕西省教育厅专项科研计划项目(18JK0922)

摘　　要：以计算机病毒的传播特征和机理为背景,借助经典的传染病仓室模型框架,建立了一类计算机病毒传播的动力学模型.首先,利用动力学中定性与稳定性知识讨论了正平衡点的存在性和稳定性.接着,考虑引入查毒杀毒、以及杀毒软件升级等控制措施的动力学模型,并给出费用最少的情况下,感染病毒的计算机数量最少的优化控制措施.最后,借助数值模拟展示了我们的理论结果的正确性.This paper takes the propagation of computer viruses as principle,the classical infection compartment model as framework.Firstly,a new epidemic model of computer viruses is proposed,and the existence and stability of positive equilibrium is discussed with the qualitative and stability theory of epidemic dynamics.Secondly,considering the controlling measure of anti-virus and software upgrade,the optimal control measures of the least cost and infection are given.Finally,by numerical simulation the theoretical results is demonstrated to be correct.

关 键 词：计算机病毒 动力学分析 稳定性 优化控制 

分 类 号：TP393[自动化与计算机技术—计算机应用技术]