具有饱和发生率的网络蠕虫病毒模型分析  

Analysis of network worm virusmodel with saturated incidence rate

作　　者：王瑞玲 薛亚奎[1] WANG Ruiling;XUE Yakui(School of Mathematics,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学数学学院,太原030051

出　　处：《华中师范大学学报（自然科学版）》2023年第3期347-353,共7页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金青年项目(11301491);山西省自然科学基金青年项目(2018010221040);山西“1331”工程重点创新团队项目.

摘　　要：该文研究了一类具有饱和发生率的网络蠕虫病毒的VEIQS模型,此模型考虑了疫苗接种策略和隔离控制策略.通过计算得到了病毒能否被控制的阈值R 0,论证了平衡点的存在性与稳定性.当R 0<1时,利用构造Lyapunov函数的方法得到了无病平衡点P 0是全局渐近稳定的,病毒传播得到了有效控制;当R 0>1时,利用Li-Muldowney几何准则得到了地方病平衡点P*是全局渐近稳定的,病毒仍然存在.最后,对理论结果做了数值仿真并通过敏感性分析探究了各参数与阈值R 0之间的关系.The VEIQS model of a class of network worm virus with saturated incidence rate is studied,which takes vaccination and quarantine control strategies into account.The threshold of whether the virus can be controlled is obtained by calculation,and the existence and stability of the equilibria are demonstrated.The method of constructing Lyapunov function is used to obtain that the disease-free equilibrium is globally asymptotically stable when R 0<1,and the virus transmission is controlled effectively.At that time,the global asympotical stability of the endemic equilibrium is proved by using Li-Muldowney geometric criterion when R 0>1,and the virus still existed.Finally,the theoretical results are illustrated by numerical simulation and the relationship between each parameter and threshold is explored through sensitivity analysis.

关 键 词：网络蠕虫病毒 VEIQS模型 饱和发生率 稳定性分析 

分 类 号：O175[理学—数学]