具有非线性免疫的P2G网络蠕虫传播模型  

Worm Propagation Model in P2G Network with Nonlinear Vaccination Strategy

作　　者：赖际颖 高淑京[1] LAI Jiying;GAO Shujing(College of Mathematics and Computer Science,Gannan Normal University,Ganzhou 341000,China)

机构地区：[1]赣南师范大学数学与计算机科学学院,江西赣州341000

出　　处：《赣南师范大学学报》2019年第6期20-24,共5页Journal of Gannan Normal University

基　　金：国家自然科学基金项目(11561004);赣南师范大学研究生专项资金项目(YCX18B002)。

摘　　要：基于蠕虫病毒在P2G网络中传播的特性,提出一类具有非线性免疫策略的P2G网络蠕虫传播模型.计算得到基本再生数R 0,并证明,当R 0<1时,无蠕虫平衡点是全局渐近稳定的;当R 0>1时,正平衡点是局部渐近稳定的.通过数值模拟,验证了理论结果并分析了非线性控制策略的有效性.Based on the typical propagation character of worm in P2G network,a worm propagation model with nonlinear vaccination strategy is established and analyzed.By using the next generation matrix,we obtain the basic reproduction number R 0.The theoretical analysis reveals,if R 0<1,the worm-free equilibrium is globally asymptotically stable,whereas if R 0>1,the unique positive equilibrium is locally asymptotically stable.The simulation results not only demonstrate the validity of theoretical results,but also show the effectiveness of the nonlinear vaccination strategy.

关 键 词：P2G网络 蠕虫病毒 传播模型 非线性免疫 

分 类 号：O175.13[理学—数学]