移动环境下网络病毒传播模型及其稳定性研究

摘要

In this paper,considering the random motion of nodes,we propose an epidemic spreading model on network of mobile environment based on the mean-filed theory.Using the theory of differential dynamical system,the behaviors of epidemic spreading are further analyzed.It is shown that if R0≤1,the epidemic always dies out and the disease-free equilibrium is globally asymptotically stable;and if R0〉1,the epidemic is uniformly persistent and the endemic equilibrium is globally asymptotically stable.Numerical simulations are given to validate the results of theoretical analysis.%考虑网络节点的随机移动,基于平均场理论提出一个移动环境下网络病毒传播的数学模型,利用微分动力学系统理论研究了病毒传播行为.研究表明,当病毒基本再生数R0≤1时,网络中病毒逐渐消除,系统的无病毒平衡点全局渐进稳定;当R0〉1时,网络中病毒持续存在,系统的地方病平衡点全局渐进稳定.通过仿真验证了所得结论的正确性.