一种网络病毒传播的时滞微分方程模型

A Differential Equation Model with Delay for Network Virus Propagation

利用微分动力系统理论分析计算机单种病毒的传播规律,并提出不考虑时滞的计算机病毒传播(the propagation regularity of network viruses without the latent period,PRNV_NWPL)模型和考虑时滞的计算机病毒传播(the propagation regularity of network viruses with the latent period,PRNV_WLP)模型,并得到病毒是否最终消除的临界值R0。当R0<1时,得到无病平衡点(计算机病毒不流行),R0>1时,得到地方病平衡点(计算机病毒流行)。由此给出清除计算机病毒的方法,并证明无病平衡点和地方病平衡点的局部渐近稳定性。这些方面与统计方法相比可节省人力、物力。

In this paper,by using the theory of differential equations,we discuss the propagation regularity of network viruses without the latent period and with the latent period.We also obtain the critical value R0 which determine whether the network viruses remove or not.It is proved that there is a free equilibrium（the network virus remove） if R0〈1,and an epidemic equilibrium（the network virus prevalent） if R0〉1,so that we put forward a method of removing the network viruses.Stability of the free equilibriums and the endemic equilibriums are discussed.This research can use manpower and material resources more sparingly than the method of statistics.