一种新的计算机病毒模型的稳定性分析

Stability in a Novel Computer Virus Model

目前,网络中计算机病毒的威胁引起了对计算机病毒传播建模和分析的研究热潮.为了更好地反映实际情况,该文基于现有的SIR模式,提出一个新的计算机病毒传播模型.该模型主要考虑了多种状态下的预先免疫措施.同时,利用特征方程的特征值分布和线性微分系统对该模型在平衡点处的稳定性进行了讨论.理论分析和数值模拟表明,这一模型的动力学行为依赖于基本再生数,该模型可以帮助我们更好地了解和预测计算机病毒在网络中的传播行为.

The threat of computer viruses in networks has stimulated some activities to model and analyze the computer virus prevalence. In order to model a virus prevalence to better reflect realistic situations, in this paper, based on the existing SIR models, we propose a novel computer virus model. This model has mainly taken into account the following factor： multi-state antivirus measures. Furthermore, stability at equilibria for this model are carefully analyzed by considering the distributed ranges of eigenvalues of charac- teristic equations associated with linear differential systems. The results of mathematical analysis and nu- merical simulations show that the dynamical features of the proposed model rely on the basic reproduction number R0. This novel model can help us to better understand and predict the propagation behaviors of viruses in networks.