基于直接免疫的SEIR计算机病毒传播模型

SEIR Computer Virus Propagation Model Based on Direct Immunization

对计算机病毒传播特性的研究可以为控制计算机病毒的传播提供理论依据。本文根据计算机病毒具有潜伏性的特点,提出了一类带有直接免疫的SEIR计算机病毒传播模型;利用微分方程理论分析了传播阈值R0的取值是影响网络中病毒能否被控制的关键;说明了提高直接免疫率可以有效控制R0,从而进一步控制计算机病毒在网络中的传播;分析了计算机病毒在网络传播过程中无病平衡点和地方病平衡点的稳定性:1)当R0≤1时,无病平衡点P0局部渐近稳定,且全局渐近稳定,在当R0>1时,无病平衡点P0不稳定;2)当R0>1时,地方病平衡点P*全局稳定;最后通过模型仿真验证了1)和2)结论的正确性。

The research on the features of computer virus can provide the theory basis for controlling the computer viruses. Accord ing to the latent features of computer virus, a SEIR computer virus propagation model is put forward based on direct immunization. Using the theory of differential equation, it indicates that the value of threshold R0 play a role in the spreading of computer virus. Through improving immunization rates, R0 can be controlled effectively, and further control the spreading of computer virus. Though qualitative analysis proved that： 1） The virus-free equilibrium P0 is locally asymptotically stable if R0 〈1. whereas is un stable if R0 〉1 and 2） the viral equilibrium P0is locally asymptotically stable if R0〉1. Numerical simulations are given to sup port results of 1） and 2）.