摘要： 为研究网络中节点输入率和移出率的差异性对蠕虫病毒传播的影响，基于仓室建模思想分析各个仓室之间的转化关系，构建一种具有不同输入率和移出率的蠕虫病毒传播SEIR模型。计算模型的平衡点和基本再生数，给出平衡点稳定性规范，并通过Hurwitz定理、LaSlle不变性原理和Bendixson定理证明平衡点的稳定性。在此基础上，利用数值仿真验证理论分析的结果，分析影响蠕虫病毒传播的关键因素，进而提出抑制蠕虫病毒传播的建议措施。

关键词: SEIR模型, 蠕虫病毒, 基本再生数, 平衡点, 稳定性

Abstract: In order to study the impact of the difference of input rates and removal rates of nodes in the network on worm virus propagation,this paper analyzes the transformation relationship between each compartment based on the idea of compartment modeling and constructs a worm virus propagation SEIR model with different input rates and removal rates.It calculates the equilibrium point and basic regeneration number of the model,gives the stable specification of equilibrium point,and uses the Hurwitz theorem,the LaSlle invariance principle and the Bendixson theorem to prove the stability of equilibrium point.On this basis,this paper verifies the results of theoretical analysis by numerical simulation and analyzes the key factors that affect the worm virus propagation,then proposes some suggestions and measures to suppress the worm virus propagation.

Key words: SEIR model, worm virus, basic reproduction number, equilibrium point, stability

中图分类号: 

• TP309