基于点对群网络反馈机制的恶意代码传播模型

在点对群信息共享网络中，群体成员之间交流频繁并且同一群体内的成员可以同时从信息源接收到相同信息，依据点对群网络的这2个特点，考虑从恶意代码感染中恢复后的节点作用，在点对群网络中建立一种具有动态反馈防治信息功能的易感-感染-反馈-免疫(SIFR)模型。在经典易感-感染-免疫(SIR)传播模型的基础上引入反馈节点，通过动态共享防治信息遏制恶意代码在点对群网络中的传播。根据计算得到SIFR模型的平衡点和传播阈值，构建相应的Lyapunov函数，证明了平衡点的局部和全局稳定性。数值模拟实验结果显示：当反馈率取0.000 1时，SIFR模型相较于经典SIR模型在传播阈值小于1的情况下，感染节点在峰值处的数量降低了36.16%，能更早更快地趋近于0；当传播阈值大于1时，同一时间的感染节点数量有所减少，趋于稳定的感染节点数量降低了80%。上述实验结果表明SIFR模型应用在点对群网络中能够更好地遏制恶意代码的传播，且反馈率越高，遏制效果越好。

Malware Propagation Model Based on Feedback Mechanism in Point-to-Group Networks

In Point-to-Group(P2G) information-sharing networks, the communication between group members is frequent, and members in the same group can receive the same information from the information source simultaneously. Based on these two characteristics of P2G networks, this study establishes a Susceptible-Infected-Feedback-Recovered(SIFR) model with the function of dynamic feedback prevention information in P2G networks, considering the role of nodes recovered from malware infection.First, based on the classic Susceptible-Infected-Recovered(SIR) propagation model, the feedback nodes are introduced.After introducing feedback nodes, the SIFR model can dynamically share prevention information to suppress the spread of malware in P2G networks.Second, the equilibrium point and propagation threshold of the SIFR model are obtained through calculations.The corresponding Lyapunov function is derived, and the local and global stabilities of the equilibrium point are verified.Finally, the results of the numerical simulation experiments show that compared with the classical SIR model, the number of infected nodes at the peak decreases by 36.16% in the SIFR model when the feedback rate is 0.000 1, and the propagation threshold is lower than 1, and the number of infected nodes tends to zero earlier and faster.When the propagation threshold is higher than 1, the number of infected nodes at this same time is lower than that for the classical SIR model, and the number of stably infected nodes decreases by 80%.Therefore, the proposed model can effectively curb the spread of malware in P2G networks, and the higher the feedback rate, the better the containment effect.