考虑社交网络用户行为的网络病毒传播建模

针对已有病毒传播模型都没有考虑不同社交网络间的用户交互行为对网络病毒传播规律的影响，建立了考虑不同社交网络用户交互行为的微分方程动力学模型。利用稳定性理论分析了模型反映的网络病毒传播动力学性态，得到了控制网络病毒传播的基本再生数的精确数学表达式。进一步，采用龙格-库塔数值方法，通过仿真实验，验证了理论分析的正确性。研究结果表明，基本再生数是网络病毒扩散基本态势的直接决定因素，当基本再生数的值小于等于1时，随着时间演化，网络病毒的扩散会被彻底控制。另外还发现，分散用户到不同社交网络更有利于缓解网络病毒的扩散。

Network virus propagation modeling considering social network user behaviors

Concerning that the existing networks virus propagation models do not consider the influence of interactive behaviors among the users in different social networks on network virus propagation, a dynamic model of differential equations was established. The stability theory was used to analyze the dynamical behaviors of the network virus propagation, and the accurate expression of the basic reproduction number was obtained, which is the threshold of controlling the network virus propagation. Furthermore, using Runge-Kutta numerical method, the correctness of theoretic analysis was verified by simulations. The results show that the basic reproduction number is the direct decisive factor of network virus prevalence situations. When the value of the basic reproduction number is less than or equal to one, the propagation of the network viruses will be controlled with the evolution of time. Additionally, the research reveals that it is helpful for distributing the users to different social networks to slow the prevalence of network viruses.