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.

Least absolute shrinkage and selection operator (Lasso) has performance superiority in dimension reduction of data and anomaly detection. Concerning the problem that the accuracy is low in anomaly detection based on Lasso, a Least Angle Regression (LARS) algorithm based on multi-dimensional weight was proposed. Firstly, the problem was considered that each regression variable had different weight in the regression model. Namely, the importance of the attribute variable was different in the overall evaluation. So, in calculating angular bisector of LARS algorithm, the united correlation of regression variable and residual vector was introduced to distinguish the effect of different attribute variables on detection results. Then, the three weight estimation methods of Principal Component Analysis (PCA), independent weight evaluation and CRiteria Importance Though Intercriteria Correlation (CRITIC) were added into LARS algorithm respectively. The approach direction and approach variable selection in the solution of LARS were further optimized. Finally, the Pima Indians Diabetes dataset was used to prove the optimal property of the proposed algorithm. The experimental results show that, the LARS algorithm based on multi-dimensional weight has a higher accuracy than the traditional LARS under the same constraint condition with smaller threshold value, and can be more suitable for anomaly detection.