Dynamics Stability and Optimal Control of Virus Propagation Based on the E-Mail Network

Currently, E-mail has become one of the most common communication methods in daily life, while Email virus constitutes one of the major Internet security threats and has attracted considerable attention. This paper addresses the optimal control problem when encountering out-breaks of E-mail virus. Based on the email network of North University of China, we establish a SEI email virus propagation model, study the influence of the heterogeneity of the email network on the worm virus propagation. We give a detail analysis for the model and the propagation threshold of system is obtained by stability theory, etc. Moreover, the effects of the heterogeneity of user for the spreading of worms are analyzed, and the optimal control theory is used to further study the time-varying control of worms. In final, the stability of system and the effectiveness of optimal control strategy are confirmed by numerical simulations.