Hybrid control strategy and optimal control for rumor spreading

The malicious rumor has adverse effect in public interests, social order and public safety. Therefore, it is imperative to put forward an effective method of restrain rumor for reducing economic losses and maintaining social stability. The existing methods of control rumor have the shortcomings in single control strategy and neglect of the control cost. To improve the effectiveness of the scheme for controlling rumor and decreasing the control cost, an effective rumor spreading hybrid control strategy is proposed by combining the protection and block strategies. By utilizing the optimal control theory, the method minimizes the expenditure in containing rumors. The existence of the optimal control is proved based on the Pontryagin's minimum principle and an optimal control system is obtained. The proposed rumor hybrid control strategy theory is verified by analyzing equilibrium and stability. The effectiveness of the hybrid control strategy is further tested by a series of experiments. The results illustrate that the proposed strategy can more effectively control rumors than the single block and protection strategies and reduce the expenditure of the control strategy. The research results will provide some effective theoretical schemes for solving the problem of restraining rumors in real social networks.