An effective hybrid method for the optimal control of fraud rumor propagation on online social networks

This paper develops an SEIR-type control model for an optimal control problem (OCP) related to rumor propagation (RP), aiming to address three control strategies designed to reduce the amount of false information and defrauders in online social networks (OSNs). We explore an OCP to analyze the behavior of uninformed individuals against false rumors, the effectiveness of filtering information propagation within OSNs, and the implementation of punitive measures against defrauders. To solve this OCP, we employ a hybrid discretization-metaheuristic approach that integrates the collocation method to transform the OCP of the RP model into a nonlinear programming (NLP) with a Botox optimizer for the NLP to detect the optimal control, state variables, and objective functional. By collecting data on RP from relevant existing literature, we can better verify the SEIR-type control model to stop RP. Numerical simulations confirm the meaningful effect of three strategies that reduce the persons' exposure to rumors and the defrauder's tendency to mislead individuals over OSNs in controlling and stopping the RP.