Modeling and simulation of rumor propagation and optimal control strategy based on social positive reinforcement

Rumor spreading not only disrupts internet order and damages economic interests, but also seriously affects social stability. The social positive reinforcement mechanism was introduced to integrate social media with a positive reinforcement effect into the process of rumor propagation, and an improved rumor propagation model was established. The model’s dynamics are analyzed using mean field theory, revealing a close relationship between the propagation threshold and social positive reinforcement. According to the Hurwitz criterion and LaSalle invariant principle, the stability of the rumor free equilibrium is proved, and the existence of rumor spread equilibrium is proved. To combat rumor spreading under social positive reinforcement, a real-time optimal control method is proposed, incorporating science popularization education for susceptible individuals, enhancing management of rumor spreading individuals, and strengthening the restriction on social media with positive reinforcement effect. Numerical simulations verify the theoretical results, the results show that social positive reinforcement is conducive to rumor propagation, and the control strategies can effectively curb the rumor propagation. Finally, the validity of the model was verified by fitting the model parameters using the least square method. Compared with similar studies, the results of the experiments show that the improved rumor propagation model has a stronger predictive ability.