Rumor spreading model with a focus on educational impact and optimal control

Rumor spreading brings great misconception and harm to society. To control the spread of rumors, it is essential to model rumor propagation and provide appropriate interference in inhibiting the propagation. In this paper, we establish an extended rumor-spreading model with a focus on the influence of knowledge education and intervention strategies in reducing rumor propagation. The mathematical rationality of the proposed model is examined, which demonstrates the existence of equilibrium and local asymptotic stability. To simulate the dynamics of rumor spreading in the proposed model and calibrate its unknown variables to a real case, we employ a novel rumor-informed neural network (RINN), which is constructed based on the physics-informed neural network (PINN) and real rumor spreading. The numerical simulation experiments indicate that the reinforcement of education on rumor identification and timely refutation of false information is effective in controlling the propagation of rumors. Moreover, the optimal control strategies are further proposed to determine the efficient means of mitigating the risk associated with the rapid spread of rumors. Our findings present that proactive dissemination of publicity and educational content can effectively enhance individuals’ awareness of rumor information. Specifically, prompt dispelling of false information can result in a higher success rate of dispelling rumors, a shorter duration of rumor dissemination, and a lower peak in the number of rumor disseminators, thereby facilitating effective control of the spread of rumors.