Abstract
A novel rumor propagation model with education mechanism is firstly proposed in multi-lingual environment and heterogeneous networks. Firstly, the threshold behaviour and dynamics of model are examined through analyzing the acquired differential equations. Next, based on Routh-Hurwitz judgment, Lyapunov method and LaSalle’s invariance principle, the existence and stability of rumor-free/spreading equilibrium points (RFEP/RSEP) are carried out. Furthermore, we found that the educational mechanism has significance influence on rumor spreading through sensitivity analysis. Therefore, the optimal control is presented to optimize the educational mechanism. Additionally, numerical simulations is given to show the correctness of theoretical results. Finally, combine with practice, a model application is presented to verify the effectiveness of the established model and the proposed optimal control.
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