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.

首先在多语言环境和异构网络中，提出了一种具有教育机制的新型谣言传播模型。首先，通过分析所获得的微分方程来研究模型的阈值行为和动力学。接下来，基于劳斯·赫维茨的判断，Lyapunov方法和LaSalle不变性原理，进行了无谣言/传播平衡点（RFEP / RSEP）的存在和稳定性。此外，我们通过敏感性分析发现，教育机制对谣言传播具有重要影响。因此，提出了最优控制以优化教育机制。此外，数值模拟表明了理论结果的正确性。最后，结合实践，