The spread of rumors will make a big influence on people's life. This paper aims to study the dynamic behavior of rumor propagation. We consider the effects of transmission rates between different groups and establish 2ISR rumor propagation models with diffusions and time delay in both homogeneous and heterogeneous networks. In the homogeneous network model, we gain the basic reproduction number through the next generation matrix. The existence of two equilibrium points is discussed according to the basic reproduction number. Besides, based on the LaSalle's invariance principle, we obtain the global stability of two equilibrium points. In the heterogeneous network model, we further discuss the global stability of the rumor-free equilibrium point. Moreover, a set of useful rumor control strategies are put forward respectively in two systems. Finally, some necessary numerical simulations are displayed, which also suggest the effectiveness of theories.

谣言的传播将对人们的生活产生重大影响。本文旨在研究谣言传播的动态行为。我们考虑了不同组之间的传输速率的影响，并在同质和异质网络中建立了具有扩散和时间延迟的2ISR谣言传播模型。在同构网络模型中，我们通过下一代矩阵获得基本的再现数。根据基本再生数讨论两个平衡点的存在。此外，基于拉萨尔不变性原理，我们获得了两个平衡点的全局稳定性。在异构网络模型中，我们进一步讨论了无谣言平衡点的全局稳定性。此外，分别在两个系统中提出了一套有用的谣言控制策略。