In recent years, rumor propagation in social networks attracts more researchers’ attention. In this paper, we have established I2S2R rumor spreading models in both homogeneous networks and heterogeneous networks considering the effect of time delay. In the homogeneous network model, we obtain the basic reproduction number by means of the next-generation matrix. Besides, the local stability and the global stability of the equilibrium points are discussed by linearization approach of nonlinear systems and Lyapunov function. In the heterogeneous network model, we calculate the basic reproduction number through algebraic method. In addition, Lyapunov functional method and Lasalle invariance principle are applied to study the stability of equilibrium points in the complex network model. Further, we put forward some useful strategies to control the spreading of rumor based on the complex network theory. Finally, we take advantage of numerical simulations to verify the theory above and come up with necessary conclusions.

近年来，社交网络中的谣言传播引起了更多研究者的关注。在本文中，考虑到时延的影响，我们在同构网络和异构网络中都建立了I2S2R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。此外，通过非线性系统的线性化方法和李雅普诺夫函数讨论了平衡点的局部稳定性和全局稳定性。在异构网络模型中，我们通过代数方法计算基本的再现数。另外，应用Lyapunov泛函法和Lasalle不变性原理研究了复杂网络模型中平衡点的稳定性。进一步，基于复杂网络理论，我们提出了一些控制谣言传播的有用策略。最后，我们利用数值模拟来验证上述理论并得出必要的结论。