Dynamic analysis of stochastic rumor model with education effect

With the development of the economy and society, rumors have become increasingly popular. Therefore, quantitative research on rumors has become essential. In this paper, a new rumor model with age of education is introduced by considering two different types of populations. First, we obtain the existence of global positive solutions by utilizing Itô's formula and the Lyapunov functional method. Then, several sufficient conditions for the disappearance and persistence of rumors are given, where the threshold will be affected by the age of education. Finally, to support the main results of this article, several illustrative numerical simulations are conducted.