In this paper, we study the SIR model and give a strategy to control the epidemic. Based on discrete-time observation, the linear control term is added and the upper bound of time delay is given in order to make the epidemic disappear. Both the deterministic and stochastic cases are considered. The novelty of this paper lies in the fact that it only controls for the infected population. Numerical examples verify the theory results.

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.