A rumor propagation model integrated with psychological factors

Rumors can bring great harm to the development of society, and thus studying the spread of rumors has an important significance. Meanwhile, the spread of rumors may vary depending on the psychology of susceptible individuals. In this paper, based on the effect of psychology, a stochastic SEIR model with mean-reversion Ornstein–Uhlenbeck process is investigated. A unique global solution is first obtained for the stochastic SEIR model. By constructing a Lyapunov function, a sufficient criterion [Formula: see text] for the existence of a stationary distribution is proved, which means that rumors will persist for a long time under psychological influence. The conditions for the disappearance of rumors are also given. Finally, the theoretical results were validated through numerical simulations.