Information flow retains a critical role in decision making among investors. In this paper, we employ a diffusion model based on epidemiology theory to study the rumor spreading process within investors. The paper introduce the feedback mechanism of classical control theory into the model, which helps to reflect the interaction between rumor spreaders and information supervision. Further we apply a time delay factor to give investors access to transparent information and change their behavior. Subsequently, the stability of the rumor disappearance equilibrium and the rumor existence equilibrium are analyzed and the condition for the system undergoes a Hopf-bifurcation is given. The mathematical arguments are subjected to numerical simulations to present the ideal case scenarios. The results suggest that, increase the general strength of information supervision and the proportion coefficient associated with the infected population in the short-term delay are conducive to better control.
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