Dynamics of a stochastic epidemic-like rumor propagation model with generalized nonlinear incidence and time delay

Abstract

Rumors are abnormal children of public opinion, they usually arise with environmental crisis and have serious negative functions. Hence, how to control rumor propagation has become an urgent topic for the government. Since the communication between people in the real world is inevitably interfered by random factors, and time delay exists in the process of rumor propagation not only influence rumor-forwarding individuals by rumor-hesitant individuals but also in government decision-making. Based on these premises, we propose a stochastic delayed rumor propagation model with generalized incidence function. By setting the suitable Lyapunov functions, we show that the asymptotic behavior of stochastic rumor spreading model is constrained by some conditions. Finally, our analytical results are supported by numerical simulations. The results show that (1) the increase of noise intensity in social environment will reduce rumor propagation; (2) time delay has an impact on rumor propagation to a certain extent. Extending the thinking time may reduce the number of rumor-forwarding individuals and even lead to the disappearance of rumors; (3) improve scientific literacy and accelerate rumor refutation (i.e. reduce the value of β), strengthen rumor suppression (i.e. increase the value of γ) can effectively control rumor transmission.