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.

Rumor spreading and control in both homogeneous and heterogeneous networks with guidance mechanism

“…To control the spread of rumors, it is suggested to increase the government's efforts in isolating the initial rumor and encourage the public to become debunkers. Furthermore, the nonlinear propagation rate was considered [22][23][24][25][26]. Chen et al discussed a novel SEIR delayed propagation model with saturation incidence in heterogeneous networks and found the optimal control strategy [22].…”

A Deterministic and Stochastic Fractional-Order ILSR Rumor Propagation Model Incorporating Media Reports and a Nonlinear Inhibition Mechanism

“…Moreover, it is more reasonable to utilize the nonlinear propagation function by introducing the psychological factor, which effectively depicts the crowding effect and more complex behaviors on rumor propagation [9,10]. Many scholars employed the saturation functions to reflect the nature of certain phenomena and obtain more accurate results in related rumor propagation [11][12][13]. Thus, we incorporate a saturated incidence rate in our model.…”