Modelling and analysis of rumour propagation based on stochastic optimal control

Abstract

Considering the decay of information with time, this paper proposes a rumour propagation model based on information intervention. Applying optimal control and stochastic noise propagation, we explain the influence of the information intervention mechanism on the dynamics of rumour propagation. First, we calculate the equilibrium points and basic reproduction number of our model. Second, this paper selects the intensity of information intervention and the control rate of spreaders as control variables and explores the dynamics of rumour propagation in deterministic and stochastic systems under optimal control. Finally, to support the theoretical results, we verify the stationarity condition through numerical simulation and analyse the changes in different populations. Additionally, we compare the performance of the deterministic and stochastic models to each other, as well as with existing models.