Dynamic analysis and optimal control of a reaction-diffusion rumor propagation model in multi-lingual environments

Abstract

The development of networking technologies has broken down the restrictions of language and region, greatly increasing the destructive power of rumors. To explore the influence of spatial factors on rumors, a new spatial distance on online social networks is first defined by considering friendship hops and the intimacy level among friends. On that basis, a novel reaction-diffusion SIR rumor spreading model with the general nonlinear propagation function is proposed in multi-lingual environments. Firstly, the global existence and ultimate boundedness of solutions are strictly proven. Theoretical analysis further reveals the existence of equilibrium points and the global stability of the rumor-free/prevailing equilibrium points of the proposed model. Secondly, an optimal control strategy with an education mechanism and a forced silence method is introduced to better curb rumor propagation. Moreover, the sensitivity analysis of the threshold is conducted to discuss the relative importance of model parameters on rumor propagation. Finally, some necessary numerical simulations are performed to verify the validity of the theoretical analysis.