Dynamic Analysis of the Multi-Lingual S2IR Rumor Propagation Model Under Stochastic Disturbances

This paper proposes a multi-lingual S2IR rumor propagation model with white noise disturbances, aiming to study its dynamics and stochastic optimal control strategies. Firstly, a deterministic model is developed within a multi-lingual environment to identify rumor-free and rumor-spreading equilibria and calculate the basic reproduction number R0. Secondly, a stochastic model incorporating white noise perturbation is developed, and the uniqueness of its global positive solution is examined. Meanwhile, the asymptotic behaviors of the model's global solution near the steady states are discussed. Thirdly, the stochastic optimal control is designed to suppress the spread of rumors. Finally, the correctness and validity of the theoretical results are verified through numerical simulation.