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

Area of Science:

• Mathematical modeling
• Epidemiology
• Control theory

Background:

• Rumor propagation models are essential for understanding information diffusion.
• Existing models often lack multilingual considerations and stochastic disturbances.
• Controlling rumor spread requires robust strategies accounting for real-world uncertainties.

Purpose of the Study:

• To propose and analyze a multi-lingual rumor propagation model with white noise.
• To investigate the dynamics, equilibria, and stability of the proposed model.
• To design and validate a stochastic optimal control strategy for rumor suppression.

Main Methods:

• Development of a deterministic multi-lingual rumor propagation model.
• Analysis of rumor-free and rumor-spreading equilibria and basic reproduction number (R0).
• Formulation of a stochastic model with white noise and examination of its global solution uniqueness and asymptotic behavior.
• Design of a stochastic optimal control strategy.
• Numerical simulations for validation.

Main Results:

• Identification of rumor-free and rumor-spreading equilibria and calculation of R0 in a multilingual context.
• Proof of the uniqueness of the global positive solution for the stochastic model.
• Analysis of the model's asymptotic behavior near steady states.
• Demonstration of the effectiveness of the stochastic optimal control in suppressing rumor spread.
• Validation of theoretical findings through numerical simulations.

Conclusions:

• The proposed multi-lingual stochastic rumor propagation model provides a robust framework for analyzing information diffusion under uncertainty.
• Stochastic optimal control is a viable strategy for mitigating the spread of rumors in complex linguistic environments.
• Numerical simulations confirm the theoretical results, highlighting the model's practical applicability.