Stochastic IE2SR for multilingual rumor dynamics: varying contact rates on heterogeneous networks

Addressing the overlooked stochastic, language-specific interactions on heterogeneous networks, we put forward a multilingual stochastic IE2SR rumor model with variable contact rates. We first develop a deterministic IE2SR model and prove the existence and uniqueness of its equilibrium. Subsequently, we extend it to a stochastic version, deriving explicit conditions for rumor existence and extinction using the strong law of large numbers. Numerical simulations confirm our theoretical findings and reveal that both contact rates and stochastic noise significantly impact rumor thresholds, offering practical insights for rumor control in multilingual environments.