Abstract

This paper investigates rumor dissemination dynamics with generalized nonlinear incidence in multilingual environments. We propose a novel stochastic modeling framework that integrates age structure, mandatory isolation mechanisms, and media intervention. Firstly, a deterministic model is constructed by coupling ordinary differential equations (ODEs) and partial differential equations (PDEs), followed by a thorough analysis of the positive invariant set of the model solutions. Secondly, we further establish a relevant stochastic differential system to account for environmental randomness in networks, and prove the existence and uniqueness of its global positive solution. Subsequently, using Itô’s formula and the strong law of large numbers, several sufficient conditions for the disappearance of rumors are derived. Meanwhile, based on the Khasminskii method, the existence of a unique stationary distribution is analyzed under the continuous spread of rumors. Finally, the theoretical findings are verified through numerical simulations, which demonstrate that strengthening isolation intervention can markedly reduce the peak size of rumor spread and accelerate rumor extinction. Meanwhile, real case data from the Weibo platform further verify the favorable practical adaptability of the proposed model.

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