Dynamic Analysis of a Cross-Lingual Coupled Rumor Propagation Model with Response Delay in Online Social Networks.

Publication date: Jun 15, 2026

As online social networks (OSNs) evolve into multilingual ecosystems, rumors can cross language boundaries through translation and bilingual re-expression, increasing governance difficulty. To characterize cross-lingual coupling and response delay, this study proposes a time-delay S2LCHR dynamical model for bilingual OSNs, in which the coupled spreader state C describes cross-lingual coupled rumor transmission and a fixed response delay represents cross-lingual comprehension, judgment, and re-expression. The basic reproduction number R0 is derived using the next-generation matrix method. Lyapunov analysis, the Routh-Hurwitz criterion, characteristic-equation analysis, and numerical simulations are combined to examine equilibrium stability, delay-induced Hopf bifurcation, parameter sensitivity, and social-impact indicators. A real-world aggregate trend-fitting case study using English-Spanish COVID-19-related tweet data is further conducted to assess empirical plausibility. The results show that R0 determines the threshold between rumor extinction and persistence in the delay-free system, while an excessive response delay can destabilize the rumor-prevailing equilibrium and induce bounded oscillatory behavior. Sensitivity and social-impact analyses indicate that α and β promote rumor persistence, whereas σ and φ associated with state C are key inhibitory factors. These findings suggest that coupled spreaders should be prioritized in cross-lingual rumor governance.

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Semantics

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