A Stochastic Duplex SEIR Model on Heterogeneous Networks: Threshold Dynamics, Stationary Distribution, and Wasserstein Robust Control

This study examines how misinformation can persist when broadcast exposure and social feedback reinforce one another under stochastic platform conditions. Text classifiers and single-layer cascade models omit latent exposure, reply-driven amplification, random attention shocks, and uncertainty in intervention response. A stochastic duplex SEIR model is developed on heterogeneous networks, with an information exposure layer for broadcast and recommendation channels and a social feedback layer for replies, discussion, and amplification. The analysis combines degree-weighted mean-field equations, next-generation threshold calculations, Lyapunov stability arguments, Fokker–Planck linear noise approximation, Milstein simulation, and Wasserstein distributionally robust control. Theoretical results provide positivity, stochastic threshold conditions, extinction and persistence regimes, and sufficient conditions for stationary behavior and robust control stability. Numerical simulations show extinction–persistence transitions, cross-layer resonance, noise-induced threshold shifts, stationary bands, control cost–safety trade-offs, and sensitivity to unidentifiable stochastic parameters. A CoAID tweet–reply case study maps public interaction traces to observable duplex indicators, including tweet–reply densities, propagation elasticities, coupling proxies, and classifier features. Duplex observable features improve over a single-layer public data baseline, while model-assisted stochastic features add modest gains in the available public projection. Structural fitting of the stochastic duplex process would require time-stamped user-level multiplex trajectories, recommendation exposures, and intervention logs. The case study also clarifies the data granularity needed for future platform-level calibration and operational readiness. The framework supports data-informed platform governance by linking propagation thresholds, algorithmic down-ranking, reply thread moderation, intervention cost, and robustness bounds within a common threshold control language for practical settings.