Uniform Information Coverage Drives Mean-Field Convergence and Reverse Influence in Multiplex Epidemic–Belief Systems

Epidemic trajectories are jointly determined by biological transmission dynamics and the social processes governing belief formation and behavioral adherence. This paper introduces a coupled epidemic–belief–compliance model embedded on a multiplex network to investigate how misinformation and fact-checking interact to shape infection outcomes. The framework combines an SEIR disease process operating on a physical contact layer with a bounded-confidence belief diffusion model on an information layer, capturing the opposing effects of misinformation propagation and corrective messaging. Through analytical derivation and large-scale Monte Carlo simulations (N = 10³–10⁴, 3,460 realizations), we show that uniformly distributed fact-checking meaningfully reduces epidemic peaks (by 26–39%), maintains higher compliance levels, and stabilizes belief dynamics compared to influencer-targeted interventions. Uniform coverage suppresses local network correlations, allowing the coupled system to converge toward a tractable mean-field representation; peak infection variance scales as Var ∝ N⁻¹, confirming self-averaging behavior as population size increases. A Graph Neural Network surrogate offers no predictive benefit over a Random Forest baseline (R² ≈ 0.98), further supporting the conclusion that fine-grained topological structure becomes uninformative under broad information coverage. We identify and formally characterize a reverse influence mechanism: well-informed peripheral nodes function as belief anchors that stabilize the attitudes of highly connected influencers, counteracting misinformation accumulation at network hubs. This feedback loop explains why uniform coverage outperforms hub-targeted strategies even in polarized or clustered networks, where targeted approaches are conventionally assumed to hold an advantage. These results provide a theoretical basis for designing public health communication strategies that prioritize inclusiveness and consistency over precision targeting, with direct implications for misinformation-resilient epidemic response at population scale.