A Perturbation-Theoretic Model for Fact-Checker Deployment in Dynamic Disinformation Networks

Disinformation undermines public trust and weakens democratic institutions. It is without doubt that effective interventions are necessary to mitigate these risks. Counter narratives based on empirical evidence assist in limiting the dissemination of false information and preserve the integrity of public discourse. In this paper, we present a perturbation-based framework that integrates message passing algorithms to model and optimize the deployment of factcheckers in social media networks. Instead of removing key influential accounts that spread disinformation, we dynamically introduce fact-checking nodes at optimal times. We analyze how small perturbations in network structure affect global disinformation spread, incorporating a message passing mechanism to iteratively track belief evolution across users. The proposed framework leverages activation strategies based on belief thresholds and network acceleration metrics, ensuring that fact-checkers intervene only when it is necessary. We validate the effectiveness of our method through extensive simulations, demonstrating its capability to suppress disinformation while preserving network stability.