Stochastic threshold model for the spread of memetic viruses in social media

• Date: 2026
• Main Authors: Качинський, А. Б., Ланде, Д. В., Іванюта, С. П.
• Format: Article
• Language: Ukrainian
• Published: Інститут проблем реєстрації інформації НАН України 2026
• Subjects: probabilistic threshold model; cybersecurity; information security; social networks; information influence; bimodal degree distribution; cascading spread
• Online Access: https://drsp.ipri.kiev.ua/article/view/363137
• Journal Title: Data Recording, Storage & Processing

Modern social media have become a key environment for the rapid diffusion of information, where disinformation and manipulative narratives spread with extreme intensity, shaping public opinion and coordinating collective actions. Traditional analytical tools, such as the PageRank and HITS algorithms, focus on assessing the static centrality of nodes and are unable to capture the temporal dynamics of social contagion. Deterministic threshold models, despite their theoretical value, ignore the stochastic nature of real-world communications, which significantly limits their predictive accuracy in highly uncertain digital environments. This research proposes a stochastic modification of the classical linear threshold model that accounts for the randomness in the number of active contacts and the heterogeneity in the influence strength of individual messages. Based on the assumptions of a Poisson distribution for active neighbors and a uniform distribution for influence intensity, an analytical expression for the node activation probability is derived using normal approximation and Laplace transforms. This enables a shift from computationally expensive simulation experiments to a rigorous mathematical description of social contagion processes, formalizing users' cognitive barriers and the nonlinearity of cascading interactions. A comparative analysis of the proposed approach with classical structural ranking algorithms reveals their fundamental ontological limitations. While PageRank and HITS capture the static state of graph topology through eigenvectors of adjacency matrices, the probabilistic threshold model describes the dynamics of a system's phase transition — from local spread to a global information cascade. The model is capable of identifying critical «tipping points», where minimal changes in influence intensity lead to qualitative shifts in network behavior, a feature fundamentally inaccessible to deterministic centrality metrics. The proposed framework can be applied in the fields of information and cybersecurity, as well as strategic communications. It enables the prediction of uncontrolled disinformation spread, quantitative assessment of countermeasure effectiveness, and modeling of the "Overton Window" mechanism through the dynamics of threshold distributions. The transition from static topological centrality to dynamic stochastic approaches opens new opportunities for real-time monitoring and neutralization of information threats, as well as for building interdisciplinary models of societal cognitive resilience. Tabl.: 1. Refs: 10 titles.