A PROBABILISTIC THRESHOLD MODEL OF THE SPREAD OF MEME-VIRUS IN SOCIAL MEDIA

Abstract

This article is devoted to an approach to quantitatively describing and forecasting the mechanisms of information dissemination in modern social networks. Under current conditions, digital communication platforms have created an ideal environment for the instantaneous spread of disinformation, fake news, and manipulative “meme-viruses,” which poses a serious threat to national information security and social stability. Traditional deterministic threshold models of collective behavior, despite their fundamental importance, do not fully capture the stochastic nature of real-world social interactions, while widely used metrics, such as the PageRank algorithm, are limited to estimating the static centrality of nodes, completely ignoring the temporal dynamics of influence propagation. To overcome these limitations, this work proposes a stochastic modification of the linear threshold model that systematically accounts for the random nature of the number of active contacts and the significant variability in the influence strength of individual informational messages. The methodological foundation of the model is based on assumptions regarding the Poisson distribution of the number of active neighbors of a network node and the uniform distribution of the influence intensity exerted by each of them. Applying the apparatus of mathematical statistics has made it possible to derive a complete analytical expression for the probability of activating a social network node without conducting extremely resource-intensive simulation experiments. An important feature of the developed approach is its fundamental difference from static graph metrics: the proposed model describes the dynamics of the system’s phase transition from local information assimilation to global cascading propagation through the temporal evolution of probabilities, directly modeling individuals’ cognitive barriers. The practical value of the research is realized in three areas. Firstly, the model allows for an accurate assessment of the effectiveness of information and psychological operations based on the dynamics of shifts in the perception threshold across various social groups. Secondly, the analysis identifies critical points at which a slight change in the intensity of the influence triggers a phase transition, which is crucial for the preventive suppression of disinformation cascades. Third, the proposed concept can serve as a tool for assessing the effectiveness of countermeasures.