Component-Based Prediction of Epidemic Prevalence in Directed Social Networks

Predicting epidemic spreading in directed social networks is a core challenge at the intersection of social computing and epidemic dynamics, as real-world social interactions are characterized by inherent directionality and structural heterogeneity of social groups. Traditional epidemic prediction models based on undirected networks fail to effectively capture the complexity of directed social networks. To bridge this gap, we partition directed networks into four functional social components: the Giant Strongly Connected Component (GSCC), Giant In-component (GIN), Giant Out-component (GOUT), and Tendrils. For each component, an infection contribution function is defined based on its topological role and transmission capability. We further propose a novel component-based epidemic prediction model that formulates the global fraction of infected nodes as a weighted sum of individual component contributions, which is influenced by the multinomial probability distribution of random infection sources. Extensive simulations conducted on directed ER networks validate the effectiveness of the proposed model across SI, SIS, and SIR epidemic models. Results show that the predicted values are highly consistent with simulation outcomes, and the model can accurately capture the expected epidemic prevalence (the fraction of infected nodes) in directed social networks. This research not only enriches the theoretical framework of social network epidemiology from a computational sociology perspective, but also provides a practical computational tool for epidemic forecasting and social intervention in real social systems.