Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks

2025-07-17

AI Summary

This study investigates the spillover mechanism from social media topic engagement to offline protest mobilization, focusing on how cross-domain transmission rates and network topology influence the emergence of offline collective action. Method: We introduce the concept of a “cross-domain transmission critical threshold” and develop a stochastic dynamical model coupling online social networks with offline behavioral dynamics, analyzed theoretically via mean-field approximation and validated empirically. Contribution/Results: We find that offline protest outbreaks occur only when the online-to-offline transmission rate lies within an intermediate range—challenging single-domain modeling assumptions. Network density critically affects model accuracy: low-density networks require higher-order approximations, whereas high-density networks permit simplified models; however, excessive complexity degrades predictive performance on real-world networks. Our model accurately estimates the activity reproduction number and precisely forecasts the timing of surges in participation intensity, establishing a novel paradigm for modeling social movements in the digital age.

Technology Category

• Application Domains: Humanities & Computational Social Science
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior

Application Category

• Social Networks and Social Media: Applications and emergent phenomena
• Economics, Online Markets and Human Computation: Social networks and social learning
• Web Mining and Content Analysis: Models for Web evolution

Abstract

Social media is transforming various aspects of offline life, from everyday decisions such as dining choices to the progression of conflicts. In this study, we propose a coupled modelling framework with an online social network layer to analyse how engagement on a specific topic spills over into offline protest activities. We develop a stochastic model and derive several mean-field models of varying complexity. These models allow us to estimate the reproductive number and anticipate when surges in activity are likely to occur. A key factor is the transmission rate between the online and offline domains; for offline outbursts to emerge, this rate must fall within a critical range, neither too low nor too high. Additionally, using synthetic networks, we examine how network structure influences the accuracy of these approximations. Our findings indicate that low-density networks need more complex approximations, whereas simpler models can effectively represent higher-density networks. When tested on two real-world networks, however, increased complexity did not enhance accuracy.

Problem

• Model spillover from online engagement to offline protest
• Analyze transmission rate between online and offline domains
• Examine network structure influence on model accuracy

Innovation

• Coupled online-offline stochastic modeling framework
• Mean-field approximations for network dynamics
• Critical transmission rate range analysis