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

TL;DR

This paper develops stochastic and mean-field models to analyze how online social media engagement can lead to offline protests, highlighting the importance of transmission rates and network structure in predicting surges.

Contribution

It introduces a coupled online-offline protest model with mean-field approximations, providing insights into critical transmission rates and network effects on offline mobilization.

Findings

Critical transmission rate range for offline protests

Simpler models suffice for dense networks

Model accuracy varies with network structure

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.