Modelling the spillover from online engagement to offline protest: stochastic dynamics and mean-field approximations on networks
For researchers studying social mobilization, this provides a mathematical framework to quantify the spillover from online to offline protest, though the findings are incremental and domain-specific.
The paper proposes a coupled stochastic model linking online social media engagement to offline protest activity, deriving mean-field approximations to estimate the reproductive number and predict activity surges. It finds that the online-to-offline transmission rate must lie within a critical range for offline outbursts to occur, and that simpler models suffice for high-density networks.
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.