A Stochastics Branching Process Model for Analyzing Rumor Spreading in Social Media Networks

This paper introduces a stochastics branching process model as an analytical tool to study the dynamics of rumor spreading in social media networks. Employing a specialized first-order conditional probability generating function method, we derive a second-order linear regressive equation to characterize the intricate dynamics of rumor propagation. The validation of our model's accuracy is established through a comparative analysis between numerical computations and Monte Carlo simulations. Additionally, we present a derived threshold condition for the spread control factor, also known as the reproduction rate. Numerical simulation results demonstrate that the interactions and responses within social platforms contribute to the rapid onset of rumors while simultaneously diminishing the maximum density of spreaders and the overall scale of the rumors. To provide further insights, we explore analogies between rumor-spreading models and epidemic models. In conclusion, our proposed stochastics branching process model not only enhances our understanding of rumor spreading in social media networks but also offers a valuable framework for investigating the interplay between various factors influencing the dynamics of information diffusion.