Modeling Information Diffusion in Online Social Networks with Partial Differential Equations

This book presents a new mathematical approach to understanding information diffusion in online social networks, highlighting its applications and theoretical foundations.

In Modeling Information Diffusion in Online Social Networks with Partial Differential Equations, the authors explore the intersection of mathematics, social media analysis, and data science. They introduce a novel dynamic modeling approach that utilizes partial differential equations to effectively describe how information spreads across online social networks. This innovative method proposes a paradigm shift in understanding information diffusion, establishing a solid theoretical foundation for addressing various spatio-temporal modeling challenges that arise in the big-data era.

The core of the book focuses on utilizing the eigenvalues and eigenvectors of the Laplacian matrix associated with social networks to identify communities or clusters of users. By embedding these clusters in a Euclidean space, the authors develop mathematical models based on reaction-diffusion equations, which are informed by the intuitive social distances among the clusters. This approach not only enhances the modeling of information flow but also provides a framework for analyzing data from prominent social media platforms like Twitter.

The book further validates these models through real-world applications, including a detailed examination of the social media dynamics during the Egyptian revolution in 2011 and a predictive analysis of influenza prevalence. By combining mathematical rigor with practical insights, Modeling Information Diffusion in Online Social Networks with Partial Differential Equations offers a comprehensive resource for researchers and practitioners seeking to understand the complexities of information dissemination in today's digital landscape.