Social media platforms have become integral to modern society, shaping communication, culture, and even political landscapes. The sheer volume and complexity of data generated by these platforms necessitate sophisticated analytical techniques. Mathematical modeling provides a powerful framework for understanding and predicting social media phenomena, from the spread of information and influence to the dynamics of online communities and the evolution of social networks. Social media has upgraded communication and influenced many parts of social behavior, business strategies and global connectivity’s by which vast opportunities and challenges arouses to study and understanding about user’s behavior and content dynamics. Mathematical modeling serves as a fundamental tool for understanding, analyzing, and predicting patterns in this dynamic and complex domain. This paper explores the intersection of mathematical modeling and social media analytics, examining key areas of research, challenges, and future directions.