The rapid advancement of information technology has redefined distance education as a fundamental component of modern education systems. The extensive deployment of online learning platforms has further propelled this transformation, catalyzing innovation in educational methodologies while simultaneously presenting novel challenges and demands in the realm of community engagement. In the sphere of online learning, considerable research has been conducted on the efficacy of these platforms. However, studies specifically dedicated to the effective cultivation and maintenance of community engagement through these platforms are notably scarce. Recognized as pivotal for educational outcomes, student satisfaction, and enduring academic success, community engagement within the context of distance education warrants comprehensive exploration. This study delves into this exploration by developing a dynamic model of interaction and a coupled network evolutionary game model that incorporates the nuances of social group dynamics. Initiating with a critical review of existing literature on community engagement in distance learning, the study identifies prevalent limitations. These limitations include an over-reliance on qualitative data, the absence of dynamic analyses, and an oversight of the intricacies of group interactions. To bridge these gaps, we propose a data-driven interaction dynamics model tailored for online learning platforms. Additionally, we suggest a network evolutionary game model that considers the interplay among social groups. These models collectively deepen our understanding of the evolution of community engagement over time and elucidate how both individual and collective behaviors influence the communal health of online learning environments.