Accurate caseload prediction is of considerable importance for the regulation and control of government agencies. Many studies on the environmental factor of caseload using time series analysis (TSA) are available. However, minimal attention has been provided to the interaction factor, which is substantially complex at the microlevel of social networks. A new model, graphical evolution game theory model (GEGT) is proposed in this paper to describe case formation based on the graphical evolutionary game theory. A parameter estimation method is developed on the basis of the GEGT model, and the estimated parameters are used for prediction. Furthermore, a fusion algorithm (GETS) that combines the predictions given by the proposed GEGT and TSA models is introduced to improve the caseload prediction accuracy. The fusion algorithm GETS highlights the accuracy of the GEGT model in the early stage of prediction. This algorithm integrates the precision of the TSA model in the later stage, thus balancing model strengths. The contribution of this paper lies in its proposed caseload prediction method based on the GEGT model to analyze the interaction factor and design a novel fusion algorithm GETS. The proposed model in this work is more accurate than the existing model on the actual dataset.