Emotional propagation research aims to discover and show the laws of opinion evolution in social networks. The short-term observation of the emotional propagation process for a predetermined time window ignores situations in which users with different emotions compete over a long diffusion time. To that end, we propose a dynamic emotional propagation model based on an independent cascade. The proposed model is inspired by the interpretable factors of the reinforced Poisson process, portraying the “rich-get-richer” phenomenon within a social network. Specifically, we introduce a time-decay mechanism to illustrate the change in influence over time. Meanwhile, we propose an emotion-exciting mechanism allowing prior users to affect the emotions of subsequent users. Finally, we conduct experiments on an artificial network and two real-world datasets—Wiki, with 7194 nodes, and Bitcoin-OTC, with 5881 nodes—to verify the effectiveness of our proposed model. The proposed method improved the F1-score by 3.5% and decreased the MAPE by 0.059 on the Wiki dataset. And the F1-score improved by 0.4% and the MAPE decreased by 0.013 on the Bitcoin-OTC dataset. In addition, the experimental results indicate a phenomenon of emotions in social networks tending to converge under the influence of opinion leaders after a long enough time.