<p>Over the past twenty years, topic modeling has gradually become popular as a powerful tool, extracting useful and meaningful latent representations from large texts. Research on topic evolution, focusing on the representation of changes in topics over time, has begun to attract extensive attention in the fields of information retrieval and data mining. The dynamic topic model is a classical model for topic evolution. It assumes all topics exist throughout the entire time period, overlooking the fact that topics that were previously important are no longer considered, and new topics can also emerge. To address this issue, we propose a novel Bayesian sparse dynamic topic model, utilizing a spike-and-slab prior distribution to capture topic birth and death. The results demonstrate that our proposed model can effectively estimate both the topic distribution and topic sparsity at the same time. Furthermore, simulations and empirical studies on two real-world datasets demonstrate that our proposed model outperforms the classical dynamic topic model and provides rich semantic information on focused topics.</p>