Dengue fever remains a significant public health challenge globally, necessitating effective surveillance of key data such as dates, locations, and case counts. This study evaluates the potential of large language models and com-pares their performance with deep learning methods in predicting epidemiological data from dengue fever case reports. Although initially hypothesized that large language models would outperform due to their advanced capabilities, the empirical results indicated that deep learning approaches were more precise. Specifically, deep learning models, such as TextCNN and LSTM, achieved superior F1-scores of 0.998 and 0.997, respectively, compared to large language models, which achieved 0.882 for GPT-4 Zero-shot and 0.634 for Few-shot. Despite this, the rapid deployment and scalability of LLMs highlight their potential utility in real-time public health emergencies. The findings suggest that while deep learning methods currently outperform large language models in precision, targeted fine-tuning could enhance the utility of large language models in public health surveillance. This research supports the continued development of AI technologies to improve global health responses, leveraging both deep learning and large language model capabilities for effective disease management.