Detecting and preventing outbreaks of mosquito-borne diseases such as Dengue and Zika in Brasil and other tropical regions has long been a priority for governments in affected areas. Streaming social media content, such as Twitter, is increasingly being used for health vigilance applications such as flu detection. However, previous work has not addressed the complexity of drastic seasonal changes on Twitter content across multiple epidemic outbreaks. In order to address this gap, this paper contrasts two complementary approaches to detecting Twitter content that is relevant for Dengue outbreak detection, namely supervised classification and unsupervised clustering using topic modelling. Each approach has benefits and shortcomings. Our classifier achieves a prediction accuracy of about 80\% based on a small training set of about 1,000 instances, but the need for manual annotation makes it hard to track seasonal changes in the nature of the epidemics, such as the emergence of new types of virus in certain geographical locations. In contrast, LDA-based topic modelling scales well, generating cohesive and well-separated clusters from larger samples. While clusters can be easily re-generated following changes in epidemics, however, this approach makes it hard to clearly segregate relevant tweets into well-defined clusters.