Social media platforms, such as Twitter, are crucial resources to obtain situational information during disease outbreaks. Due to the sheer volume of user-generated content, providing tools that can automatically classify input texts into various types, such as symptoms, transmission, prevention measures, etc., and generate concise situational updates is necessary. Apart from high classification accuracy, interpretability is an important requirement when designing machine learning models for tasks in medical domain. In this article, we provide annotated epidemic-related datasets with labels of information types and rationales, which are short phrases from the original tweets, to support the assigned labels. Next, we introduce a trustworthy approach for the automatic classification of tweets posted during epidemics. Our classification model is able to extract short explanations/rationales for output decisions on unseen data. Moreover, we propose a simple graph-based ranking method to generate short summaries of tweets. Experiments on two epidemic-related datasets show the following: 1) our classification model obtains an average of 82% Macro-F1 and better interpretability scores in terms of Token-F1 (20% improvement) than baselines; 2) the extracted rationales capture essential disease-related information in the tweets; 3) our graph-based method with rationales is simple, yet efficient for generating concise situational updates.