Social media platforms, such as Twitter, are attracting a growing number of people with diverse demographic characteristics to share and obtain information about various topics. As a result, these platforms have become one of the main targets for practitioners and decision-makers from various fields, such as politics and public health, to study public opinion and at the same time to spread their messages. Two challenges in utilizing social platforms as a means of communication are how to craft and how to deliver a message such that it reaches a great number of audiences and keeps them engaged. Addressing these problems is hardly possible without thoroughly analyzing how a piece of information goes viral on a social platform. This doctoral dissertation aims to model the dissemination of health-related information on Twitter from various perspectives. First, I investigate driving forces of the general public's engagement on social media during health emergencies. The two contributors that I consider are 1) real-world events, such as announcements by World Health Organization, and 2) the role of highly active users and also those who receive great attention from other users. Second, I systematically model and investigate information cascades through the retweeting processes of tweets. My analysis in this part reveals that the propagation patterns of tweets carrying misinformation are different from those containing true information. I propose a framework to operationalize and test the hypothesis "misinformation tweets are propagated differently from true information tweets." Finally, based on the differences that I discover by analyzing (mis)information propagation, I propose a feature-rich machine learning model to identify misinformation on Twitter. The above three perspectives offer a holistic overview of the main challenges and prospective/feasible solutions for beneficially applying social media in public health.