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The outbreak of the novel coronavirus, COVID-19, has become one of the most severe pandemics in human history. In this paper, we propose to leverage social media users as social sensors to simultaneously predict the pandemic trends and suggest potential risk factors for public health experts to understand spread situations and recommend proper interventions. More precisely, we develop novel deep learning models to recognize important entities and their relations over time, thereby establishing dynamic heterogeneous graphs to describe the observations of social media users. A dynamic graph neural network model can then forecast the trends (e.g. newly diagnosed cases and death rates) and identify high-risk events from social media. Based on the proposed computational method, we also develop a web-based system for domain experts without any computer science background to easily interact with. We conduct extensive experiments on large-scale datasets of COVID-19 related tweets provided by Twitter, which show that our method can precisely predict the new cases and death rates. We also demonstrate the robustness of our web-based pandemic surveillance system and its ability to retrieve essential knowledge and derive accurate predictions across a variety of circumstances. Our system is also available at http://scaiweb.cs.ucla.edu/covidsurveiller/ . This article is part of the theme issue ‘Data science approachs to infectious disease surveillance’.