Computer audition (CA) has experienced a fast development in the past decades by leveraging advanced signal processing and machine learning techniques. In particular, for its noninvasive and ubiquitous character by nature, CA-based applications in healthcare have increasingly attracted attention in recent years. During the tough time of the global crisis caused by the coronavirus disease 2019 (COVID-19), scientists and engineers in data science have collaborated to think of novel ways in prevention, diagnosis, treatment, tracking, and management of this global pandemic. On the one hand, we have witnessed the power of 5G, Internet of Things, big data, computer vision, and artificial intelligence in applications of epidemiology modeling, drug and/or vaccine finding and designing, fast CT screening, and quarantine management. On the other hand, relevant studies in exploring the capacity of CA are extremely lacking and underestimated. To this end, we propose a novel multitask speech corpus for COVID-19 research usage. We collected 51 confirmed COVID-19 patients' in-the-wild speech data in Wuhan city, China. We define three main tasks in this corpus, i.e., three-category classification tasks for evaluating the physical and/or mental status of patients, i.e., sleep quality, fatigue, and anxiety. The benchmarks are given by using both classic machine learning methods and state-of-the-art deep learning techniques. We believe this study and corpus cannot only facilitate the ongoing research on using data science to fight against COVID-19, but also the monitoring of contagious diseases for general purpose.