Epidemic outbreaks such as Coronavirus disease 2019 (COVID-19) impact the health of our society and bring significant disruptions to the US and the world. Each country has to dynamically adjust health policies, plan healthcare resources, control travels with little time latency to mitigate risks and safeguard the population. With rapid advances in health and information technology, more and more data are collected in the dynamically evolving process of epidemic outbreaks. The availability of data calls upon the development of analytical methods and tools to gain a better understanding of virus spreading dynamics, optimize the design of healthcare policies for epidemic control, and improve the resilience of health systems. This paper presents a holistic review of the system informatics approach, i.e., Define, Measure, Analyze, Improve, and Control (DMAIC), for epidemic response and management through the intensive use of data, statistics and optimization. Despite the sustained successes of system informatics in a variety of established industries such as manufacturing, logistics, services and beyond, there is a dearth of concentrated review and application of the data-driven DMAIC approach in the context of epidemic outbreaks. First, we define specific challenges posed by epidemic outbreaks to populational health, health systems, as well as economic challenges to different industries such as retailing, education and manufacturing. Second, we present a review of medical testing and statistical sampling methods for data collection, as well as existing efforts in data management and data visualization. Third, we discuss the importance to realizing the full potential of data for epidemic insights, and emphasize the need to leverage analytical methods and tools for decision support. Fourth, an epidemic brings imperative changes to health systems. We discuss the new trend of healthcare solutions to improve system resilience, including telehealth, artificial intelligence, resource allocation, and system re-design. In closing, prescriptive approaches are discussed to optimize the health policies and action strategies for controlling the spread of virus. We posit that this work will catalyze more in-depth investigations and multi-disciplinary research efforts to accelerate the application of system informatics methods and tools in epidemic response and risk management.