Ongoing COVID-19 pandemic poses many challenges to the research of artificial intelligence. Epidemics are important in network science for modeling disease spread over networks of contacts between individuals. To prevent disease spread, it is desirable to introduce prioritized isolation of the individuals contacting many and unspecified others, or connecting different groups. Finding such influential individuals in social networks, and simulating the speed and extent of the disease spread are what we need for combating COVID-19. This article focuses on the following topics, and discusses some of the traditional and emerging research attempts: (1) topics related to epidemics in network science, such as epidemic modeling, influence maximization and temporal networks, (2) recent research of network science for COVID-19 and (3) datasets and resources for COVID-19 research.