Animal Disease and Disaster Prevention, Surveillance, and Rapid Response Act of 2018 This bill establishes the Animal Disease and Disaster Prevention, Surveillance, and Rapid Response Program within the Department of Agriculture (USDA) to support activities to prevent, detect, and rapidly respond to animal pests and diseases affecting the economic interests of the livestock industry and related U.S. industries. The bill also establishes a National Livestock Vaccine Bank within USDA to leverage, as appropriate, the mechanisms and infrastructure that have been developed for the management, storage, and distribution of the National Veterinary Stockpile. The vaccine bank must maintain a sufficient quantity of animal vaccine, antiviral, or therapeutic products: (1) to appropriately respond to the most damaging animal diseases affecting human health and the economy, and (2) be capable of deployment within 24 hours of an outbreak of the animal disease.