The celebrated 1980 announcement that smallpox had been eradicated was made using the following definition of eradication: "Permanent reduction to zero of the worldwide incidence of infection caused by a specific agent as a result of deliberate efforts: intervention measures are no longer needed." Public health around the world works with this definition of "eradication," setting it as a goal for other infectious disease control programs. The definition is simple. Its application, however, has produced long-running and complex public health campaigns that threaten the commitment of funders, health care providers, and governments. In this paper, the authors demonstrate the disease-specific challenges of eradication through the example of the Global Polio Eradication Initiative (GPEI). While many deem eradication worth its high costs because it is the end of morbidity and mortality from a disease, it does not mean the end of disease control efforts. Public health must be prepared for the possibility of disease reoccurrence in the form of undetected natural reservoirs of disease, lab leaks from stored samples, bioterror attacks using stolen samples, and the synthetic recreation of microbes. This paper clarifies the role of reoccurrence prevention in eradication, calling for its addition in the definition of eradication.