A disease is controlled if, by means of a public policy, the circulation of an infectious agent is restricted below the level that would be sustained by individuals acting independently to control the disease. A disease is eliminated if it is controlled sufficiently to prevent an epidemic from occurring in a given geographical area. Control and elimination are achieved locally, but a disease can only be eradicated if it is eliminated everywhere. Eradication is plainly a more demanding goal, but it has two advantages over control. First, the economics of eradication can be very favourable when eradication not only reduces infections but also avoids the need for vaccinations in future. Indeed, when eradication is feasible, it will either pay to control it to a fairly low level or to eradicate it. This suggests that, from an economics perspective, diseases that are eliminated in high-income countries are prime candidates for future eradication efforts. Second, the incentives for countries to participate in an eradication initiative can be strong; indeed they can be even stronger than an international control programme. Moreover, high-income countries typically benefit so much that they will be willing to finance elimination in developing countries. Full financing of an eradication effort by nation-states is not always guaranteed, but it can be facilitated by a variety of means. Hence, from the perspective of economics and international relations, eradication has a number of advantages over control. The implications for smallpox and polio eradication programmes are discussed.