To live in a world without diseases, is one of the oldest dreams of the men. But this objective is certainly impossible, because new diseases appear regularly.

At first, what is eradication ?
The WHO distinguishes three types of « eradications » :
- the damming up of a disease, which consists in reducing the mortality caused by the disease. This type of operation must be continual, to maintain the obtained results.
- the elimination of a disease, i.e. reduction to zero of the mortality in a given geographical area. There too, an action must be maintained to avoid a reappearance.
- the real eradication, which consists in eliminating a disease from all planet. So that the disease is regarded as eradicated, there shouldn't be any later action : disappearance must be final.
Moreover, these three operations relate to only the « infectious » diseases, i.e. due to a parasite, a bacterium or a virus. One thus excludes for example the genetic diseases or cancers.

The example of variola :
This very old disease (it was already present in ancient Egypt) probably appeared in Africa and in Asia then spread itself in Europe in Sixth century, because of the seat of Mecque into 572, and America in Sixteenth century, transported by the European colonists. In Europe, it reappeared every ten years and killed 10 000 to 20 000 people, of which a fifth of babies.
The first vaccines, obtained starting from cows variola, appear in 1796. The programme of eradication of variola was launched by WHO in 1950 (two years after its creation). It was estimated whereas it was enough to vaccinate 85 % of the world population to make disappear the disease. But at the end of 20 years, the program was a failure. This was particularly due to the fact that certain populations, not very accessible, were not vaccinated. One then changed strategy to vaccinate in priority the populations those where one announced cases. It was this time a success and WHO announced the eradication of variola in 1979, the last case having been announced in 1977 in Somalia.

One has several examples of dammings up and eliminations of diseases, sometimes without vaccine. For example, benefitting from its insular insulation, Great Britain eradicated the rage simply with measurements of forty. However, the eradication is a much more difficult operation. Variola is besides the only eradicated disease at the beginning of the third millenium. That is explained by its relative facility to being fought : one has an effective vaccine and, especially, these symptoms (appearance of pustules, often final blindness) make it easily identifiable, which is far from being the case of the majority of the diseases.
Moreover, one cannot be definitively certain that variola is really eradicated. This is why WHO still preserves important stocks of vaccines (different from the one that was used for the eradication).
Some diseases will probably never be removed, at least not by methods of vaccination. An example is the influenza : the virus which causes it transfers almost each year, and the vaccines lose their effectiveness regularly. In the same way, one can note the difficulties of eradication of paludism (or malaria): this disease is carried by a parasite (psalmodium) transported by the mosquitos. One thus tried to remove the mosquitos in the concerned areas by pulverizing DDT but the mosquitos became resistant to this insecticide. For this type of reasons, it is important for the programs of eradication to be international : a country which would carry out only an attempt with a bad strategy would be likely to create resistant hearths.

In spite of these difficulties, other diseases appear in the program of WHO for the eradication, for example the poliomyelitis (500 000 patients every year). There are also many programs of elimination, like measles (in the United States and Europe)