Parents are beginning to vaccinate their children again following a sharp decline in the wake of a paper that linked the MMR jab to autism.
In 2001, the Irish infant vaccination rate fell to 69pc.
Dr Suzanne Cotter, a specialist in public health medicine at the Health Protection Surveillance Centre, said vaccination rates are beginning to recover.
"What we saw was a massive drop in the uptake of MMR vaccinations, especially in certain parts of the community," the doctor said.
"This corresponded with a big upsurge in the number of cases of measles, including three associated deaths, and this directly resulted from the decline in immunisation."
Dr Cotter said the optimal rate of vaccination for "herd immunity" was 95pc by the age of 24 months; this could mean the total eradication of the diseases here.
"We're getting there. There has been a renewed drive to remind parents to get their children vaccinated.
"The vaccine is very, very effective and safe," she said.
HSE figures show there were 4,242 cases of potentially fatal measles, mumps or rubella in the seven years between 1997 and 2003.
However, as the effect of a reduced level of immunisation took hold, the number more than doubled to 8,708 between 2004 and 2010.
There were also significant disease outbreaks, including more than 1,600 reported cases of measles in Ireland in 2000, with three associated deaths.
In 2009 there was a major outbreak of mumps, with 3,619 cases reported. The disease can lead to meningitis.
Following the publication of a research paper by disgraced English doctor Andrew Wakefield in the Lancet, there was an international collapse in MMR vaccination.
The paper was published in February 1998 and linked the MMR jab to bowel disease and autism.
However a 2010 investigation by the British General Medical Council (GMC) branded Dr Wakefield dishonest and irresponsible.