(CNN) The human papillomavirus vaccine was first recommended for adolescent girls in the United States in 2006. Since that time, the prevalence of the cancer-causing virus has been dropping among young women, according to a new study.

Researchers at the Centers for Disease Control and Prevention compared the rates of HPV infection in women 14 to 34 years of age during the years before the vaccine was recommended, between 2003 and 2006, with the most recent years for which data are available, 2009 to 2012.

Among girls 14 to 19 years old, rates of infection with the four types of HPV included in the 4vHPV vaccine decreased from 11.5% to 4.3%. There was also a drop, although smaller, in women 20 to 24 years old, from 18.5% to 12.1%. Among the older groups, women ages 25 to 29 and 30 to 34, the prevalence of these HPV types did not change and was about 12% and 9%, respectively.

"These results are very encouraging and show the effectiveness of the vaccine," said Dr. Lauri E. Markowitz, a medical epidemiologist at the CDC and lead author of the study, which was published Monday in the journal Pediatrics. "Eventually we expect to see decreases in HPV in older groups as women who were young (enough to get the vaccine) age," Markowitz added.

Among the 14- to 24-year-old women in the study who were sexually active, rates of infection with the HPV types in the vaccine was only 2.1% among those who were vaccinated, compared with 16.9% among their unvaccinated counterparts.

The CDC Advisory Committee on Immunization Practices recommends the three-dose HPV vaccine for girls, and as of 2011 also boys, 11 to 12 years of age. The vaccine is recommended for women and men up to ages 26 and 21, respectively.

The researchers found that 51% of girls 14 to 19 years old reported having received at least one dose of the HPV vaccine. Rates were 33% and 15% among the women 20 to 24 and 25 to 29, respectively. Among the 30- to 34-year-olds, only 3% said they had gotten the vaccine because they were generally too old to receive it by the time it was first recommended.

There are signs that rates of HPV vaccination are on the rise. National surveys reported that the number of girls 13 to 17 years of age who received at least one dose of the HPV vaccine climbed from 44% in 2009 to 54% in 2012.

More vaccine coverage coming

In keeping with the trend toward greater vaccine coverage, an earlier study by Markowitz and her colleagues found that the prevalence of HPV types was 5.1% among 13- to 17-year-olds between 2007 and 2010, the first years after the vaccine was available, slightly higher than the 4.3% in the current study among 14- to 19-year-olds between 2009 and 2012. The waning prevalence of HPV among adolescent girls in more recent years is probably the result of more adolescent girls getting the HPV vaccine, Markowitz said.

However, among women in their 20s and 30s, there was no decrease in the prevalence of HPV between 2007 and 2010, compared with 2003 to 2006, because these women were already too old to receive the vaccine when it became available.

It may be possible for HPV to go the way of other largely eliminated infectious diseases in the United States such as measles, but only if vaccination rates improve, Markowitz said. The CDC is working with many groups, including large medical organizations such as the American Cancer Society, to increase knowledge among health care professionals and give them guidance for talking with families about the vaccine.

"Like all vaccines, having a strong recommendation by the clinician is one of greatest predictors of getting vaccinated," Markowitz said.

It's important for patients and parents to think of the HPV vaccine as another one of the vaccines that you get, like those for measles, mumps and rubella, said Dr. Sarah Feldman, co-director of ambulatory gynecologic oncology at Brigham and Women's Hospital.

There have been some safety concerns , though unfounded, about the HPV vaccine, but the bigger issue is probably that parents shy away from vaccines for young children that protect against sexually transmitted diseases, Feldman said. But as people become more familiar with the vaccine, Feldman hopes there will be less focus on how HPV is transmitted. "We don't talk about sexual activity as a way of transmitting hepatitis B, we just give the vaccine," so when children get older and become sexually active, they are protected, she said.

"More and more, it's becoming clear that this is a cancer prevention vaccine, and if we could get 100% of our boys and 100% of our girls vaccinated, we could probably eradicate the worst HPV types," Feldman said.

New HPV vaccine

The current study did not detect a difference in rates of infection with HPV types other than the types present in the 4vHPV vaccine, or another vaccine called 2vHPV. Both vaccines include the two HPV types responsible for 66% of cervical cancers in the United States. Markowitz suspects that it is still possible that some cross-protection is happening, if, for example, other HPV types look similar enough to the types in the vaccine that the immune system recognizes them.

However, this question is largely a moot point now that many people in the United States are receiving a new HPV vaccine called 9vHPV, approved in 2014, which protects against a total of nine HPV types, said Dr. Rebecca B. Perkins, associate professor of obstetrics and gynecology at Boston University School of Medicine and Boston Medical Center.

Join the conversation See the latest news and share your comments with CNN Health on Facebook and Twitter.

The Advisory Committee on Immunization Practices included 9vHPV as an option in this year's immunization schedule , along with 4vHPV and 2vHPV. The 9vHPV vaccine protects against five additional cancer-causing HPV types, giving it the potential to prevent about 90% of HPV-associated cancers.

But even with the earlier forms of HPV vaccines, "the vaccine is doing exactly what it's supposed to," Perkins said. The current study is a "really strong call to get people vaccinated," she added.

HPV vaccination could benefit more groups than in the current study, and in more ways. The CDC researchers are planning to look at the rates of HPV infection in males after the vaccine was recommended for boys in 2011. "You should expect to see similar effects in men because trials showed the vaccine worked as well in men as women," Perkins said.