The number of measles cases associated with an outbreak in western Texas has grown to 259, with 36 cases reported over the last three days, according to new data released Friday.

Almost all of the cases are in unvaccinated individuals or in individuals whose vaccination status is unknown. Two cases have occurred in persons vaccinated with two doses, according to the Texas Department of State Health Services (DSHS). Breakthrough infections, when a vaccinated person is infected are rare, as the measles vaccine provides up to 97% protection after 2 doses.

At least 34 people have been hospitalized so far.

In the Texas outbreak, children and teenagers between ages 5 and 17 make up the majority of cases, with 115, followed by children ages 4 and under comprising 86 cases, according to the data.

DSHS said in its update that it expects more cases to be confirmed in the area and in surrounding communities.

Two likely measles deaths have been reported so far in the U.S. One is a confirmed death associated with measles, while the other has been definitively linked to the measles virus but the cause of death officially remains under investigation.

The first reported death was an unvaccinated school-aged child in Texas, according to the DSHS. The child did not have any known underlying conditions, according to the department.

The Texas death was the first measles death recorded in the U.S. in a decade, according to data from the Centers for Disease Control and Prevention.

Another probable measles death was recorded last week after an unvaccinated New Mexico resident tested positive for the virus.

Gaines County is the epicenter of the Texas outbreak, with 174 cases confirmed among residents, according to the DSHS. State health data shows the number of vaccine exemptions in Gaines County has grown dramatically in the last dozen years.

In 2013, roughly 7.5% of kindergartners in the county had parents or guardians who filed for an exemption for at least one vaccine. Ten years later, that number rose to more than 17.5% – one of the highest in all of Texas, according to state health data.

The Centers for Disease Control and Prevention (CDC) has confirmed hundreds of cases in at least 12 states so far this year, including Alaska, California, Florida, Georgia, Kentucky, New Jersey, New Mexico, New York City, Pennsylvania, Rhode Island, Texas and Washington

The majority of nationally confirmed cases are in people who are unvaccinated or whose vaccination status is unknown. Of those cases, 4% are among those who received just one dose of the MMR (measles, mumps and rubella) inoculation and 2% are among those who received the required two doses, according to the CDC.

Measles is one of the most contagious diseases known to humans. Just one infected patient can spread measles to up to nine out of 10 susceptible close contacts, according to the CDC.

Health officials have been urging anyone who isn’t vaccinated to receive the MMR vaccine.

The CDC currently recommends that people receive two vaccine doses, the first at ages 12 to 15 months and the second between 4 and 6 years old. One dose is 93% effective, and two doses are 97% effective, the CDC says. Most vaccinated adults don’t need a booster.

Measles was declared eliminated from the U.S. in 2000 due to the highly effective vaccination program, according to the CDC. However, CDC data shows vaccination rates have been lagging in recent years.

ABC News Youri Benadjaoud contributed to this report.