From the original article: "Fourty-six of the 48 confirmed cases (of measles) are in children 10 years old or younger."
These are almost certainly not illegal immigrants. These are American citizens, born in the USA.
According to CNN (excluding the specific situation in the Somali community, who are not recent migrants anyway):
Families who refuse to vaccinate their children are:
Wealthier than average, with annual incomes more than four times the poverty level.
Non-Hispanic white.
Married couples in English-speaking households.
Educated, with college degrees.
Covered by private health insurance.
Source:
http://www.cnn.com/2015/02/03/health/the-unvaccinated/
I can find nothing online to support the idea that the majority of adult Somali immigrants are undocumented or arrived illegally. Considering they had to fly to the US, this seems unlikely.
Also, speaking of undocumented migrants, Mexico's vaccination rate in children is 97 percent, compared to the US's 92 percent. So if anyone's spreading disease, it'd be unvaccinated American vacationers spreading it south of the border, not illegal Mexican immigrants.
Source:
http://data.worldbank.org/indicator/SH.IMM.MEAS
Edited to add:
Far as I can tell, most Somalis (and other foreign-born African-Americans) likely emigrated legally either through the Refugee Act of 1980 or through the Diversity Visa Program, which was an act passed in 1990. They are required to be fully vaccinated:
https://travel.state.gov/content/visas/en/immigrate/vaccinations.html
There was also a second influx of Somali refugees, who arrived in 2014, but they came through refugee camps, and would likewise have been completely up to date on their vaccinations. (Like these people:
http://www.startribune.com/new-somali-refugee-arrivals-in-minnesota-are-increasing/281197521/#1)
There are roughly 11 million unauthorized immigrants in the US, most of whom are from Mexico, followed by South America and Asia. Almost all the countries they come from have higher vaccine compliance rates than the US.