Anytime the vax rate for measles is below 85%, outbreaks occur. Every time, illegals or not. It’s a fact.
Anytime you allow exemptions to mandatory vaccination campaigns you will get outbreaks among the unvaccinated, and some of the vaccinated too that are the 3-5% who immunity didn’t take. So the choice is force the 95% penetration rate by force of law and back it up with force of violence or accept periodic outbreaks. The right has chosen the latter given the rights propensity for religious zealotry as well.