Foreigners aren't necessarily illegal immigrants. To systematically describe every foreigner as an "illegal alien" would be a xenophobic black-and-white fallacy. In fact, Daniel Salmon in the article you posted explicitly stressed that the people involved in these outbreaks are not illegal immigrants, but rather people who have enough wealth to travel legally. Many, many people have the resources for international travel, and travelling around the world is always associated with a risk of disease transmission. The solution is to vaccinate the population and render them immune to these outbreaks rather than shut off everyone travelling to America. Had the kids who interacted with Patient Zero been vaccinated, the disease would have remain contained. So no, illegal immigrants have little, if any, relevance to these outbreaks.