Think of a potential issue that could arise and I've probably dealt with it while abroad!
During my three years working in Perú with Davidson College, I dealt with serious physical injuries, serious illnesses, deaths in the family back in the US, homesickness, and students unhappy with their living arragements, etc. I've learned more valuable lessons than I could possibly enumerate.
While in Perú, students live with families who -- and this isn't an exaggeration -- treat their visitors like their very own children. Because of the immense importance of family in Latin American culture, this means that your students will, quite sincerely, have caring, concerned parents living with them. Moreover, these families have years of experience working with foreign students and have seen every problem that can arise.
While in Arequipa, Cusco, and Lima, we have access to a multitude of public and private hospitals, clinics, and specialists. We're never more than a short drive from whatever sort of assistance we might need. More importantly, Patrick and the program's Assistant Director live near the students and are available 24/7.
When we're traveling, we're accompanied by professional tour guides, guides who know their routes intimately and who always err on the side of caution. With the exception of a few days of travel to more remote areas, students will always have easy access to telephones and internet. And even when we're in those remote areas, we always travel prepared for emergency, equipped with first aid and knowledge of the nearest emergency facilities.