i guess dominicans refer to lots of intestinal parasite infections as amoeba. there are also many species of amoeba that cause amoebiasis. basically you get infected by injecting food and/or water contaminated with the feces of another carriers. their stool contains cysts that then develop in the intestines of an infected person.
because amoebas live off the "leftovers" passing the intestines they may happily stay there for a while and not cause any symptoms, even for years. they can, however damage intestinal walls, liver and even stomach cavity. treatments are not necessarily successful. full course of treatment can last close to a month. you just know that people here would not continue to take their medication for that long, seeing that you start to feel better within two days or so.
you could say that it is possible to get rid of amoebas completely but it takes dedication. in addition to this many get reinfected continuously, especially if they live in poor and dirty barrios where the risk of contamination of the water is high.