Ebola is a hemorrhagic fever. It kills about half of those who contract it. It sometimes, though not always, leads to uncontrollable bleeding. But it's difficult to contract. The only way to catch Ebola is to have direct contact with the bodily fluids — vomit, sweat, blood, feces, urine or saliva — of someone who has Ebola and has begun showing symptoms.
Modern public-health systems can manage diseases that travel through bodily fluids. The techniques are laborious, but known. You isolate those who have contracted the disease, or might have contracted it. You find out who's been near them. You screen them for the disease. You isolate anyone who shows symptoms. You do this until the disease is stamped out. It works. And modern public-health systems know how to do it.