I actually will be surprised if the family totally vanishes, it is possible but I think the amount of screaming from some quarters along with "interventions" from certain politicians etc are likely to limit that; rather they will keep them isolated and with no news unless or until one of them ends up in the hospital and then "family privacy" will prevent many updates.
As for getting sick, probably some (if not all) of them will but viruses are funny things as are human beings, it isn't 100 percent certain that anyone WILL be infected with something, just that they have a high chance of doing so. If this was not the case, every single person in the Liberian slums would likely be ill or dead now; many are but not everyone. Even in the Black Death of the 14th century there were people who for no obvious reason caught it in either of the two first waves that happened 12 years apart. Today we know that some of these people carried a favored gene mutation (as did some of those who survived getting ill) that also in a weird twist of fate, helps prevent or limit the damage from HIV/AID's. Other people may just not have caught it for whatever-reason that we don't understand; even in North America 10 percent of the people survived (at least) even if up to 90 percent died from European diseases. So most Native Americans alive to today, had ancestors who were from that ten percent...
So while it is unlikely, it is possible that Duncan's girlfriend might get lucky and not get sick; obviously some people living in similar circumstances in West Africa do not become infected even after caring for family members. But one of the children who maybe barely touched "Uncle Duncan's" hand might become very ill and die, diseases are like that, unpredictable. You can make very educated guesses but you still can't predict them for certain.
Finally, I've noticed that the majority of people I've seen (and seen in reports) in Africa who are ill appear to be age 40 and under; I am sure some elderly people do become ill and die but if the area were not such a horrific "hot zone" looking to see if there might be previous illnesses that would not have to be Ebola but something that turns out to provide limited protection. This DID turn out to be the case in the 1918 flu epidemic and was also the case in the second wave of the Black Death in the 14th century, though of course we can't be as certain on the 14th century stuff except that the majority of deaths were children and teenagers in the second round.
I will however, but happy but surprised if no one from the family catches it, ultimately while his behavior is understandable, Duncan will go down in history as a very selfish man...