MOSUL, Iraq — In the last square mile of Islamic State territory in this city, terrified families trapped in their basements are bracing for a final ferocious showdown.

As many as 150,000 residents are crammed into Mosul’s Old City, as Islamic State fighters fortify their positions in the warren of narrow streets and alleyways.

With no safe drinking water, sickness and disease are spreading as food and medicine run dangerously low. Mortars fired by security forces trying to dislodge the militants “rain down,” while airstrikes tear down buildings in the packed neighborhood, one resident said by phone from the besieged area.

But attempting to escape is just as dangerous, with militants determined to keep civilians as human shields and gunning down hundreds who have tried to flee in recent weeks — men, women and children.