MEDELLIN, Colombia—As 21-year-old Jarvis Sanchez fled Venezuela—walking hours through dangerous informal border crossings, packing into hotel rooms with 20 other people and clinging to the backs of speeding trucks—he could barely even think about the global pandemic playing out around him.

“There were things way scarier than COVID,” Sanchez said. “When you’re constantly under threat, when you’re on a truck driving at such fast speeds, and so many other things, you almost forget about it.” ...