Jamila Begom and 6 of her kin share a modest bamboo-and-tarpaulin hut in a Bangladesh settlement that is now dwelling to just about a million Rohingya refugees from Myanmar. Structures in her camp—one of 34 in the settlement—are so close together she can listen to her neighbors whisper.

Ms. Begom has attempted not to leave the shelter considering the fact that March 26, when Bangladesh declared a nationwide lockdown to slow the spread of the new coronavirus.

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