Raju Sarker had been sick in his dormitory for two days, staying away from the Singapore construction site where he worked. He had a headache and chills. His stomach didn’t feel right. He was exhausted.

But on a phone call with his wife on Feb. 5, the 39-year-old put on a brave face. She was back home in Bangladesh, two months from giving birth. Mr. Sarker, hoping for a baby girl, had been thinking about what his firstborn would call him: Baba, or perhaps Abba.

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