PISCO, Peru—Several nights a week, 4-year-old Sofia Felices jolts awake in tears and calls out for her mother, who used to cuddle her youngest daughter in bed. Sofia’s mom died from the coronavirus in April, so that job now falls to the girl’s great-aunt, Janette Navarro.

“She cries and she cries,” said Ms. Navarro, who has three children of her own but has become caregiver to her niece’s five children in this coastal fishing city. “She screams with her eyes closed, ‘I want my mommy. I want my mommy.’ ”