An 11-year-old girl presents with a 6-week history of a persistent non-productive cough, low-grade fevers, malaise, and a 3-kg weight loss. Her blood work is notable for a peripheral eosinophil count of 3,500/mm³. A chest x-ray reveals bilateral, fluffy, patchy infiltrates located in the periphery of the lung fields, with clear central areas. What is the most likely diagnosis?