Sleep patterns in infancy and early childhood vary greatly and change rapidly during development. In adults, sleep patterns are regulated by interactions between neuronal populations in the brainstem and hypothalamus, driven by the circadian and sleep homeostatic processes. However, the neurophysiological mechanisms underlying the sleep patterns and their variations across infancy and early childhood are poorly understood. We investigated whether a well-established mathematical model for sleep regulation in adults can model infant sleep characteristics and explain the physiological basis for developmental changes. By fitting longitudinal sleep data spanning 2 to 540 days after birth, we inferred parameter trajectories across age. We found that the developmental changes in sleep patterns are consistent with a faster accumulation and faster clearance of sleep homeostatic pressure in infancy and a weaker circadian rhythm in early infancy. We also find greater sensitivity to phase-delaying effects of light in infancy and early childhood. These findings reveal fundamental mechanisms that regulate sleep in infancy and early childhood. Given the critical role of sleep in healthy neurodevelopment, this framework could be used to pinpoint pathophysiological mechanisms and identify ways to improve sleep quality in early life.