Modeling the long term effects of thermoregulation on human sleep

•Math model of human sleep stages incorporating effects of ambient temperature.•Temperature-dependent quantities promote REM sleep in an opportunistic manner.•Model is used to investigate long-term effects of sleep away from thermoneutrality.•Model indicates that dynamics may be more complicated at other temperatures.•REM quantities relate quadratically to ambient temperatures away from thermoneutral. The connection between human sleep and energy exertion has long been regarded as part of the reasoning for the need to sleep. A recent theory proposes that during REM sleep, energy utilized for thermoregulation is diverted to other relevant biological processes. We present a mathematical model of human sleep/wake regulation with thermoregulatory functions to gain quantitative insight into the effects of ambient temperature on sleep quality. Our model extends previous models by incorporating equations for the metabolic processes that control thermoregulation during sleep. We present numerical simulations that provide a quantitative answer for how humans adjust by changing the normal sleep stage progression when it is challenged with ambient temperatures away from thermoneutral. We explore the dynamics for a single night and several nights. Our results indicate that including the effects of temperature is a vital component of modeling sleep.