Structured Sleep Augmentation: A Mathematical Model for Individual Cognitive Recovery Through Daytime Naps

A significant portion of the population experiences fragmented non-restorative sleep. Examples include individuals whose circadian rhythms are misaligned with conventional work or classroom schedules and older adults who experience repeated nighttime sleep interruptions associated with bladder-related needs. Such sleep disruption results in daytime cognitive impairment, affecting memory, productivity, and mood. This paper introduces a mathematical model for developing individual-specific structured daytime nap schedules designed to augment nighttime sleep and reduce the cognitive consequences of sleep disruption. The schedule defines a time-specific nap window that includes both sleep latency and nap duration, with nap duration adjusted to the individual’s characteristics and sleep history. The objective is not simply to increase daytime sleep, but to identify a nap strategy that restores cognitive performance while minimizing adverse effects on subsequent nighttime sleep and late-day napping. The model predicts relative cognitive ability as a function of age, sleep history, and daytime work/break experience. It incorporates a nonlinear relationship between nap duration and cognitive recovery, characterized by a disproportionately large recovery effect during the early stages of a nap. Consequently, model-derived nap schedules are relatively short. The model also incorporates algorithms for optimizing structured workplace and classroom breaks to maximize sustained cognitive productivity. Potential applications include education, workplace scheduling, and mission-critical work. Initial model validation was performed by comparing model predictions with results reported in a wide range of publications.