Mathematical Modeling Sheds Light on Sleep Patterns Across Life Stages

Understanding why babies tend to nap unpredictably, adolescents often sleep late, and older adults wake up early has long challenged scientists. A groundbreaking study from the University of Surrey utilizes mathematical models to explain these common sleep behaviors. The research primarily focuses on the two-process model (2PM) of sleep regulation, first proposed in the 1980s, which describes sleep as the result of two interacting factors: the increasing sleep pressure during wakefulness and the near 24-hour rhythm governed by our internal body clock.

By analyzing and simulating this model mathematically, researchers discovered how these internal processes influence sleep patterns in various age groups. For instance, the concept called the "Devil's staircase" helps explain the irregular napping habits observed in certain developmental stages of infants, while the model also extends to other species, indicating a fundamental biological mechanism.

Furthermore, the team integrated the effects of light exposure into their mathematical framework. Light significantly influences the body’s internal clock, and their combined model clarifies how environmental factors like bright evening light can push sleep timings later, particularly in teenagers who naturally experience a slower buildup of sleep pressure. This explains why adolescents often stay awake longer and wake up later.

Interestingly, the study suggests that the earlier waking times seen in older adults may not solely be due to changes in their circadian clock. Instead, these shifts might stem from altered interactions among different sleep-regulating systems, affected by aging, environment, and individual differences.

Professor Anne Skeldon, the study's lead author, emphasizes that this mathematical approach opens new avenues for understanding sleep issues. It offers hope that tailored interventions, like adjusting light exposure or routines, can improve sleep health on a personal level. The models demonstrate how minor environmental or behavioral modifications can significantly impact sleep patterns, paving the way for more personalized sleep therapies.

Using nonlinear oscillator systems—representing sleep-wake cycles, internal clocks, and light-dark exposure—the researchers simulated how modern routines, such as late-night screen use and inconsistent schedules, disrupt natural sleep rhythms. These insights highlight the importance of environmental management and individual differences in achieving better sleep quality.