Sleep and circadian rhythms

Our lives have an approximately daily (circadian) rhythm of wake and sleep, feeding and fasting. These rhythms are part of a complex, hierarchical, coupled oscillator system with rhythmicity generated within nearly every cell of our bodies and coordinated by the so-called 'master' clock in the suprachiasmatic nucleus of the brain. There is increasing evidence that disrupting our biological rhythms is bad for our health and a contributory factor to obesity, cardiovascular disease, mood disorders and cognitive decline.

We use mathematical models at many different scales to help understand the structure of this complex system – from detailed models of gene transcription/translation cycles at the molecular level through to human scale models of the sleep/wake cycle.

Research leads

Analysis of mathematical models of sleep/wake regulation: Non-smooth dynamics and bifurcations

Alarm clock.

The most influential model of sleep/wake regulation is the two process model. This model postulates that sleep and wake occur as a result of the interaction of two oscillators, one describing circadian rhythmicity (the body clock) and one describing sleep homeostasis (sleep need). This model has formed the theoretical framework for sleep researchers for the last 30 years, and forms the backbone of recent `physiological' models of sleep. The two process model is an interesting example of a non-smooth dynamical system.

Anne Skeldon, with PhD student Matt Bailey, are investigating the bifurcations and dynamics of the two process model, which can be represented as a circle map. In collaboration with Paul Glendinning (University of Manchester), they have also analysed a broader class of `threshold models' of which the two process model is an example.

Interactive models

Man yawning whilst sat in kitchen looking at his laptop

We are interested in developing interactive tools to help explain the interactions of sleep, light and social rhythms. Take a look at an early example of this work from Anne Skeldon.

Sleep, maths and technology

Anne Skeldon and Derk-Jan Dijk are interested in developing new data analytics/mathematical modelling techniques for extracting meaning from data, particularly in the context of sleep and circadian rhythms. Some of their work is funded by the Dementia Research Institute, which aims to develop technological solutions to help people live in their own homes as long as possible. They also collaborate with researchers in the Centre for Vision Speech and Signal Processing.

Biomathematical models of fatigue

When people are sleep deprived, they make poorer decisions, are slower to react and are more at risk of having accidents. In the workplace, employers have a duty to manage fatigue risk – a particular issue for shift work. Anne SkeldonDerk-Jan Dijk, and Steven Lockley (Surrey Sleep Research Centre) develop and apply biomathematical models of fatigue. Read a report on fatigue, alertness and risk prediction for shift workers from a recent collaboration with TFL.

Find us


School of Mathematics and Physics
University of Surrey
See map