Speaker
Description
Insomnia is one of the most prevalent sleep disorders, associated with increased risk of conditions ranging from diabetes to heart disease \cite{b23}. Yet, much about its physiological causes and processes is still far from understood.
Mathematical modelling has had an important role to play in understanding the process of sleep itself. Some of the most important of these contributions have been the two-process model, composing sleep as interacting circadian and homeostatic drives \cite{b82}, the flip-flop model, inspired by neurological processes to model a ‘natural’ switch between the sleeping and waking state \cite{s01}, and physiology-inspired network models, incorporating REM and non-REM sleep states through physically realistic networks \cite{f08}.
In this talk our new three-process model for insomnia-like awakenings will be presented, introducing a new wakefulness drive to the two-process model of sleep. This will include sensitivity analysis of the original model and an exploration of its dynamical regimes, and the new insights these provide into the mechanisms by which insomnia can arise. These results will be further contextualised with dynamical analysis of key existing sleep models, demonstrating the need for this new approach to incorporate insomnia.
Finally, a new framework for mathematically representing insomnia based on this model will be discussed, including its implications for further modelling developments to understand more insomnia features.
Bibliography
@article{b23,
title = {Diurnal rhythms of wrist temperature are associated with future disease risk in the {UK} {Biobank}},
volume = {14},
issn = {2041-1723},
url = {https://www.nature.com/articles/s41467-023-40977-5},
doi = {10.1038/s41467-023-40977-5},
language = {en},
number = {1},
urldate = {2026-03-15},
journal = {Nature Communications},
author = {Brooks, Thomas G. and Lahens, Nicholas F. and Grant, Gregory R. and Sheline, Yvette I. and FitzGerald, Garret A. and Skarke, Carsten},
month = aug,
year = {2023},
pages = {5172},
}
@article{b82,
title = {A two process model of sleep regulation},
volume = {1},
issn = {0721-9075},
number = {3},
journal = {Human Neurobiology},
author = {Borbély, A. A.},
year = {1982},
keywords = {Human Biological Rhythms, Sleep, Models},
pages = {195--204},
}
@article{s01,
title = {The sleep switch: hypothalamic control of sleep and wakefulness},
volume = {24},
copyright = {https://www.elsevier.com/tdm/userlicense/1.0/},
issn = {01662236},
shorttitle = {The sleep switch},
url = {https://linkinghub.elsevier.com/retrieve/pii/S0166223600020026},
doi = {10.1016/S0166-2236(00)02002-6},
language = {en},
number = {12},
urldate = {2026-03-15},
journal = {Trends in Neurosciences},
author = {Saper, Clifford B and Chou, Thomas C and Scammell, Thomas E},
month = dec,
year = {2001},
pages = {726--731},
}
@article{f08,
title = {Modeling the impact of impulsive stimuli on sleep-wake dynamics},
volume = {78},
copyright = {http://link.aps.org/licenses/aps-default-license},
issn = {1539-3755, 1550-2376},
url = {https://link.aps.org/doi/10.1103/PhysRevE.78.051920},
doi = {10.1103/PhysRevE.78.051920},
language = {en},
number = {5},
urldate = {2026-03-15},
journal = {Physical Review E},
author = {Fulcher, B. D. and Phillips, A. J. K. and Robinson, P. A.},
month = nov,
year = {2008},
pages = {051920},
}
