A Mathematical Model of the Human Sleep Wake System

A model and analysis of the human sleep/wake system is presented. The model is derived using the known neuronal groups, and their various projections, involved with sleep and wake. Inherent in the derivation is the existence of a slow time scale associated with homeostatic regulation, and a faster time scale associated with the dynamics within the sleep phase. A significant feature of the model is that it does not contain a periodic forcing term, common in other models, reflecting the fact that sleep/wake is not dependent upon a diurnal stimulus. Once derived, the model is analyzed using a linearized stability analysis. We then use experimental data from normal sleep-wake systems and orexin knockout systems to verify the physiological validity of the equations.