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Model Mathematics

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Component: environment

Component: v

Qv = \frac{Qmax}{1 + ⅇ^{\frac{- (Vv - theta)}{sigma}}}

\frac{d}{d time} (Vv) = \frac{v_vm Qm + D - Vv}{\frac{tau_v}{3600}}

Component: a

Qa = \frac{Qmax}{1 + ⅇ^{\frac{- (Va - theta)}{sigma}}}

Va = Vao

Component: m

Qm = \frac{Qmax}{1 + ⅇ^{\frac{- (Vm - theta)}{sigma}}}

\frac{d}{d time} (Vm) = \frac{v_maQao + v_mv Qv - Vm}{\frac{tau_m}{3600}}

Component: H

\frac{d}{d time} (H) = \frac{mu Qm - H}{chi}

Component: D

D = v_vc C + v_vh H

C = c0 + \cos (omega time)

omega = \frac{2 π}{24}

Component: model_parameters

Source: Derived from workspace Phillips 2007 at changeset bd4ea8932605.

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A quantitative model of sleep-wake dynamics based on the physiology of the brainstem ascending arousal system