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Model Mathematics

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Component: environment

Component: H1

\frac{d}{d time} (H1) = (- (beta_I H1)) + A

Component: H2

\frac{d}{d time} (H2) = beta_I H1 - (beta_C H2)

Component: A

A = \{\begin{matrix} A_max \frac{1.0 - (ⅇ^{(- lamda) (time - t_on)})}{1.0 - (ⅇ^{(- lamda) (t_off - t_on)})} if time < t_off \land time \geq t_on \\ A_max ⅇ^{(- alpha) (time - t_off)} if time \geq t_off \\ 0.0 otherwise \end{matrix}

Component: model_parameters

beta_I = \frac{\ln 2.0}{tau_I} beta_C = \frac{\ln 2.0}{tau_C} alpha = \frac{\ln 2.0}{tau_alpha} lamda = \frac{\ln 2.0}{tau_lamda}

Source: Derived from workspace Brown, Choe, Shanahan, Czeisler, 1997 at changeset 0a3138798f53.

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A mathematical model of diurnal variations in human plasma melatonin levels