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Model Mathematics

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Component: environment

Component: H1

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

Component: H2

\frac{d}{d time} (H2) = betaI H1 - (betaC H2)

Component: A

\frac{d}{d time} (A) = \{\begin{matrix} Amax \frac{1.0 - (ⅇ^{(- lamda) (time - t_on)})}{1.0 - (ⅇ^{(- lamda) (t_off - t_on)})} if time < t_off \lor time \geq t_on \\ Amax ⅇ^{(- alpha) (time - t_off)} if time \geq t_off \end{matrix}

Component: model_parameters

betaI = \frac{\log_{10} 2.0}{tauI} betaC = \frac{\log_{10} 2.0}{tauC} alpha = \frac{\log_{10} 2.0}{taualpha} lamda = \frac{\log_{10} 2.0}{taulamda}

Source: Derived from workspace Brown, Choe, Shanahan, Czeisler, 1997 at changeset da0e0bccce38.; This exposure was expired. A more up-to-date exposure is available, or view related resources.

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A mathematical model of diurnal variations in human plasma melatonin levels