# Model Mathematics

### Component: r

$ddtime r = Ir - k6 ⁢ r Ir = 0.0 if time ≥ 0.0 ∧ time ≦ 90.0 10.0 if time ≥ 91.0 ∧ time ≦ 92.0 0.0 if time ≥ 93.0 ∧ time ≦ 113.0 10.0 if time ≥ 114.0 ∧ time ≦ 115.0 0.0 if time ≥ 116.0 ∧ time ≦ 136.0 10.0 if time ≥ 137.0 ∧ time ≦ 138.0 0.0 if time ≥ 139.0 ∧ time ≦ 159.0 10.0 if time ≥ 160.0 ∧ time ≦ 161.0 0.0 if time ≥ 162.0 ∧ time ≦ 252.0 10.0 if time ≥ 253.0 ∧ time ≦ 254.0 0.0 if time ≥ 255.0 ∧ time ≦ 275.0 10.0 if time ≥ 276.0 ∧ time ≦ 277.0 0.0 if time ≥ 278.0 ∧ time ≦ 298.0 10.0 if time ≥ 299.0 ∧ time ≦ 300.0 0.0 if time ≥ 301.0 ∧ time ≦ 321.0 10.0 if time ≥ 322.0 ∧ time ≦ 323.0 0.0 otherwise$

### Component: s

$ddtime s = Is - k7 ⁢ s$

### Component: f

$ddtime f =- k1 ⁢ r + c ⁢ f + k2 + k3 ⁢ phi_b_s ⁢ 1.0 - f phi_b_s = 1.0 1.0 +ⅇ-log10⁡ 1.0 ⁢ s - sb delta_b$

### Component: h

$ddtime h = j1 ⁢ k4 + k5 ⁢ 1.0 - phi_r_s ⁢ r + c ⁢ f - k8 ⁢ h phi_r_s = 1.0 1.0 +ⅇ-log10⁡ 1.0 ⁢ s - sr delta_r$

### Component: model_parameters

$Is = 10.0 if time > 0.0 ∧ time ≦ 90.0 0.0 if time > 90.0 ∧ time ≦ 180.0 10.0 if time > 180.0 ∧ time ≦ 270.0 0.0 if time > 270.0 ∧ time ≦ 360.0 0.0 otherwise$
Source
Derived from workspace Macgregor, Leng, 2005 at changeset 6c915634a4f2.
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