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Model Mathematics

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Component: environment

Component: h

\frac{d}{d time} (h) = - (Tn + Tp)

Component: n

\frac{d}{d time} (n) = Tn - (lamda_n n)

Component: p

\frac{d}{d time} (p) = Tp - (lamda_p p)

Component: s1

\frac{\partial}{\partial time} (s1) = (K1 n - (lamda_1 s1)) + D1 s1

Component: s2

\frac{d}{d time} (s2) = (K2 n - (lamda_2 s2)) + D2 s2

Component: Tn

Tn = \{\begin{matrix} eta_n h (s1 - s1_min) if s1_min < s1 \\ 0.0 otherwise \end{matrix}

Component: Tp

Tp = eta_p h E s2

Component: E

\frac{d}{d time} (E) = fw (s2_- s2_min) - (lamda_E E)

Component: fw

fw = \frac{1.0}{1.0 + ⅇ^{\frac{- (x - c)}{w}}}

Component: s2_

s2_= s2

Component: model_parameters

Source: Derived from workspace Nevo, Golding, Neumann, Schwartz, Akselrod, 2004 at changeset 4926e8383778.

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Nevo et al.'s 2004 mathematical model of autoimmunity.