Team:KU Leuven/Modeling/Top
1-D continuous model
The Keller segel model used is [1] : $$\frac{\partial A}{\partial t} = D_a \bigtriangledown^2 A + k_A A(1 - \frac{A}{k_{p}}),$$ $$\frac{\partial B}{\partial t} = D_b \bigtriangledown^2 B + \bigtriangledown (X(B,H,R) \bigtriangledown R)+ k_B B(1 - \frac{B}{k_{p}}), $$ $$ \frac{\partial R}{\partial t} = D_r \bigtriangledown^2 B + k_r A - k_lossH R $$ $$\frac{\partial H}{\partial t} = D_h \bigtriangledown^2 B + k_h A - k_lossR H . $$ With: $$ X(B,H,R) = -B K_{c1} (K_{c2} H(t,:)/R(t,:)). $$ When $a \ne 0$, there are two solutions to \(ax^2 + bx + c = 0\) and they are $$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$
References
Reference 1
