a_{t,x} = a_{t-\Delta t,x} + \Delta t \cdot \left ( s \cdot \left ( \frac{a_{t-\Delta t,x}^2 + b_a}{b_{t-\Delta t,x} + c_{t-\Delta t,x}} \right ) - r_a a_{t-\Delta t,x} + D_a \frac{\partial^2 a_t}{\partial x^2} \right )

b_{t,x} = b_{t-\Delta t,x} + \Delta t \cdot \left ( s \cdot a_{t-\Delta t,x}^2 - r_b \cdot a_{t-\Delta t,x} + b_b + D_b \frac{\partial^2 b_t}{\partial x^2} \right )

c_{t,x} = c_{t-\Delta t,x} + \Delta t \cdot \left ( r_c \cdot a_{t-\Delta t,x} - r_c \cdot c_{t-\Delta t,x} + D_c \frac{\partial^2 c_t}{\partial x^2} \right )