\frac{dx_{1}}{dt} = \left(1 \cdot k_{7} \cdot k_{1} \cdot x_{1} \cdot \left(1 - k_{2} \cdot x_{1}\right) + -1 \cdot k_{7} \cdot k_{3} \cdot x_{1} \cdot x_{2}\right) / k_{7}\\
\frac{dx_{2}}{dt} = 1 \cdot k_{7} \cdot \left(k_{4} \cdot x_{2} \cdot \left(1 - k_{5} \cdot x_{2}\right) + k_{6} \cdot x_{1} \cdot x_{2}\right) / k_{7}