\frac{dx_{1}}{dt} = 0 / k_{23}\\
\frac{dx_{2}}{dt} = \left(1 \cdot 1 / k_{2} \cdot \left(1 - k_{6}\right) \cdot x_{1} + -1 \cdot 1 / k_{2} \cdot x_{2} + -1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot x_{2} \cdot \left(x_{3} + x_{10}\right) / x_{1} + -1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot x_{2} \cdot \left(x_{4} + x_{9} + x_{8}\right) / x_{1} + 1 \cdot 1 / k_{14} \cdot x_{5} + 1 \cdot 1 / k_{14} \cdot x_{6} + 1 \cdot 1 / k_{14} \cdot x_{11} + 1 \cdot 1 / k_{15} \cdot x_{7}\right) / k_{23}\\
\frac{dx_{3}}{dt} = \left(-1 \cdot 1 / k_{2} \cdot x_{3} + 1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot x_{2} \cdot \left(x_{3} + x_{10}\right) / x_{1} + -1 \cdot 365 / k_{13} \cdot x_{3}\right) / k_{23}\\
\frac{dx_{4}}{dt} = \left(-1 \cdot 1 / k_{2} \cdot x_{4} + 1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot x_{2} \cdot \left(x_{4} + x_{9} + x_{8}\right) / x_{1} + -1 \cdot 365 / k_{13} \cdot x_{4}\right) / k_{23}\\
\frac{dx_{5}}{dt} = \left(-1 \cdot 1 / k_{2} \cdot x_{5} + 1 \cdot 365 / k_{13} \cdot x_{3} + -1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot \left(1 - k_{8}\right) \cdot x_{5} \cdot \left(x_{4} + x_{9} + x_{8}\right) / x_{1} + -1 \cdot 1 / k_{14} \cdot x_{5}\right) / k_{23}\\
\frac{dx_{6}}{dt} = \left(-1 \cdot 1 / k_{2} \cdot x_{6} + 1 \cdot 365 / k_{13} \cdot x_{4} + -1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot \left(1 - k_{8}\right) \cdot x_{6} \cdot \left(x_{3} + x_{10}\right) / x_{1} + -1 \cdot 1 / k_{14} \cdot x_{6}\right) / k_{23}\\
\frac{dx_{7}}{dt} = \left(1 \cdot 1 / k_{2} \cdot k_{6} \cdot x_{1} + -1 \cdot 1 / k_{2} \cdot x_{7} + -1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot \left(1 - k_{7}\right) \cdot x_{7} \cdot \left(x_{4} + x_{9} + x_{8}\right) / x_{1} + -1 \cdot 1 / k_{15} \cdot x_{7}\right) / k_{23}\\
\frac{dx_{8}}{dt} = \left(-1 \cdot 1 / k_{2} \cdot x_{8} + 1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot \left(1 - k_{7}\right) \cdot x_{7} \cdot \left(x_{4} + x_{9} + x_{8}\right) / x_{1} + -1 \cdot 365 / k_{13} / \left(1 - k_{10}\right) \cdot x_{8}\right) / k_{23}\\
\frac{dx_{9}}{dt} = \left(-1 \cdot 1 / k_{2} \cdot x_{9} + 1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot \left(1 - k_{8}\right) \cdot x_{5} \cdot \left(x_{4} + x_{9} + x_{8}\right) / x_{1} + -1 \cdot 365 / k_{13} / \left(1 - k_{9}\right) \cdot x_{9}\right) / k_{23}\\
\frac{dx_{10}}{dt} = \left(-1 \cdot 1 / k_{2} \cdot x_{10} + 1 \cdot k_{4} \cdot \left(365 / k_{13} + 1 / k_{2}\right) \cdot \left(1 - k_{8}\right) \cdot x_{6} \cdot \left(x_{3} + x_{10}\right) / x_{1} + -1 \cdot 365 / k_{13} / \left(1 - k_{9}\right) \cdot x_{10}\right) / k_{23}\\
\frac{dx_{11}}{dt} = \left(-1 \cdot 1 / k_{2} \cdot x_{11} + 1 \cdot 365 / k_{13} / \left(1 - k_{9}\right) \cdot x_{10} + 1 \cdot 365 / k_{13} / \left(1 - k_{9}\right) \cdot x_{9} + 1 \cdot 365 / k_{13} / \left(1 - k_{10}\right) \cdot x_{8} + -1 \cdot 1 / k_{14} \cdot x_{11}\right) / k_{23}