Solution
= Solution
The first reaction is reversible, with reverse rate $k_{-1}c_1$. Applying the <law of mass action> to each reaction gives
$$
\boxed{
\begin{aligned}
\dot e&=-k_1es+k_{-1}c_1,\\
\dot s&=-k_1es+k_{-1}c_1-k_2c_1s,\\
\dot c_1&=k_1es-k_{-1}c_1-k_2c_1s+k_3c_2,\\
\dot c_2&=k_2c_1s-k_3c_2,\\
\dot p&=k_3c_2.
\end{aligned}}
$$
Each term has the sign dictated by whether the corresponding species is consumed or produced.