Coming up with a Mathematical Model to Predict how long a redox reaction can last
In addition to the redox reactions the transport of material towards the electrodes also needs to be considered. This involves using Fick's equations for diffusion to calculate the concentration of species at distances away from the electrodes as reaction starts and reaches constant conditions. The steady state equations are of the form

$$ D_{ox} \frac{\partial C_{ox}}{\partial x}= k_cC_{ox}-k_aC_{rd} \\
   D_{rd} \frac{\partial C_{rd}}{\partial x}= -k_cC_{ox}+k_aC_{rd}$$

These lead to the Cottrell equation for the limiting flux (current density)  $j=-nFC^o_{ox}\sqrt{D_{ox}/\pi t}$. To get what you want you will probably need to consult some specialist text books on electrochemistry.