\begin{equation}\label{eq:boundary-mutation-drift_diffusion3}
\begin{split}
\frac{\partial\phi_I(x,t)}{\partial t}&=\lim_{\epsilon_x\to 0}\bigg(\frac{\beta\theta b_0(t)}{\epsilon_x}\delta(x-\epsilon_x)+\frac{\alpha\theta b_1(t)}{\epsilon_x}\delta(x-1+\epsilon_x)\bigg)\\
    &\qquad+\frac{\partial^2}{\partial x^2} x(1-x)\phi_I(x,t)\,.
\end{split}
\end{equation}
