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\frac{d\textcolor{limegreen}{Q(z)}}{dz} = \frac{\textcolor{blue}{\dot{n}_{\mathrm{ion}}(z)}/n_{\mathrm{H}}(z) - \textcolor{limegreen}{Q(z)}/\textcolor{red}{\mathrm{t_{rec}}(z)}}{(1+z)\times H(z)} \\[1em] \tiny \begin{align*} 1 -\textcolor{limegreen}{Q(z)} &= \mathrm{Neutral \; fraction} \\[0.0em] \textcolor{blue}{\dot{n}_{\mathrm{ion}}(z)} &= \mathrm{Lyman \; continuum \; emissivity} \\[0.0em] \textcolor{red}{\mathrm{t_{rec}}(z)} &= \mathrm{Recombination \; timescale} \end{align*}
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