Find a function

Question

It's a cuttout from Rempe article "A mathematical model of the sleep/wake cycle" about a function which I don't understand how to describe: $h(t)$ decays exponentially while the system is asleep and increases while awake. We scale the variables so that the system is defined to be asleep if $x_A < 0$ and awake if $x_A > 0$. Then $h(t)$ satisfies $h' = α_h(h_{max} − h)$ while awake (when $x_A > 0$) and $h' = −β_hh$ while asleep (when $xA < 0$). Here, $α_h, β_h$ and $h_{max}$ are constants. Also, a period of cycle last 24h, 16h system is awake and sleeps for 8h.
How to describe a function $h(t)$ in one equation? I think it should be somehow related with $H_{\infty}(x)=\frac{1}{1+e^{-x/0.01}}$ as it widely used in this article.
Here are links to original article and some corrections Article, corrections . $h(t)$ mentioned on $620$page.