= Solution
With the <travelling wave> coordinate $\xi=x-ct$, the <reaction–diffusion system> becomes
$$
D f''+cf'+rf(1-f)=0,
\qquad f(-\infty)=1,quad f(+\infty)=0.
$$
At the advancing leading edge the healthy-tissue density is small. Put $f(\xi)\sim e^{-\lambda\xi}$ with $\lambda>0$. The <linearization> at $f=0$ gives
$$
D\lambda^2-c\lambda+r=0,
$$
so a nonoscillatory decaying front requires real positive roots,
$$
\lambda=\frac{c\pm\sqrt{c^2-4Dr}}{2D},
\qquad c\geq2\sqrt{Dr}.
$$
The <pulled travelling front> selects the <Fisher-KPP minimum wave speed>, and therefore
$$
\boxed{c_{\min}=2\sqrt{Dr}.}
$$
For the initial wound $0<x<W$, two mirror-image fronts enter from its endpoints. The left front moves right from $x=0$ and the right front moves left from $x=W$, each with speed approximately $c_{\min}$. A sequence of sketches would show the initial rectangular depression becoming two smooth monotone transition layers, the zero-density plateau shrinking, and the two layers meeting near $x=W/2$ before the profile relaxes to $S=1$. Their meeting time is
$$
\boxed{t_{\rm heal}\approx\frac{W/2}{c_{\min}}
=\frac{W}{4\sqrt{Dr}}.}
$$
There is an additional local relaxation time of order $1/r$ if “close to one” is assigned a fixed numerical tolerance, so the displayed estimate is the dominant healing time when $W$ is large compared with the front width $\sqrt{D/r}$.
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