When is weakly almost periodic equivalent to uniformly almost periodic for semiflows?

Let $\pi \text{\hspace{0.17em}⁣}:T\times X\to X$ be a semiflow on a compact Hausdorff space $X$ with phase semigroup $T$. This paper provides us with some conditions under which \textsl{weakly almost periodic} is equivalent to \textsl{uniformly almost periodic} or to \textsl{equicontinuous} for $(T,X,\pi )$.