Wang's minimum semi-degree conjecture for disjoint directed cycles

Let $D$ be a digraph of order $n$, where $k\geq 1$ is an integer and $n\geq 3k$.

Wang's conjecture. If $\delta^0(D)\geq (9k-3)/4$, then $D$ contains $k$ vertex-disjoint directed cycles, each of order at least $3$.

The source presents this as one of Wang's conjectures on disjoint cycles in digraphs. Its status is not established in the source.