Knizhnik-Zamolodchikov equations in Deligne categories

We consider the Knizhnik-Zamolodchikov equations in Deligne Categories in the context of $({\mathfrak{g}\mathfrak{l}}_m,{\mathfrak{g}\mathfrak{l}}_n)$ and $({\mathfrak{s}\mathfrak{o}}_m,{\mathfrak{s}\mathfrak{o}}_{2n})$ dualities. We derive integral formulas for the solutions in the first case and compute monodromy in both cases.