  We design new deterministic CONGEST approximation algorithms for
\emph{maximum weight independent set (MWIS)} in \emph{sparse graphs}. As our
main results, we obtain new $\Delta(1+\epsilon)$-approximation algorithms as
well as algorithms whose approximation ratio depend strictly on $\alpha$, in
graphs with maximum degree $\Delta$ and arboricity $\alpha$. For
(deterministic) $\Delta(1+\epsilon)$-approximation, the current
state-of-the-art is due to a recent breakthrough by Faour et al.\ [SODA 2023]
that showed an $O(\log^{2} (\Delta W)\cdot \log (1/\epsilon)+\log ^{*}n)$-round
algorithm, where $W$ is the largest node-weight (this bound translates to
$O(\log^{2} n\cdot\log (1/\epsilon))$ under the common assumption that
$W=\text{poly}(n)$). As for $\alpha$-dependent approximations, a deterministic
CONGEST $(8(1+\epsilon)\cdot\alpha)$-approximation algorithm with runtime
$O(\log^{3} n\cdot\log (1/\epsilon))$ can be derived by combining the
aforementioned algorithm of Faour et al.\ with a method presented by
Kawarabayashi et al.\ [DISC 2020].
