  We numerically study level statistics of disordered interacting quantum
many-body systems. A two-parameter plasma model which controls level repulsion
exponent $\beta$ and range $h$ of interactions between eigenvalues is shown to
reproduce accurately features of level statistics across the transition from
ergodic to many-body localized phase. Analysis of higher order spacing ratios
indicates that the considered $\beta$-$h$ model accounts even for long range
spectral correlations and allows to obtain a clear picture of the flow of level
statistics across the transition. Comparing spectral form factors of
$\beta$-$h$ model and of a system in the ergodic-MBL crossover, we show that
the range of effective interactions between eigenvalues $h$ is related to the
Thouless time which marks the onset of quantum chaotic behavior of the system.
Analysis of level statistics of random quantum circuit which hosts chaotic and
localized phases supports the claim that $\beta$-$h$ model grasps universal
features of level statistics in transition between ergodic and many-body
localized phases also for systems breaking time-reversal invariance.
