  We analyse two analytic fitting profiles to model the ram pressure exerted
over satellites galaxies for different environments and epochs, using
hydrodynamical resimulations of groups and clusters of galaxies to measure the
ram pressure from the gas particle distribution. First, we compare the
predictions given by a known $\beta$-profile model with the simulation
measurements, finding that the profile is not in agreement with the expected
behaviour by missing the dependence with the halo mass and halocentric
distance. It features a systematic underestimation of the predicted ram
pressure at high redshifts ($z > 1.5$), which increases towards the central
regions of the halos and it is independent of halo mass, reaching differences
larger than two decades for satellites at $r < 0.4 R_\mathrm{vir}$. This
behaviour reverses as redshift decreases, featuring an increasing
over-estimation with halocentric distance at $z = 0$. As an alternative, we
introduce a new universal analytic model for the profiles consisting in a
damped power law, and we provide a new set of fitted parameters which can
recover the ram pressure dependence on halo mass and redshifts. Finally, we
analyse the impact of these analytic profiles in the galaxy properties by
applying a semi-analytic model of galaxy formation and evolution on top of the
simulations. We find the number of galaxies experiencing large amounts of
accumulated ram pressure stripping have low stellar mass ($M_\star \leq 10^9
\mathrm{M}_\odot$), and their specific star formation rates depend
significantly on the ram pressure modelling, particularly at high redshifts ($z
> 1.5$).
