  We present a new analytic fitting profile to model the ram pressure exerted
over satellite galaxies on different environments and epochs. The profile is
built using the information of the gas particle distribution in hydrodynamical
simulations of groups and clusters of galaxies to measure the ram pressure
directly. We show that predictions obtained by a previously introduced
$\beta$-profile model can not consistently reproduce the dependence of the ram
pressure on halocentric distance and redshift for a given halo mass. It
features a systematic underestimation of the predicted ram pressure at high
redshifts ($z > 1.5$), which increases towards the central regions of the
haloes and it is independent of halo mass, reaching differences larger than two
decades for satellites at $r<0.4R_\mathrm{vir}$. 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 which can recover the ram pressure dependence on halo
mass, halocentric distance and redshift. We analyse the impact of our new
profile on galaxy properties by applying a semi-analytic model of galaxy
formation and evolution on top of the simulations. We show that galaxies
experiencing large amounts of cumulative ram pressure stripping typically have
low stellar masses ($M_\star \leq 10^{9.5} \text{M}_\odot$). Besides, their
specific star formation histories depend on the ram pressure modelling applied,
particularly at high redshifts ($z > 1.5$).
