We present the results of model calculations, using our new, four-species, spherical MHD model. Our results are compared with the relevant and limited available data. The resulting comparisons help us to increase our understanding of the interaction processes between the solar wind and the Martian atmosphere/ionosphere. This new model with a spherical grid structure allowed us to use small (~10 km) radial grid spacing in the ionospheric region. We found that the calculated bow shock positions agree reasonably well with the observed values. The calculated results vary with interplanetary magnetic field orientation, solar cycle conditions, and subsolar location. We found that our calculated ion densities, with parameters corresponding to solar cycle minimum conditions, reproduced the Viking 1 observed ion densities well. The calculated solar cycle maximum densities, above ~140 km, are also consistent with the appropriate Mars Global Surveyor radio occultation electron densities. Both the calculated solar cycle maximum and solar cycle minimum total transterminator and escape fluxes are significantly smaller than our previously published values. This decrease is due to the improved temperature values used for the recombination rates in this new model, which in turn results in lower ion densities and lower fluxes.