  In this work we use an eikonalized minijet model where the effects of the
first nonlinear corrections to the DGLAP equations are taken into account. The
contributions coming from gluon recombination effects are included in the
DGLAP+GLRMQ approach for the free proton in the context of saturation models.
The parameters of the model are fixed to fit total $pp$ and $\bar p p$ cross
sections, including the very recent data from LHC, HiRes and P. Auger
Collaborations. Glauber and multiple scattering approximations are then used to
describe the inclusive inelastic proton-Air cross section. Photoproduction
cross sections, without change of parameters fixed before, are also obtained
from the model using Vector Meson Dominance and the Additive Quark Model. We
show and discuss our main results as well as the implications of saturation
effects in the behavior of total hadronic and photonic cross sections at very
high energies.
