  In this paper we apply to photoproduction total cross-section a model we have
proposed for purely hadronic processes and which is based on QCD mini-jets and
soft gluon re-summation. We compare the predictions of our model with the HERA
data as well as with other models. For cosmic rays, our model predicts
substantially higher cross-sections at TeV energies than models based on
factorization but lower than models based on mini-jets alone, without soft
gluons. We discuss the origin of this difference.
