  Motivated by the renewed interest in studying the pion production on nuclei
with protons at few GeV incident energies, we investigate the pion production
in proton-proton collisions over an energy range of 300 $MeV$ to 2 $GeV$.
Starting from a realistic one-boson exchange model with parameters fitted to
the amplitudes of the elastic nucleon-nucleon scattering, we perform fully
covariant calculations for the total, double and triple differential
cross-sections of the $p(p,n\pi^+)p$ and $p(p,p\pi^0)p$ reactions. The
calculations incorporate the exchange of $\pi, \rho,\omega$ and $\sigma$ mesons
and treat nucleon and delta isobar as intermediate states. We obtain a
reasonably good agreement with the experimental data in the entire range of
beam energies. The form of the covariant delta propagator, the cut-off
parameter for the $\pi NN$ and $\pi N\Delta$ vertex form factors and the energy
dependence of the delta isobar decay width is investigated.
