  We investigate the $pp \to pK^{+}\Lambda$ reaction within an effective
Lagrangian model where the contributions to the amplitudes are taken into
account within the tree level. The initial interaction between the two nucleons
is modeled by the exchange of $\pi$, $\rho$, $\omega$ and $\sigma$ mesons and
the $\Lambda K^{+}$ production proceeds via the excitation of the $N^*$(1650),
$N^*$(1710), $N^*$(1720) baryonic resonances. The parameters of the model at
the nucleon-nucleon-meson vertices are determined by fitting the elastic
nucleon-nucleon scattering with an effective interaction based on the exchange
of these four mesons, while those at the resonance vertices are calculated from
the known decay widths of the resonances as well as the vector meson dominance
model. Available experimental data is described well by this approach. The
one-pion-exchange diagram dominates the production process at both higher and
lower beam energies. The $\rho$ and $\omega$ meson exchanges make negligible
contributions. However, the $\sigma$-exchange processes contribute
substantially to the total cross sections at lower beam energies. The
excitation of the $N^*$(1710) and $N^*$(1650) resonances dominate this reaction
at beam momenta above and below 3 GeV/c respectively. The interference among
the amplitudes of various resonance excitation processes is significant. For
beam energies very close to the $K^{+}$ production threshold the hyperon-proton
final state interaction effects are quite important. The data is selective
about the model used to describe the low energy scattering of the two final
state baryons.
