  Integral and derivative dispersion relations (IDR and DDR) are considered for
the proton-proton and antiproton-proton forward scattering amplitudes. A scheme
for calculation of the corrections to asymptotic form for the DDR is presented.
The data on the total proton-proton and antiproton-proton cross sections as
well as the data on the ratios $\rho $ of real to imaginary part of the forward
scattering amplitudes have been analyzed by the IDR and DDR methods within
high-energy Regge models. Regge parametrizations of high-energy total cross
sections supplemented by the properly calculated low-energy part of the
dispersion integral (from the two-proton threshold up to center-of-mass energy
5 GeV) allow to reproduce well the $\rho $ data at low energies with the only
free parameter, subtraction constant. It is shown that three models for the
pomeron, simple pole pomeron (with intercept large than unity), tripole pomeron
and dipole pomeron (the both with the unit value intercept) lead to practically
equivalent description of the available data at $\sqrt{s}>$5 GeV. Predictions
for the TOTEM measurements of cross section and $\rho$ at the center-of-mass
energies 7 and 14 GeV are given.
