  Extreme-mass-ratio-inspiral (EMRI) is one of the most important sources for
the future space-borne gravitational wave detectors. In such kind of systems,
the compact objects usually orbit around the central supermassive black holes
with complicated trajectories. Usually, the trajectory is approximated as
geodesic of a test-particle in Kerr space-time, and the orbital evolution are
simulated with the help of adiabatic approximation. However, this omits the
influence of the compact object on the back ground. In the present paper,
employing effective-one-body formalism, we analytically calculate out the
trajectories of a compact object around a massive Kerr black hole in
equatorial-eccentric orbit, and express the fundamental orbital frequencies in
explicit forms. Our formalism include the first-order corrections of mass-ratio
in the conservative orbital motion. Furthermore, we insert the mass-ratio
related terms in the first post-Newtonian energy fluxes. By calculating the
gravitational waves from the Teukolsky equations, we quantitatively reveal the
influence of the mass of the compact object on the data analysis. We find that
the shrinking of geodesic motion by taking the small objects as test particles
may be not appropriate for the detection of EMRIs.
