  Photospheric stellar activity might be an important source of noise and
confusion in the radial-velocity measurements. RV planet search surveys as well
as follow-up of photometric transit surveys require a deeper understanding and
characterization of the effects of stellar activities to disentangle it from
planetary signals. We simulate dark spots on a rotating stellar photosphere.
The variations of the photometry, RV and spectral line shapes are characterized
and analyzed according to the stellar inclination, the latitude and the number
of spots. The Lomb-Scargle periodograms of the RV variations induced by
activity present power at the rotational period Prot of the star and its
two-first harmonics Prot/2 and Prot/3. Three adjusted sinusoids fixed at Prot
and its two-first harmonics allow to remove about 90% of the RV jitter
amplitude. We apply and validate our approach on four known active planet-host
stars: HD189733, GJ674, CoRoT-7 and iHor. We succeed in fitting simultaneously
activity and planetary signals on GJ674 and CoRoT-7. This simultaneous modeling
of the activity and planetary parameters leads to slightly larger masses of
CoRoT-7b and c: respectively, 5.7+/-2.5ME and 13.1+/-4.1ME. The larger
uncertainties take into account properly for the stellar active jitter. We
excluded short-period low-mass exoplanets around iHor. For data with realistic
time-sampling and white Gaussian noise, we use simulations to show that our
approach is efficient to disentangle reflex-motion due to a planetary companion
and stellar-activity induced-RV variations provided that 1) the planetary
orbital period is not close to that of the stellar rotation or one of its
two-first harmonics 2) the semi-amplitude of the planet exceeds 30% of the
semi-amplitude of the active signal 3) the rotational period of the star is
accurately known 4) the data cover more than one stellar rotational period.
