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Photospheric stellar activity (i.e. dark spots or bright plages) might be an important source of noise and confusion in stellar radial-velocity (RV) measurements. Radial-velocimetry 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 differentiate them from planetary signals. We simulate dark spots on a rotating stellar photosphere. The variations in the photometry, RV, and spectral line shapes are characterized and analyzed according to the stellar inclination, the latitude, and the number of spots. We show that the anti-correlation between RV and bisector span, known to be a signature of activity, requires a good sampling to be resolved when there are several spots on the photosphere. 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 the fundamental period and its two-first harmonics allow us to remove about 90% of the RV jitter amplitude. We apply and validate our approach on four known active planet-host stars: HD 189733, GJ 674, CoRoT-7, and ι Hor. 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 higher masses of CoRoT-7b and c of respectively, 5.7 ± 2.5 MEarth and 13.2 ± 4.1 MEarth. The larger uncertainties properly take into account the stellar active jitter. We exclude short-period low-mass exoplanets around ι Hor. For data with realistic time-sampling and white Gaussian noise, we use simulations to show that our approach is effective in distinguishing 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, and 4) the data cover more than one stellar rotational period.