[Abridged] In high density environment, the gas content of galaxies is stripped, leading to a rapid quenching of their star formation activity. This dramatic environmental effect is generally not taken into account in the SFHs usually assumed to perform spectral energy distribution (SED) fitting of these galaxies, yielding to a poor fit of their stellar emission and, consequently, a biased estimate of the SFR. We aim at reproducing the SFH of galaxies that underwent a rapid star formation quenching using a truncated delayed SFH that we implemented in the SED fitting code CIGALE. We show that the ratio between the instantaneous SFR and the SFR just before the quenching ($r_{SFR}$) is well constrained as long as rest frame UV data are available. This SED modelling is applied to the Herschel Reference Survey (HRS) containing isolated galaxies and sources falling in the dense environment of the Virgo cluster. The latter are HI-deficient due to ram pressure stripping. We show that the truncated delayed SFH successfully reproduces their SED while typical SFH assumptions fail. A good correlation is found between $r_{SFR}$ and HI-def, the parameter quantifying the gas deficiency of cluster galaxies, meaning that SED fitting results can be used to provide a tentative estimate of the gas deficiency of galaxies for which HI observations are not available. The HRS galaxies are placed on the SFR-$M_*$ diagram showing that the HI-deficient sources lie in the quiescent region confirming previous studies. Using the $r_{SFR}$ parameter, we derive the SFR of these sources before quenching and show that they were previously on the main sequence relation. We show that the $r_{SFR}$ parameter is also well recovered for deeply obscured high redshift sources, as well as in absence of IR data. SED fitting is thus a powerful tool to identify galaxies that underwent a rapid star formation quenching.
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