We study the evolution of dwarf ( L _ { H } < 10 ^ { 9.6 } L _ { H \odot } ) star forming and quiescent galaxies in the Virgo cluster by comparing their UV to radio centimetric properties to the predictions of multizone chemo-spectrophotometric models of galaxy evolution especially tuned to take into account the perturbations induced by the interaction with the cluster intergalactic medium . Our models simulate one or multiple ram pressure stripping events and galaxy starvation . Models predict that all star forming dwarf galaxies entering the cluster for the first time loose most , if not all , of their atomic gas content , quenching on short time scales ( \leq 150 Myr ) their activity of star formation . These dwarf galaxies soon become red and quiescent , gas metal-rich objects with spectrophotometric and structural properties similar to those of dwarf ellipticals . Young , low luminosity , high surface brightness star forming galaxies such as late-type spirals and BCDs are probably the progenitors of relatively massive dwarf ellipticals , while it is likely that low surface brightness magellanic irregulars evolve into very low surface brightness quiescent objects hardly detectable in ground based imaging surveys . The small number of dwarf galaxies with physical properties intermediate between those of star forming and quiescent systems is consistent with a rapid ( < 1 Gyr ) transitional phase between the two dwarf galaxies populations . These results , combined with statistical considerations , are consistent with the idea that most of the dwarf ellipticals dominating the faint end of the Virgo luminosity function were initially star forming systems , accreted by the cluster and stripped of their gas by one or subsequent ram pressure stripping events .