The in-medium spectral functions of $rho$ and $omega$ mesons and the broadening of the nucleon resonances at finite baryon density are calculated self-consistently by combining a resonance dominance model for the vector meson production with an extended vector meson dominance model. The influence of the in-medium modifications of the vector meson properties on the dilepton spectrum in heavy-ion collisions is investigated. The dilepton spectrum is generated for the C+C reaction at 2.0$A$ GeV and compared with recent HADES Collaboration data. The collision dynamics is then described by the Tubingen relativistic quantum molecular dynamics transport model. We find that an iterative calculation of the vector meson spectral functions that takes into account the broadening of the nucleon resonances due to their increased in-medium decay branchings is convergent and provides a reasonable description of the experimental data in the mass region $0.45leq M leq 0.75$ GeV. On the other side, the theoretical calculations slightly underestimate the region $m_pileq M leq 0.4$ GeV. Popular in-medium scenarios such as a schematic collisional broadening and dropping vector mesons masses are discussed as well.
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