  We use the microscopic GiBUU transport model to calculate dilepton ($e^+e^-$)
production in heavy-ion collisions at SIS18 energies focusing on the effect of
collisional broadening of the $\rho$-meson. The collisional width of the
$\rho$-meson at finite temperature and baryon density in nuclear matter is
calculated on the basis of the collision integral of the GiBUU model. A
systematic comparison with HADES data on dilepton production in heavy-ion
collisions is performed. The collisional broadening of the $\rho$ improves the
agreement between theory and experiment for the dilepton invariant-mass
distributions near the $\rho$ pole mass and for the excess radiation in Au+Au
at $1.23 A$ GeV. We furthermore show that some remaining underprediction of the
experimental dilepton spectra in C+C at $1 A$ GeV and Au+Au at $1.23 A$ GeV at
intermediate invariant masses $0.2-0.4$ GeV can be accounted for by adjusting
the $pn$ bremsstrahlung cross section in a way to agree with the inclusive
dilepton spectrum from $dp$ collisions at $1.25 A$ GeV.
