  The Hadron-Resonance Gas (HRG) approach - used to model hadronic matter at
small baryon potentials $\mu_B$ and finite temperature $T$ - is extended to
finite and large chemical potentials by introducing interactions between
baryons in line with relativistic mean-field theory defining an interacting HRG
(IHRG). Using lattice data for $\mu_B=0$ as well as information on the nuclear
equation of state at $T=0$ we constrain the attractive and repulsive
interactions of the IHRG such that it reproduces the lattice equation of state
at $\mu_B=0$ and the nuclear equation of state at $T=0$ and finite $\mu_B$. The
formulated covariant approach is thermodynamically consistent and allows us to
provide further information on the phase boundary between hadronic and partonic
phases of strongly interacting matter by assuming constant thermodynamic
potentials.
