  Mean-field model quantum field theories of hadrons were traditionally
developed to describe cold and dense nuclear matter and are by now very well
constrained from the recent neutron star merger observations. We show that when
augmented with additional known hadrons and resonances but not included
earlier, these mean-field models can be extended beyond its regime of
applicability. Calculating some specific ratios of baryon number
susceptibilities for finite temperature and moderate values of baryon densities
within mean-field approximation, we show that these match consistently with the
lattice QCD data available at lower densities, unlike the results obtained from
a non-interacting hadron resonance gas model. We also estimate the curvature of
the line of constant energy density, fixed at its corresponding value at the
chiral crossover transition in QCD, in the temperature-density plane. The
number density at low temperatures and high density is found to be about twice
the nuclear saturation density along the line of constant energy density of
$\epsilon=348 \pm 41$ MeV/$\text{fm}^3$. Moreover from this line we can
indirectly constrain the critical end-point of QCD to be beyond $\mu_B=596$ MeV
for temperature $\sim 125 $ MeV.
