  Thermodynamic functions, the (higher-order) fluctuations and correlations of
conserved charges at $\mu_B = 0$, and the Fourier coefficients of net-baryon
density at imaginary $\mu_B$, are considered in the framework of a Hagedorn
bag-like model with a crossover transition. The qualitative behavior of these
observables is found to be compatible with lattice QCD results. Fair
quantitative description of the lattice data is obtained when
quasiparticle-type quarks and gluons with non-zero masses are introduced into
the bag spectrum. The equation of state of the model exhibits a smooth and wide
crossover transition.
