  We extend the effective dynamical quasiparticle model (DQPM) - constructed
for the description of non-perturbative QCD phenomena of the strongly
interacting quark-gluon plasma (QGP) - to large baryon chemical potentials,
$\mu_B$, including a critical end-point and a 1st order phase transition. The
DQPM description of quarks and gluons is based on partonic propagators with
complex selfenergies where the real part of the selfenergies is related to the
quasiparticle mass and the imaginary part to a finite width of their spectral
functions. In DQPM the determination of complex selfenergies for the partonic
degrees of freedom at zero and finite $\mu_B$ has been performed by adjusting
the entropy density to the lQCD data. The temperature-dependent effective
coupling (squared) $g^2(T/T_c)$, as well as the parton effective masses and
widths are based on this adjustment. The novel extended dynamical quasiparticle
model, named "DQPM-CP", makes it possible to describe thermodynamical and
transport properties of quarks and gluons in a wide range of $T$ and $\mu_B$,
and reproduces the equation-of-state (EoS) of lQCD calculations in the
crossover region of finite $T, \mu_B$. We apply a scaling ansatz for the strong
coupling constant near the CEP, located at ($T^{CEP}$, $\mu^{CEP}_B) = (0.100,
0.960)$ GeV. We show the EoS as well as the speed of sound for $T>T_c$ and for
a wide range of $\mu_B$, which can be of interest for hydrodynamical
simulations. Furthermore, we consider two settings for the strange quark
chemical potentials (I) $\mu_s=\mu_B/3$ and (II) $\mu_s=0$. The isentropic
trajectories of the QGP matter are compared for these two cases. The phase
diagram of DQPM-CP is close to PNJL calculations. The leading order pQCD
transport coefficients of both approaches differ. This elucidates that the
knowledge of the phase diagram alone is not sufficient to describe the
dynamical evolution of QGP.
