  In framework of linear $\sigma$-model (LSM) with three quark flavors, the
chiral phase-diagram at finite temperature and density is investigated. At
temperatures higher than the critical temperature ($ T_c $), we added to LSM
the gluonic sector from the quasi-particle model (QPM), which assumes that the
interacting gluons in the strongly interacting matter, the quark-gluon plasma
(QGP), are phenomenologically the same as non-interacting massive
quasi-particles. The dependence of the chiral condensates of strange and
non-strange quarks on temperature and chemical potential is analysed. Then, we
have calculated the thermodynamics in the new approach (combination of LSM and
QPM). Confronting the results with recent lattice QCD simulations shows an
excellent agreement in almost all thermodynamic quantities. The first and
second order moments of particle multiplicity are studied in dependence on the
chemical potential but at fixed temperature and on the chemical potential but
at fixed temperature. These are implemented in characterizing the large
fluctuations accompanying the chiral phase-transition. The results of first and
second order moments are compared with the SU(3) Polyakov linear $\sigma$-model
(PLSM). Also, the resulting phase-diagrams deduced in PLSM and LSM$+$QPM are
compared with each other.
