  We study the interaction of leading jet partons in a strongly interacting
quark-gluon plasma (sQGP) medium based on the effective dynamical
quasi-particle model (DQPM). The DQPM describes the non-perturbative nature of
the sQGP at finite temperature $T$ and baryon chemical potential $\mu_B$ based
on a propagator representation of massive off-shell partons (quarks and gluons)
whose properties (characterized by spectral functions with $T,\mu_B$ dependent
masses and widths) are adjusted to reproduce the lQCD EoS for the QGP in
thermodynamic equilibrium. We present the results for the jet transport
coefficients, i.e. the transverse momentum transfer squared per unit length
$\hat{q}$ as well as the energy loss per unit length $\Delta E =dE/dx$, in the
QGP and investigate their dependence on the temperature $T$ and baryon chemical
potential $\mu_B$ as well as on jet properties such as the leading jet parton
momentum, mass, flavor, and the choice of the strong coupling constant. In this
first study only elastic scattering processes of a leading jet parton with the
sQGP partons are explored discarding presently the radiative processes (such as
gluon Bremsstrahlung). We present a comparison of our results for the elastic
energy loss in the sQGP medium with the pQCD results obtained by the BAMPS and
LBT models as well as with other theoretical approaches such as lattice QCD and
the LO-HTL and also with estimates of $\hat{q}/T^3$ by the color string
percolation model (CSPM) and the JET and JETSCAPE Collaborations based on a
comparison of hydrodynamical calculations with experimental heavy-ion data.
