  A confining extension of the quark model with nonlocal currents is proposed.
The quark propagator is modified by introducing a cut in {\alpha}-space, which
in momentum space corresponds to the subtraction of pole singularities. A
two-phase phase structure is proposed for modeling the
confinement-deconfinement phase transition. In the confined phase, the quark
propagator does not have any pole singularities, while in the deconfined phase,
there is a single quark pole.
