  We extend the confined-density-dependent-mass (CDDM) model to include isospin
dependence of the equivalent quark mass. Within the
confined-isospin-density-dependent-mass (CIDDM) model, we study the quark
matter symmetry energy, the stability of strange quark matter, and the
properties of quark stars. We find that including isospin dependence of the
equivalent quark mass can significantly influence the quark matter symmetry
energy as well as the properties of strange quark matter and quark stars. While
the recently discovered large mass pulsars PSR J1614-2230 and PSR J0348+0432
with masses around $2M_{\odot}$ cannot be quark stars within the CDDM model,
they can be well described by quark stars in the CIDDM model. In particular,
our results indicate that the two-flavor $u$-$d$ quark matter symmetry energy
should be at least about twice that of a free quark gas or normal quark matter
within conventional Nambu-Jona-Lasinio model in order to describe the PSR
J1614-2230 and PSR J0348+0432 as quark stars.
