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 2 M _ { \odot } can not 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 .