Exploring the parameter space of quasi-particle model with the strange quark stars

The properties of strange quark stars are studied within the quasi-particle model. Taking into account the chemical equilibrium and charge neutrality, the EOS of $(2+1)$-flavor quark matter is obtained. We illustrate the parameter spaces with constraints from two aspects: the one is based on the astronomical results of PSR J$0740+6620$ and GW$170817$, and another is based on the constraints proposed from the theoretical study of compact star that the EOS must ensure the tidal deformability $\varLambda_{1.4}=190^{+390}_{-120}$ and support a maximum mass above $1.97~M_{\odot}$. It is found that the both types of constraints can not restrict the parameter space of quasi-particle model in a reliable region and thus we conclude that the small compact star cannot be strange quark star.