In this paper, we make a comprehensive study of the properties gapped Dirac semimetal model, which was originally proposed in magnetoinfrared spectroscopy measurement ZeTe$_5$, and includes both linear parabolic dispersions all three directions. We find that, depending on band inversion parameters, $\zeta'$ $\zeta_z'$, model can support different phases: single point (DP) phase, double DPs phas...