The combination of high resolution and sensitivity offered by ALMA is revolutionizing our understanding of protoplanetary discs, as their bulk gas and dust distributions can be studied independently. In this paper we present resolved ALMA observations of the continuum emission ($lambda=1.3$ mm) and CO isotopologues ($^{12}$CO, $^{13}$CO, C$^{18}$O $J=2-1$) integrated intensity from the disc around the nearby ($d = 162$ pc), intermediate mass ($M_{star}=1.67,M_{odot}$) pre-main-sequence star CQ Tau. The data show an inner depression in continuum, and in both $^{13}$CO and C$^{18}$O emission. We employ a thermo-chemical model of the disc reproducing both continuum and gas radial intensity profiles, together with the disc SED. The models show that a gas inner cavity with size between 15 and 25 au is needed to reproduce the data with a density depletion factor between $sim 10^{-1}$ and $sim 10^{-3}$. The radial profile of the distinct cavity in the dust continuum is described by a Gaussian ring centered at $R_{rm dust}=53,$au and with a width of $sigma=13,$au. Three dimensional gas and dust numerical simulations of a disc with an embedded planet at a separation from the central star of $sim20,$au and with a mass of $sim 6textrm{-} 9,M_{rm Jup}$ reproduce qualitatively the gas and dust profiles of the CQ Tau disc. However, a one planet model appears not to be able to reproduce the dust Gaussian density profile predicted using the thermo-chemical modeling.
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