The role of the current profile and ion and electron temperature ratio in Tokamak A Configuration Variable (TCV) electron internal transport barrier (eITB) noninductive discharges is inspected by means of the linear gyrokinetic global code LORB5 (Bottino et al 2004 Phys. Plasmas 11 198) and the Gyro-Landau fluid transport model GLF23 (Waltz et al 1997 Phys. Plasmas 4 2482). In this work we have compared two different MHD equilibria for a TCV discharge with an eITB, corresponding to a monotonic and a reversed safety factor profile. The latter has been obtained using the calculated electron-cyclotron driven density profile, the bootstrap current and the experimental pressure. Global simulations show that the most unstable electrostatic instabilities in the spectrum are trapped electron modes (TEM) for both equilibria. In the vicinity of the reverse shear region, where the magnetic shear s is positive and small (s << 1), modes tend to preserve the ballooning structure but their mixing length estimate for the thermal diffusion coefficient is significantly reduced as compared with the monotonic q equilibrium. This effect is further increased in the reverse shear region. Simulations performed with GLF23 show that the inclusion of the Shafranov shift in the model has an important stabilizing effect in all the plasma core and, in particular, in the barrier region. However, the Shafranov shift and reverse shear stabilization are not the only mechanisms through which the q profile affects the stability of the system. The local value of q in the barrier region also contributes to the stabilization. Global gyrokinetic and local Gyro-Landau fluid results suggest that the current profile modification alone, with the consequent negative shear and Shafranov shift stabilization on TEM modes, can explain the presence of the ITB in these TCV discharges.