We use optical integral field spectroscopy and 8 and 24 micron mid-IR observations of the giant HII region NGC 588 in the disc of M33 as input and constraints for two-dimensional tailor-made photoionisation models. Two different geometrical approaches are followed for the modelling structure: i) Each spatial element of the emitting gas is studied individually using models which assume that the ionisation structure is complete in each element to look for azimuthal variations across gas and dust. ii) A single model is considered, and the two-dimensional structure of the gas and the dust are assumed to be due to the projection of an emitting sphere onto the sky. The models in both assumptions reproduce the radial profiles of Hbeta surface brightness, the observed number of ionising photons, and the strong optical emission-line relative intensities. The first approach produces a constant-density matter-bounded thin shell of variable thickness and dust-to-gas ratio, while the second gives place to a radiation-bounded thick shell sphere of decreasing particle density. However, the radial profile of the 8/24 microns IR ratio, depending on the gas and dust geometry, only fits well when the thick-shell model is used. The resulting dust-to-gas mass ratio, which was obtained empirically from the derived dust mass using data from Spitzer, also has a better fit using the thick-shell solution. In both approaches, models support the chemical homogeneity, and the ionisation-parameter radial decrease, These results must be taken with care in view of the very low extinction values that are derived from the IR, as compared to that derived from the Balmer decrement. Besides, the IR can be possibly contaminated with the emission from a cloud of diffuse gas and dust above the plane of the galaxy detected at 250 micron Herschel image.
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