The quantum-lattice-gas model has been introduced by Matsubara and Matsuda to describe the superfluid properties of 4He. It relates the Hamiltonian of a system of hard-core bosonic quasi-particles, hopping on a lattice with nearest-neighbour transfer integral t and interaction v, to that of a spin S = 1 2 , Heisenberg antiferromagnet with uniaxial anisotropy. The quasi-particle density in the boson problem maps on the magnetization in an applied magnetic field in the antiferromagnetic problem. Interest in the charged-boson version of this model has recently been revived by its application to the superconductivity (superfluidity) of local pairs of carriers (onsite and/or intersite bipolarons) by Ranninger, Micnas, Alexandrov and Robaszkiewicz. In this paper we investigate some applications of this model to the observed properties of the superconducting oxides. Here we profit from the wealth of knowledge that is available on the antiferromagnetic Heisenberg model with uniaxial anisotropy in a magnetic field. Once the idea is accepted that the superconductivity in the oxides is due to local (real-space pairs), one may directly transpose this knowledge of the magnetic analogues to the boson problem. In particular the comparison between the cubic, BaBiO 3-based superconductors and the quasi 2-dimensional copper-oxide superconductors appears to be quite rewarding. We discuss account of the phase diagrams of T c versus carrier density, the behaviour of the specific heat, the fluctuation effects, the field-dependent effects and the variation of T c with the number of sheets in the superconducting multilayer compounds.