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The SIDM model combines the isothermal Jeans model and the model of adiabatic halo contraction into a simple semi-analytic procedure for computing the density profile of self-interacting dark-matter (SIDM) haloes with the gravitational influence from the inhabitant galaxies. It agrees well with cosmological SIDM simulations over the entire core-forming stage and up to the onset of gravothermal core-collapse. The fast speed of the method facilitates analyses that would be challenging for numerical simulations.