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We present a model of a viscously evolving accretion disc around a magnetized neutron star. The model features the varying outer radius of the hot ionized part of the disc due to cooling and the varying inner radius of the disc due to interaction with the magnetosphere. It also includes hindering of accretion on the neutron star because of the centrifugal barrier and irradiation of the outer disc and companion star by X-rays from the neutron star and disc. When setting inner boundary conditions, we take into account that processes at the inner disc occur on a time-scale much less than the viscous time-scale of the whole disc. We consider three types of outflow from the disc inner edge: zero outflow, one based on MHD calculations, and a very efficient propeller mechanism. The light curves of an X-ray transient after the outburst peak can be calculated by a corresponding, publicly available code. We compare observed light curves of the 2013 burst of Aql X-1 in X-ray and optical bands with modelled ones. We find that the fast drop of the 0.3–10 keV flux can be solely explained by a radial shrinking of the hot disc. At the same time, models with the neutron star magnetic field >108 G have better fits because the accretion efficiency behaviour emphasizes the ‘knee’ on the light curve. We also find that a plato emission can be produced by a `disc-reservoir' with stalled accretion.