We present the result of a fit of an astrophysical model of UHECR sources to the energy spectrum measured using the TA surface detectors and the composition data measured by TA fluorescence detectors in stereo mode. The astrophysical model consists of identical sources, uniformly distributed in comoving volume, where groups of nuclei with varying fractions are accelerated producing a power-law source with a rigidity-dependent cutoff. The model includes the propagation effects of photo-pion production, photo-nuclear disintegration and general energy loss from universal expansion. Comparison of model data with detector data in both the energy and the \(X_{\rm max}\) distributions is done via a forward-folding description of detector effects.