We present the result of fits of an astrophysical model of UHECR sources to the energy spectrum measured using the Telescope Array (TA) surface detectors and the composition data measured by TA fluorescence detectors in stereo mode. The astrophysical model consists of identical sources, uniformly distributed with a density which evolves with age, 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 $𝑋_\mathrm{max}$ distributions is done via a forward-folding description of detector effects. A prediction of the cosmogenic neutrino flux at Earth resulting from the cosmic rays produced in the model with these fit values is also presented. The predicted flux is considerably higher than other similar fits to Auger data have previously predicted.