A composite model of wave propagation from terrestrial very low frequency (VLF) transmitters has been constructed to estimate the wave normal angles and fields of whistler mode waves in the plasmasphere. The model combines a simulation of the fields in the Earth-ionosphere waveguide, ionospheric absorption estimates, and geomagnetic field and plasma density models with fully three-dimensional ray tracing that includes refraction, focusing, and resonant damping. The outputs of this model are consistent with those of several previous, simpler simulations, some of which have underlying component models in common. A comparison of the model outputs to wavefield data from five satellites shows that away from the magnetic equator, all of the models systematically overestimate the median field strength in the plasmasphere owing to terrestrial VLF transmitters by about 20 dB at night and at least 10 dB during the day. In addition, wavefield estimates at L < 1.5 in the equatorial region appear to be about 15 dB too low, although measured fields there are extremely variable. Consideration of the models' similarities and differences indicates that this discrepancy originates in or below the ionosphere, where important physics (as yet not conclusively identified) is not being modeled. Adjustment of the low-altitude field estimates downward by constant factors brings the model outputs into closer agreement with satellite observations. It is concluded that past and future use of these widely employed trans-ionospheric VLF propagation models should be reevaluated.