Substorm-associated electron injection, starting on Apr. 5, 2017, was observed by the ERG (Arase), GOES-15 and GOES-13 spacecraft. ERG successfully observed a clear and sufficient extent of manifestations of the dispersionless injection and the successive drift echoes at radial distances shorter than geosynchronous orbit (GEO) during a unique period of the satellite mission. The GOES-15 and GOES-13 measured the drift echoes of the event as well. The observations provided constraints to study the event and opportunities to make adjustments to the previous substorm injection models. Models built on an impulsive earthward-propagating electromagnetic field have been proposed to simulate substorm injections. So far such models showed good results of dispersionless features compared to spacecraft observations, but could only produce drift echoes with periods somewhat different from geosynchronous observations. To study the substorm injection event and produce drift echoes with better periods, we modify an existing model in the literature. ERG and GOES spacecraft measured tens to a few hundred keV electrons injected during the substorm, providing important seed population for ring current and radiation belts. Since the electron energies of interest are comparable to the rest mass energy, our work further provides the relativistic form of the previous model and employs a semiempirical model as background field instead of a dipole-based one in the previous study. Our work shows that the main features of the substorm injection event are successfully reproduced with the drift echoes periods showing a better fit to the observations of this event when relativistic effects are considered. Despite possible deviation of the model magnetic fields from reality, the relativistic computations still show dominant effect on the drift echoes periods. The substorm injection expanding earthward farther than GEO was observed by ERG, and the event can be better simulated by the further-developed model shown in this work.