  We present simulation results of a gradual solar energetic particle (SEP)
event detected on 2021 October 9 by multiple spacecraft, including BepiColombo
(Bepi) and near-Earth spacecraft such as the Advanced Composition Explorer
(ACE). A peculiarity of this event is that the presence of a high speed stream
(HSS) affected the low-energy ion component ($\lesssim 5$ MeV) of the gradual
SEP event at both Bepi and ACE, despite the HSS having only a modest solar wind
speed increase. Using the EUHFORIA (European Heliospheric FORecasting
Information Asset) magnetohydrodynamic model, we replicate the solar wind
during the event and the coronal mass ejection (CME) that generated it. We then
combine these results with the energetic particle transport model PARADISE
(PArticle Radiation Asset Directed at Interplanetary Space Exploration). We
find that the structure of the CME-driven shock was affected by the non-uniform
solar wind, especially near the HSS, resulting in a shock wavefront with strong
variations in its properties such as its compression ratio and obliquity. By
scaling the emission of energetic particles from the shock to the solar wind
compression at the shock, an excellent match between the PARADISE simulation
and in-situ measurements of $\lesssim 5$ MeV ions is obtained. Our modelling
shows that the intricate intensity variations observed at both ACE and Bepi
were influenced by the non-uniform emission of energetic particles from the
deformed shock wave and demonstrates the influence of even modest background
solar wind structures on the development of SEP events.
