  Corotation of particle-filled magnetic flux tubes is generally thought to
have a minor influence on the time-intensity profiles of gradual Solar
Energetic Particle (SEP) events. For this reason many models solve the focussed
transport equation within the corotating frame, thus neglecting corotation
effects. We study the effects of corotation on gradual SEP intensity profiles
at a range of observer longitudinal positions relative to the solar source. We
study how corotation affects the duration and decay time constant of SEP events
and the variation of peak intensity with observer position. We use a 3D
full-orbit test particle code with time-extended SEP injection via a shock-like
source. Unlike with focussed transport models, the test particle approach
enables us to switch corotation on and off easily. While shock acceleration is
not modelled directly, our methodology allows us to study how corotation and
the time-varying observer-shock magnetic connection influence intensity
profiles detected at six observers. We find that corotation strongly affects
SEP profiles, for a monoenergetic population of 5 MeV protons, being a dominant
influence during the decay phase. Simulations including corotation display
dramatically shortened durations for western events, compared to those which do
not include it. When corotation is taken into account, for both eastern and
western events the decay time constant is reduced and its dependence on the
scattering mean free path becomes negligible. Corotation reduces the peak
intensity for western events and enhances it for eastern ones, thus making the
east-west asymmetry in peak intensity stronger, compared to the no-corotation
case. Modelling SEP intensity profiles without carefully accounting for
corotation leads to artificially extended decay phases during western events
and profiles with a similar shape regardless of observer longitudinal position.
