One of the scenarios actively studied during the recent trace tritium experimental campaign performed on JET includes a gas puff of small amounts of tritium into the sawtooth-unstable H-mode plasmas heated by deuterium beams. The sawtooth crashes observed in these discharges with the Electron Cyclotron Emission (ECE) diagnostics are frequently accompanied by the oscillations of the 14MeV neutron emission produced mainly due to the reaction between deuterium beam and thermal tritium. Such oscillations are clearly seen in low density plasma while they are weak or absent at high density. The dynamics of the trace tritium and beam deuterium during the sawtooth crash is studied here numerically using the TRANSP code with the goal to explain the different evolution of neutron emission with density. A test of the full and partial reconnection models in predictive simulations of neutron data with the TRANSP code is discussed.