  We present a new numerical model of the eta-Aquariid and Orionid meteor
showers. The model investigates the origin, variability and age of the
eta-Aquariid and Orionid apparitions from 1985 to the present day, in order to
forecast their activity over the next several decades. Through the numerical
integration of millions of simulated meteoroids and a custom-made particle
weighting scheme, we model the characteristics of every eta-Aquariid and
Orionid apparition between 1985 and 2050. The modeled showers are calibrated
using 35 years of meteor observations including the showers activity profiles
and interannual variability.
  Our model reproduces the general characteristics of the present-day
eta-Aquariids, and part of the Orionid activity. Simulations suggest that the
age of the eta-Aquariids somewhat exceeds 5000 years, while a greater fraction
of the Orionids are composed of older material. The 1:6 mean-motion resonance
with Jupiter plays a major role in generating some (but not all) Halleyid
stream outbursts. We find consistent evidence for a periodicity of 11.8 years
in both the observations and modeled maximum meteor rates for the Orionids. A
weaker evidence of a 10.7 year period in the peak activity for the
eta-Aquariids needs to be investigated with future meteor observations. The
extension of our model to future years predicts no significant Orionid outburst
through 2050 and four significant eta-Aquariid outbursts in 2023, 2024, 2045
and 2046.
