We present results from numerical simulations of a Jupiter family comet (JFC) population (orbital periods P < 20 yr and Tisserand parameters in the range 2 < T < 3.1) originated in the Scattered Disk and transferred to the Jupiter's zone through gravitational interactions with the Jovian planets. We shall call ‘non-JFCs’ those comets coming from the same source, but that do not fulfill the previous criteria (mainly because they have periods P > 20 yr). We have carried out series of numerical simulations of fictitious comets with a purely dynamical model and also with a more complete dynamical - physical model that includes besides nongravitational forces, sublimation and splitting mechanisms. We obtained better fits with models including physical effects, and in particular our best fits are for four splitting models with a relative weak dependence on q, and a mass loss in every splitting event that is smaller/greater for higher/lower frequencies respectively. The mean lifetime of JFCs with radii R > 1 km and q < 1.5 AU is found to be of about 150-200 revolutions (~103 yr). We find a total population of JFCs with radii R > 1 km within Jupiter's zone of 450 ± 50 and a mean lifetime of about 150-200 revolutions (~103 yr) for those getting q < 1.5 AU. The population of JFCs + non-JFCs with radii R > 1 km in Jupiter-crossing orbits may be about ~2,250 ± 250. Most of non-JFCs have perihelia close to Jupiter's orbit.

We also present maps of the densest zones of JFCs in the orbital element space.