4. We see in the Maple worksheet linked below, that it takes
about 80 time steps for the
the proportions of the three age-categories to stabilize
to their asymptotic values: very roughly 2:3:11. Once that happens the
long-term decline of the population becomes evident.
The halving time is seen to depend on the initial state:
case 1: N0=[200,400,400], the population in halved after 190 time steps
case 2: N0=[400,300,300], the population in halved after 212 time steps
case 3: N0=[200,500,300], the population in halved after 211 time steps
This shows that breaking the population into age categories is
necessary for accurate prediction, because just knowing the initial
total population is not enough to predict the halving time. See below:
HTML version of Maple worksheet for Haberman 35.5.