  We consider the effect of non-constant parameters on the human-forest
interaction logistic model coupled with human technological growth introduced
in "Deforestation and world population sustainability: a quantitative
analysis"[1]. In recent years in fact, a decrease in human population growth
rate has emerged which can be measured to about 1.7% drop per year since 1960
value which coincides with latest UN projections for next decades up to year
2100 [2]. We therefore consider here the effect of decreasing human population
growth-rate on the aforementioned model and we evaluate its effect on the
probability of survival of human civilisation without going through a
catastrophic collapse in population. We find that for realistic values of the
human population carrying capacity of the earth (measured by parameter beta)
this decrease would not affect previous results leading to a low probability of
avoiding a catastrophic collapse. For larger more optimistic values of beta
instead, a decrease in growth-rate would tilt the probability in favour of a
positive outcome, i.e. from 10-20% up to even 95% likelihood of avoiding
collapse.
