Effect of decreasing population growth-rate on deforestation and population sustainability

We consider the effect of non-constant parameters on the human-forest interaction logistic model coupled with human technological growth introduced in [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 civilization without going through a catastrophic population collapse. We find that for realistic values of the human population carrying capacity of the earth (measured by the parameter β) this decrease would not affect previous results, leading to a low probability of avoiding a catastrophic collapse. For larger more optimistic values of β instead, a decrease in growth-rate would tilt the probability in favor of a positive outcome, i.e. from 10-20% up to even 95% likelihood of avoiding collapse.