There are already far more people on earth than those of us who like a sense of space are really comfortable with. But that does not mean the population will not continue to soar. However, so much of that population is now gathered in vast urban complexes that it seems more than just probable that a new form of plague will vastly reduce this overcrowding, well before we ever find out how accurate the present long-term birth-rate projections really are. Never in human history has so large a percentage of the whole population of the earth been in so vulnerable a position. (Living in such close proximity to so many potential carriers, with so much travel in and out of those who have not had the same previous immunity building exposures.)
While some will suggest this is an alarmist projection, perhaps some with advanced mathematical skills will endeavor to actually measure the increased risk, with proximity and travel factors calculated on the basis of some formula. (Granted, the nature of the contagion may not be predictable, hence the calculation only can be based upon something known--such as a mutation of some known disease, where there is data as to the likelihood of contracting same based upon a calculatable level of exposure that can be determined.)
Unfortunately, my math skills are no better than my knowledge of pathogen to anti-body counts for any ailment. So all I can do is suggest the scenario.
William Flax Return Of The Gods Web Site.