As people become wealthier, they have fewer kids. When times are good, instead of reproducing exponentially (like rabbits), people prefer to spend resources nurturing fewer children, for instance by investing in education and saving money for the future. This trend toward smaller families has been observed throughout the developed world, from the United States to Europe to Asia.
The poorest parts of the world, most notably sub-Saharan Africa, still have sky-high fertility rates, but they are declining. The solution is just what it has been elsewhere: more education, easier access to contraception and economic growth. Catastrophe avoided.
Consequently, no serious demographer believes that human population growth resembles cancer or the plague. On the contrary, the United Nations projects a global population of 9.3 billion by 2050 and 10.1 billion by 2100. In other words, it will take about 40 years to add 2 billion people, but 50 years to add 1 billion after that. After world population peaks, it is quite possible that it will stop growing altogether and might even decline.
Despite all indications to the contrary, global population cataclysm isn’t at hand and never will be unless the well-established and widely researched trends reverse themselves. That’s not likely.