It won't.
When will it stop?
When we have a major war, pandemic, economic collapse or some other such happening.
These are events that have happened repeatedly through out history and have wiped out entire civilizations.
Those that survived were those that started with enough excess population to fill the essential slots to keep things limping along.
Those civilizations that had little to no excess population vanished.
“When we have a major war, pandemic, economic collapse or some other such happening.”
Not even necessary. Fertility in every nation is plummeting. China and India below or near fertility of 2.1, which is the number required for stable populations. Europe, Japan are way below it. The US is at stable.
These numbers will take some time to affect population growth. But by the end of the century, world population will be declining all by itself. Wars and pandemics will only augment a demographic process already baked in.
Turns out the pill is the most powerful force in the world today.
You are correct. Byzantium was a world power until the reign of Justinian when the plague hit. .
Not correct. The world population stops growing a country at a time. That is, demographically, when a country reaches an economic plateau unique to it, quickly its birthrate falls to between 2.1 and 2.3 children per family, which is the stable level of no growth.
Importantly, while government often panics with this, there is little they can directly do to increase their population growth rate. However, both government and the predominant social culture can *lower* the rate even further.
That is, every added “requirement” of potential parents by either government or culture means that fewer parents will want to have children. Added to this provision of birth control, and abortion, and the birthrate can really be driven down.
Most recently, this phenomenon has taken place in Mexico, whose population growth rate has dropped to just 1.15%, just slightly less than Iceland, at 1.17%. Most of eastern Europe are in the *negative* numbers.
https://www.cia.gov/library/publications/the-world-factbook/rankorder/2002rank.html#mx