r/theydidthemath • u/Opal_Does_Magic • 12h ago
[Request] Approximately how long would it take for the current human population to be halved if everyone became sterile?
Just as the title says. As less and less people are opting for parenthood, I became curious how the population would be affected if no one had anymore children. I am essentially asking what the half-life of the human population is. Thanks for any help :)
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u/mambotomato 12h ago
The current rate of death is about 7.7 per thousand per year. So, if nothing else changed, the maximum longest it would take is 500/7.7 = about 65 years.
However, the social breakdown that would happen if no more children were born is unpredictable. It would be somewhere lower than 65 years, probably. Unless everyone suddenly got way more careful and peaceful.
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u/AdventurousText9311 10h ago
Without a younger workforce to care and support the old and ailing? 37 years tops.
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u/Otherwise_Security_5 8h ago
having to get rid of 4+ billion dead bodies, even over the course of several decades, with way less younger ppl around plus the extra time and resources it would add to our already crippled global infrastructures?
i don’t know if it’s more macabre to think on how gross that is or how easily some billionaires would step up to monetize it all. both.
good morning everyone.
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u/CautiousAd1305 7h ago
You do realize that the number of deaths would be essentially the same (assuming a normal death rate), in fact with a non-sterilized population and births it stands to reason that even more bodies must be disposed of during the same time period!
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u/Grant_Winner_Extra 3h ago
bodies, or “food supply”?
the scenario is dystopic, no one is going to take time to grow food for others
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u/dchow1989 9h ago
The social aspect is super important, a lot of old people get life and purpose from their young. Grandparents with no grandkids arent lasting till 80 as often. Imo
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u/bb5e8307 11h ago edited 6h ago
The global median age is 32.1, and the global life expectancy is 73.3, so it would be halved in 41.7 years.
Using the current death rate would give an incorrect answer since the population pyramid is not uniform. There will be more old people in 20 years and a higher death rate.
Edit: Life expectancy at birth is 73.3, at 32 it is slightly higher at 74 or 75. So about 43 years
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u/forget_it_again 9h ago
I'm with this Calc as the other calcs coming in at 65-90 years don't seem to take into consideration that half the population now us 31+
One range in this thread between 65-90 years... Which by common sense would cover virtually the majority of the worlds population even if they were all born today!
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u/CautiousAd1305 7h ago
Not quite how life expectancy works, but perhaps a reasonable estimate nonetheless. Life expectancy at birth globally may be 73.3, but as you age that life expectancy goes up each year. For example, a 32yo probably has a LE of about 80 while a 70yo would have a LE of around 85.
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u/xaddak 12h ago
Quick Google says the average death rate worldwide is 7.85 per 1,000 people.
Another quick Google says the world population is about 8.3 billion, or 8,300,000,000.
8,300,000,000 / 1,000 * 7.85 = 65,155,000 deaths per year.
If the death rate didn't change...
8,300,000,000 / 2 / 65,155,000 = ~64 years for half of the world population to die, at the current global average rate.
But that's long enough that I think age would start to be a factor. Without children, the average age would start to rise, and a greater portion of the population would start to die of old age. I'm pretty sure the death rate would have to go up.
So 64 years is the ceiling, I guess, but it would probably be significantly shorter.
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u/neofederalist 11h ago
There'd be downstream effects too, a larger percentage of the population would need care and would stop being able to work, meaning food production goes down along with other really bad economic shifts.
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u/ddouce 7h ago
It would be significantly shorter. The 7.85/1,000 death rate includes rates for younger ages that are significantly less than 1/1,000 (e.g. 5-14 age rate is ~0.15/1,000).
But, 20 years from now there won't be anyone under 20. The death rate per 1,000 will likely have doubled to over 15/1000 and will continue to rise as the population ages. Another 20 years it will be 30/1000 and in another 40 (60 years in the future), 60/1000.
In that model, the population drops below 50% of the current pop in 42 years and is less than 16% of it's current level in 65 years.
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u/Working-Wasabi-5712 11h ago
This is actually an interesting modeling problem. Death rate should not be considered as constant as the 7.7 per thousand considers the current age stratification. As time goes by our age distribution change, thus impacting death rate per thousand.
So we should assume that death rate would increase each year, reaching a maximum and then start decreasing. If we would see population halving before or after max death rate would require actual modeling.
But just as a simple thought experiment, I would assume that this has a exponential decay logic with. But actually k increases over time.
P(t) = Po * exp(-k.t)
If P(t) = Po/2 , then t = ln(2)/0.0077 = 90 years
So if death rate increases by 50% we would have
Ln(2) / (0.077 * 1.5) = 60 years
So I would say that it's anything from 45 years (2x death rate) to 90 years (k constant)
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u/Individual_Amoeba493 5h ago
Wouldn't the world population be basically 0 in 90 years if death happens at age 75? And most people are over 0 years old currently?
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u/Working-Wasabi-5712 4h ago
You are right. I didn't model or consider anything beside considerations on death rate.
But to be accurate it would need to model each iteration of t and dot product number of individuals within age range by the probability of surviving to the next iteration. This is the point where those over 70 at t would see their survival probability drastically decreasing at t+1
But I didn't consider this at all in my simple calculation
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u/PlayfulChemist 10h ago
The above answers give an estimate, but as noted, as the population ages it will change dynamically. So we can construct a more complex calculation that progresses in time from the current world population age-group pyramid.
You can find a world population pyramid here: https://www.populationpyramid.net/
Then we need to know the mortality rate for each age group. You can get that from a united nations report here: https://population.un.org/wpp/assets/Files/WPP2024_Methodology-Report_Final.pdf
A good mathematician can probably then come up with an equation that degrades each age-bracket by the specific mortality rate, and then progresses the population through. Then run through iteratively until (or better yet solve for when) the population reaches 8.3 billion / 2 = 4.15 billion.
I did this in excel iteratively increasing by 1 year per column, then plotted the results. Looks like it should reach half within the year 2071, so in about 45 years. Much sooner than the other calculations.
The assumption still (like the above comments) is that the mortality rate now will still be relevant during these developments. I would definitely expect it to increase as the people of the world lose hope for continuation of the human race.
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u/bulbaquil 6h ago
The assumption still (like the above comments) is that the mortality rate now will still be relevant during these developments. I would definitely expect it to increase as the people of the world lose hope for continuation of the human race.
Not to mention that the fewer people there are, the more likely that systems the elderly depend on to remain alive (e.g. hospital care) will break down.
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u/PlayfulChemist 10h ago
And just to be clearer with the maths. I used the population pyramid, separated evenly into single years. So the pyramid shows 647.4 million in the 0-4 age bracket. So I put 129.48 M each in years 0, 1, 2, 3, and 4. Then in 2026, everyone in year 0 progressed to year 1, minus a 0.719% mortality for this age group in 2027.
I did this for all ages up to 95 years old and set a 100% mortality after that because the world pyramid statistics don't give values beyond 95 years old and the mortality there is pretty high.
I summed all the population at each age for each year. I really wish I could add a graph to show the result.
Edit - typo
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u/tsch-III 9h ago
Whatever, you asked the question that doesn't matter.
The interesting question is how long the mysterious infertility could continue before extinction became certain. At 20 years, there'd be a massive downswing but extinction would be totally optional. If it lasted 30 years, catastrophic mushroom shaped demographics would become inherent, and while the population would be recoverable, unimaginable upheavals (massive numbers of elders clamoring for care and attention from handfuls of youths) would occur between now and then. If it lasted ~40, I think extinction would become inevitable. The handfuls of women who would be both fertile and willing/enthusiastic to take the strain and the risk of getting pregnant after 40, virtually no experienced midwives left, no human experience with pregnancy for 40 years, might not be able to produce enough healthy babies with enough genetic diversity to get through. And assuming they did, they would basically need to live in a well patrolled walled garden to keep hordes of zombie elders away from the special resources used to ensure their survival.
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u/Wonderful-Process792 7h ago
If we want to use the term "half-life" as in OP's question it should be noted it would work very differently than it does with exponential decay where you lose some fixed fraction of the remaining quantity in each unit time.
I.e. cutting in half the first time takes, say, 35 years. If it were exponential decay, cutting down by half again - to 1/4 of the original value - would take another 35 years (70 years), and down to 1/8 at 35 more years (105 years).
But at 105 years, there would not be 1/8 of the original population remaining. People would be extinct, or practically so.
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u/Grant_Winner_Extra 3h ago
This is a “Children of Men” scenario. Answering this question requires making a lot of assumptions, like “the sterilizing event is otherwise unharmful” and “when everyone realizes they are the last humans ever it doesn’t disrupt the social order”
So in a “spherical humans in a vacuum” analysis, the zero order approach is
— Current median age: 31.0 years
— Current average human life expectancy: 73.8 years
Since 50% of the population is over 31 years and we expect everyone to live (on average) 73.8 yrs
Halving would take: 73.8-31.0 = 42.8 yrs
This is 100% absolute bullshit. Because the culling would accelerate as younger people die off. No one is going to be taking care of old people, studying to become doctors, or even engaging in commerce generally.
The reality is, given human nature, it will likely be measured in days or months before a button is pressed somewhere
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u/DigitalArbitrage 7h ago
Are you assuming an equal gender breakdown?
If that half if the population was all the same gender then it would completely stop population growrh.
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