Mathematical Biology Seminar

Date
Tue, Oct 15, 2024 12:30 pm - 1:30 pm
Location
3206 Kirwan Hall (Math Building)

Description

Speaker: Victor Yakovenko (UMD Physics)

Title: The Mathematics of Human Population Growth and CO2 Emissions

Seminar link: https://www-math.umd.edu/research/seminars/math-biology.html#view-abstract-8

Abstract:
In a paper published in the Science magazine in 1960, von Foerster et al. argued that human population growth follows a hyperbolic pattern with a singularity in 2026. Using current empirical data from 10,000 BCE to 2023 CE, we re-examine this claim. We find that human population initially grew exponentially as N(t)~exp(t/T) with T~3000 years. This growth then gradually evolved to be super-exponential with a form similar to the Bose function in statistical physics. Population growth further accelerated around 1700, entering the hyperbolic regime N(t)=C/(ts-t) with the projected singularity year ts=2030, which essentially confirms the prediction by von Foerster et al. We attribute the switch from the super-exponential to the hyperbolic regime to the onset of the Industrial Revolution and the transition to massive use of fossil fuels. This claim is supported by a linear relation that we find between population and the increase in CO2 level in the atmosphere from 1700 to 2000. Then, at the end of the 20th century, the inverse population curve 1/N(t) begins to deviate from a straight line and avoids crossing zero, thus escaping a literal singularity. We find that N(t) is well fitted by the square root of the Lorentzian function, with a maximum of slightly more than 8.2 billion people at t=ts. The width 2\tau of the population peak is given by the cutoff time \tau=32 years. We also find that the increase in CO2 level in the atmosphere since 1700 is well fitted by arccot[(ts-t)/\tau_F] with \tau_F=40 years. This fit gives a forecast of the CO2 level in the near future for the 21st century.