Did the ever dead outnumber the living and when? A birth-and-death approach

TL;DR

This paper investigates whether the number of dead outnumbers the living at any point in history using various mathematical models, including deterministic, Markov chain, and age-structured approaches.

Contribution

It introduces a formal analytical framework for the question of dead versus living populations using multiple modeling techniques.

Findings

Developed deterministic Malthusian growth models with constant and time-dependent rates.

Explored linear birth and death Markov chain models.

Analyzed age-structured population models.

Abstract

This paper is an attempt to formalize analytically the question raised in "World Population Explained: Do Dead People Outnumber Living, Or Vice Versa?" Huffington Post, \cite{HJ}. We start developing simple deterministic Malthusian growth models of the problem (with birth and death rates either constant or time-dependent) before running into both linear birth and death Markov chain models and age-structured models.