A mathematical model of human population reproduction through marriage

TL;DR

This paper presents a mathematical model of human population reproduction through marriage, incorporating marriage duration and age at marriage, to estimate fertility rates and project future population trends.

Contribution

It introduces a novel compartmental model linking marriage dynamics with fertility, providing formulas to estimate the total fertility rate from marriage data.

Findings

Model accurately estimates Japan's current TFR.

Reveals how changes in nuptiality affect fertility.

Provides a framework for future demographic projections.

Abstract

We develop a linear one-sex dynamical model of human population reproduction through marriage. In our model, a woman may marry and divorce multiple times; however, only women who are currently married are assumed to bear children. The iterative marriage process is formulated as a three-state compartmental model, which is described by a system of McKendrick equations with a marital birth rate function that depends on the duration of marriage and the age at marriage. To examine the impact of changing nuptiality on fertility, we derive new formulas for the reproduction indices. In particular, the total fertility rate (TFR) is expressed as the product of the total marriage number and the average total marital fertility. Using Japanese vital statistics, we show that our model provides a reasonable estimate of the current TFR and its future trajectory.