Analysis and Numerics for an Age- and Sex-Structured Population Model

TL;DR

This paper analyzes a two-sex population model using semigroup theory for well-posedness and stability, and introduces a convergent finite difference scheme with real data application.

Contribution

It provides a rigorous mathematical analysis of a two-sex population model and develops a stable numerical method with proven convergence.

Findings

Model is well-posed and asymptotically stable under certain conditions.

Finite difference scheme converges under minimal regularity.

Application to real demographic data demonstrates practical relevance.

Abstract

We study a linear model of McKendrick-von Foerster-Keyfitz type for the temporal development of the age structure of a two-sex human population. For the underlying system of partial integro-differential equations, we exploit the semigroup theory to show the classical well-posedness and asymptotic stability in a Hilbert space framework under appropriate conditions on the age-specific mortality and fertility moduli. Finally, we propose an implicit finite difference scheme to numerically solve this problem and prove its convergence under minimal regularity assumptions. A real data application is also given.