Analysis and Numerics for an Age- and Sex-Structured Population Model
This work provides rigorous theoretical and numerical foundations for modeling two-sex population dynamics, but is incremental as it extends existing McKendrick-von Foerster-Keyfitz models.
The authors develop a mathematical model for age- and sex-structured human population dynamics, proving well-posedness and asymptotic stability using semigroup theory, and propose a convergent numerical scheme with a real data application.
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.