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Analysis and numerics for an age‐ and sex‐structured population model

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. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 706–736, 2016