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

作者：Pokojovy Michael^*; Skvarkovskyi Yevhenii

来源：Numerical Methods for Partial Differential Equations, 2016, 32(2): 706-736.

DOI：10.1002/num.22032

• exponential stability
• finite difference scheme
• numerical convergence
• partial integro-differential equations
• population dynamics
• well-posedness

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.

• 出版日期2016-3