Global branches of equilibrium solutions of the McKendrick equations for age-structured population growth
type: Item
instance of: scholarly article
title: Global branches of equilibrium solutions of the McKendrick equations for age-structured population growth
zbMATH Open document ID: 0578.92020
DOI: 10.1016/0898-1221(85)90145-2
publication date: 1985-01-01T00:00:00Z
review text: The author studies the existence of equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population, that is \[ \partial \rho /\partial t+\partial \rho /\partial a+\mu (a,\rho)=0,\quad \rho (t,0)=\int^{A}_{0}F(a,\rho)\rho (t,a)da. \] The author shows using global bifurcation theory that there exists a continuum of equilibrium solutions with the inherent net reproductive rate \[ n=\int^{A}_{0}F(a,0)\exp (-\int^{a}_{0}\mu (s,0)ds)da \] as bifurcation parameter. The assumptions on the density dependent death and fertility rates \(\mu\) and F involve only continuity. Some circumstances are described under which positive equilibria exist for all values of n greater than the critical value \(n=1\).
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 3926706
zbMATH Keywords: population growth
zbMATH Keywords: continuity assumptions
zbMATH Keywords: existence of equilibrium solutions
zbMATH Keywords: McKendrick equations
zbMATH Keywords: age-structured population
zbMATH Keywords: global bifurcation
zbMATH Keywords: net reproductive rate
zbMATH Keywords: density dependent death and fertility rates
zbMATH Keywords: positive equilibria
author: J. M. Cushing
reviewed by: Gustaf Gripenberg
MaRDI profile type: Publication
full work available at URL: 0898-1221(85)90145-2
OpenAlex ID: W2013864669
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 3926706