Global branches of equilibrium solutions of the McKendrick equations for age-structured population growth
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 \(n=1\).
density dependent death and fertility rates
scientific article; zbMATH DE number 3926706