The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. Under only continuity assumptions on the density dependent death and tertility rates, it is shown that a global continuum of positive equilibria exists in a certain Banach space. This continuum connects from the trivial solution at n = 1 to the boundary of the domain on which the problem is posed. Results concerning the spectrum are given. In particular, some circumstances are described under which positive equilibria exist for all n values greater than the critical value n = 1.
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics