Age-structured Population Models with Applications

Abstract

A general model of age-structured population dynamics of early humans is developed and the fundamental properties of its solutions are analyzed. The model is a semilinear partial differential equation with a nonlinear nonlocal boundary condition. Existence, uniqueness and regularity of solutions to the model equations are proved. An intrinsic growth constant is obtained and linked to the existence and the stability of the trivial or the positive equilibrium. The model supports the viability of the extended juvenile and post-reproductive phases of the human species.