An age-structured population model with state-dependent delay: Dynamics

Abstract

We consider an age-structured population model with distinct immature and adult stages, wherein the populations at each stage consume different limited food sources. This gives rise to a model composed of the McKendrick-Von Förster partial differential equation, a nonlinear boundary condition describing the birth rate, and a threshold condition that yields a state-dependent delay. The state-dependence re?ects the changing age of maturity stemming from an intuitive accounting of the maturation time due to competition for resources within the immature population. Properties of solutions to this model are derived and the dynamics are compared to the corresponding constant delay case when state-dependence is ignored. As a parameter involved in birth rate is increased, we numerically observe a bifurcation from an extinction steady state to an endemic steady state, and observe both monotonic and oscillatory approaches to equilibrium.