On simple age-structured population models

This work addresses several aspects and extensions of the deterministic Leslie model, as a matrix-driven demographic evolution of an age-structured population. We first point out its duality with another matrix model, related to backward/forward in time ways of counting individuals. Then, in some special cases, we design explicitly both the eigenvalues and the offspring vector of the Leslie matrix in a consistent way. Finally, we show how embedding the dynamics in a space of larger dimension allows one to get various new results about the population. This includes access to the total lifetime asymptotic distribution and while including sterile and/or immortal individuals in the classical Leslie model, some insight into the trade-off between the different population species.