On a delayed invasive species model with harvesting

. In this paper a mathematical model will be studied that describes the connections between three species: people, trees and rats. This model, which is based on a three-dimensional system of ordinary differential equations, has been motivated by attempts to explain the ecological disaster of Easter Island. The system has four equilibria from which three ones are on the boundary of the positive octant of the phase space and - under appropriate conditions - there is a unique interior equilibrium. We incorporate discrete delay into the system in order to have a more realistic model. This delay takes into account that time is needed for the seeds to become a full-grown tree. The stability of the equilibria with delay and the possibility of an oscillatory behaviour are examined.