Oscillations in age-structured population models with an Allee effect

AbstractA nonautonomous ordinary differential delay equation for the birth rate of a model age-structured population is derived under the assumptions that nonlinear density effects on fertility exhibit an “Allee effect”. It is shown how this assumption produces an interval of inherent net reproductive numbers less than one on which there exist two stable (asymptotic) equilibria. Furthermore, in the presence of a maturation delay and a sufficiently narrow age-specific fertility window, numerical solutions show that a certain type of attracting, large amplitude “synchronous” oscillation can also exist on this interval. A heuristic argument is given for the existence of such oscillations using the model obtained when the length of the fertility window shrinks to zero