Modelling and Analysis of Stage-Structured Population Model with State-Dependent Maturation Delay and Harvesting

In 1992, Aiello, Freedman and Wu proposed a mathematical model of certain marine population in which the time from birth to maturity is directly related to the number of individuals present. In this paper we derive an alternative model where the immature birth rate is taken to be a non-monotone birth function in the kind seen in other frequently studied population model, the death rate for the matures is taken to be a general function, and with harvesting of the mature and immature populations. We study the dynamics of our model analytically, and we present results on positivity and boundedness. We also carry out a linearised analysis on the equilibria, which is algebraically very complicated in the case of the non-trivial equilibrium. We prove that the zero steady state is globally asymptotically stable in the situation when the positive equilibrium does not exist