Persistence and global stability of a stage-structured food chain model with distributed maturation delay and harvesting

Abstract

A three-species food chain model with stage-structure and harvesting is proposed and analyzed, at which the maturation delay is modeled as a distributed for each species, to allow for the possibility that individuals may take different amounts of time to mature. It is assumed in the model that immature predator (immature top predator) do not have the ability to feed on prey (predator), and the mature predator (mature top predator) do not feed on immature prey (immature predator). Mathematical analysis of the model with regard to positivity of solutions, permanence and global stability are analyzed. By using comparison arguments, some sufficient conditions are obtained to guarantee the permanence of the model. Also, by the mean of an iterative technique, we established sufficient conditions for the global attractivity of the boundary equilibria and the positive equilibrium.