Dynamical analysis of a stage-structured prey predator model with harvest effort and multiple time delays

In this paper, a prey predator model with Beddington-DeAngelis functional response and stage structure for prey population is established, where harvest effort on predator population is considered. Multiple time delays are incorporated into model system due to maturation delay for prey population and gestation delay for predator population. Positivity and boundedness of solutions of model system are investigated. By performing local stability analysis of model system around nonnegative equilibria, stability switch due to variation of multiple time delay are discussed. Especially, the lengths of multiple time delays to preserve local stability around interior equilibrium are estimated. Numerical simulations are carried out to show consistency with theoretical analysis obtained in this paper.