An Optimal Control Approach for Time-Dependent Harvesting Strategies in Delayed Predator-Prey Dynamics

Abstract

We incorporate optimal harvesting control into a prolonged predator–prey model with Holling type III functional response. Although basic analysis established time delays’ and constant effort harvesting’s influence on stability and bifurcation properties, here we replace constant effort harvesting with time-dependent control variables and formulate an optimal control problem. The objective is to optimize total harvest yield while not pushing species to extinction or overexploitation. By using Pontryagin’s maximum principle for discrete delay systems, we derive the conditions for the required optimality. Numerical simulations show that optimal control strategies outperform constant harvesting by harvesting more biomass and by adapting predator harvesting dynamically to offset oscillations caused by delays at the Hopf bifurcation boundary. This research identifies the manner in which time-progressive harvesting approaches can stabilize lagged ecological systems and offers useful insight for sustainable resource management.