Dynamics of a predator-prey model with the Allee effect for the predator induced by weighted harvesting strategy

Over-exploitation of natural resources poses cascading challenges to the environment, economy, and public health. To mitigate these adverse impacts and achieve long-term ecological and socioeconomic balance, sustainable development strategies are imperative. Thus, in this paper, we developed a predator-prey model with state-dependent impulsive control, grounded in the weighted escapement policy, to regulate resource harvesting more realistically. We investigated the model's dynamical behaviors, focusing on the existence and stability of semi-trivial and order-1 periodic solutions. To enhance economic viability while ensuring sustainability, an optimization problem was formulated to maximize long-term profits via optimal harvesting schemes. Finally, numerical simulations validated the theoretical results, quantified the optimal harvesting level and weight parameter of the weighted escapement policy, and provided actionable insights for practical resource management.