Qualitative analysis and optimal harvesting policy of Holling-III model with harvesting rates for prey and predator

A predator-prey model with Holling-III functional response is studied, in which the density restriction and harvesting policy are presented in two populations. By using qualitative analysis theory of differential equation and Pontrjagin maximum value principle, the conditions for the existence and uniqueness as well as global asymptotic stability of the positive equilibrium are obtained. The corresponding biological significance is analyzed, and the optimal sustainable harvesting policy is proposed.