Optimization of hard-to-renew resources extraction

Based on a mathematical model of the predator-prey type interacting populations, we have investigated consumption of natural resources in a system with slow recovery of harvested resource. The proposed model incorporates the saturation effect in the predator population, whose reproduction is limited by the volume of available food and the way of its consumption. The focus of the study is on the problem of optimizing predator and prey production. It is shown that there is an optimal withdrawal rate that ensures maximum income with the sustainable development of the community.