The continually increasing rate of human economic activity leads to changes in many natural systems. Their restoration is one of the most important tasks today. For this purpose, protected areas have been created, such as natural reserves, national parks, and wildlife sanctuaries. National parks are of particular interest, as they are the only protected areas listed above where tourism is allowed and organized. However, their activities cannot exist without sufficient financial support. This article describes a two-level optimal control model of the national park activity. For the purpose of exploring and analysing the proposed model, an algorithm that can be used to find the Stackelberg equilibrium guaranteeing the sustainable development of the national park is proposed and implemented in software.

Keywords: two-level hierarchical model, Stackelberg equilibrium, national park, leader, follower,subjects of management ,control parameters