The Nash optimal control of forest ecosystem at risk of fire ignition

We are exploring a mathematical model of a forest ecosystem that is at risk of fire ignition when the ambient temperature rises. We believe that the main characteristic in this case is the amount of carbon entering the atmosphere. Fire control measures are an external control factor that is at the disposal of the Forestry Administration. We were interested in finding the optimal behavior strategy, with which the Forestry Administration could take the necessary measures in a timely manner. We describe the forest ecosystem by a differential equation with two external control factors and apply the theory of differential games to the search for optimal control. By optimal control we mean the Nash equilibrium that we search for our model. We also complicate our model by introducing into consideration a differential equation with four control external factors describing the mosaic-layer phytocenosis.