Near-optimality of a stochastic delay model for spruce budworm population with chemical control

Considering the effect of climatic conditions and the side effects of spruce budworm on spruce forests, in this paper, we develop a stochastic delay model for the spruce budworm population with chemical control. In order to reduce the number of pests while minimizing the control cost, the near-optimal control problem is constructed. By applying Ekeland’s principle, the sufficient and necessary conditions for near-optimality are derived. Subsequently, numerical simulations are conducted to demonstrate the theoretical results. The numerical results indicate that chemical control can efficiently control the quantity of this insect. Moreover, accurately detecting the maturation time delay of the spruce budworm holds significant practical importance for controlling this pest and achieving the goal of protecting spruce forests. This research could provide valuable insights and potential solutions for managing the spruce budworm population and safeguarding spruce forests in the face of climate change.