Stability and Optimal Control of Tree-Insect Model under Forest Fire Disturbance

Xiaoxiao Liu and Chunrui Zhang
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Xiaoxiao Liu: College of Mechanical and Electrical Engineering, Northeast Forestry University, Harbin 150040, China
Chunrui Zhang: College of Science, Northeast Forestry University, Harbin 150040, China

Mathematics, 2022, vol. 10, issue 15, 1-12

Abstract: In this article, we propose a mathematical model for insect outbreaks coupled with wildfire disturbances and an optimization model for finding suitable wildfire frequencies. We use a refined Holling II function as a model for the nonlinear response of fire frequency against trees and insects. The results show that for the tree–insect–wildfire model, there is a coexistence equilibrium in the system. Sensitivity analysis is performed to determine the effect of wildfire on trees in the optimization model. The results show that forest fires have a significant impact on the equilibrium mechanism of tree–insect coexistence. Numerical simulations suggest that in some areas of high fire intensity, there may be positive feedback between disturbances from wildfires and insect outbreaks. The result is consistent with the present theory in this field.

Keywords: forest fire; tree–beetle system; stability; sensitivity analysis; optimal control (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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