Mathematical Modeling and Stability Analysis of the Delayed Pine Wilt Disease Model Related to Prevention and Control

Ruilin Dong, Haokun Sui and Yuting Ding ()
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Ruilin Dong: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Haokun Sui: Department of Mathematics, Northeast Forestry University, Harbin 150040, China
Yuting Ding: Department of Mathematics, Northeast Forestry University, Harbin 150040, China

Mathematics, 2023, vol. 11, issue 17, 1-21

Abstract: Forest pests and diseases have been seriously threatening ecological security. Effective prevention and control of such threats can extend the growth cycle of forest trees and increase the amount of forest carbon sink, which makes a contribution to achieving China’s goal of “emission peak and carbon neutrality”. In this paper, based on the insect-vector populations (this refers to Monochamus alternatus , which is the main vector in Asia) in pine wilt disease, we establish a two-dimensional delay differential equation model to investigate disease control and the impact of time delay on the effectiveness of it. Then, we analyze the existence and stability of the equilibrium of the system and the existence of Hopf bifurcation, derive the normal form of Hopf bifurcation by using a multiple time scales method, and conduct numerical simulations with realistic parameters to verify the correctness of the theoretical analysis. Eventually, according to theoretical analysis and numerical simulations, some specific suggestions are put forward for prevention and control of pine wilt disease.

Keywords: pine wilt disease; time delay; stability; normal form of Hopf bifurcation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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