Stability analysis and optimal control strategy for prevention of pine wilt disease
type: Item
instance of: scholarly article
title: Stability analysis and optimal control strategy for prevention of pine wilt disease
zbMATH Open document ID: 1406.92588
DOI: 10.1155/2014/182680
author: Kwang Sung Lee
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: We propose a mathematical model of pine wilt disease (PWD) which is caused by pine sawyer beetles carrying the pinewood nematode (PWN). We calculate the basic reproduction number \(R_0\) and investigate the stability of a disease-free and endemic equilibrium in a given mathematical model. We show that the stability of the equilibrium in the proposed model can be controlled through the basic reproduction number \(R_0\). We then discuss effective optimal control strategies for the proposed PWD mathematical model. We demonstrate the existence of a control problem, and then we apply both analytical and numerical techniques to demonstrate effective control methods to prevent the transmission of the PWD. In order to do this, we apply two control strategies: tree-injection of nematicide and the eradication of adult beetles through aerial pesticide spraying. Optimal prevention strategies can be determined by solving the corresponding optimality system. Numerical simulations of the optimal control problem using a set of reasonable parameter values suggest that reducing the number of pine sawyer beetles is more effective than the tree-injection strategy for controlling the spread of PWD.
Mathematics Subject Classification ID: 92D30
Mathematics Subject Classification ID: 92C80
Mathematics Subject Classification ID: 49N90
zbMATH DE Number: 7021886
zbMATH Keywords: pine wilt disease
zbMATH Keywords: optimal control
zbMATH Keywords: prevention
zbMATH Keywords: stability
Wikidata QID: Q59035835
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/182680
OpenAlex ID: W1990876440
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description: scientific article; zbMATH DE number 7021886