Stability Analysis and Optimal Control Strategy for Prevention of Pine Wilt Disease

Abstract

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.