Mathematical Modeling and Simulation for the Deadly Disease of Pine Trees

Abstract

This paper discusses the mathematical model depicting how Bursaphelenchus xylophilus infected pine trees. Firstly, according to the spread mechanism of communicable disease, we established a differential equation model with two species, i.e. pine trees and Monochamus alternatus Hop the--host of Bursaphelenchus xylophilus. Secondly, we studied the stability of system equilibrium under disease-free situations as well as disease-existing situations using Lyapunov Stability Theory. Last, we made several numerical simulations in order to test the correctness of our model. One merit of our work is providing theoretical basis for the practical control and prevention of this disease.