TITLE:
Global Dynamic Analysis of a Vector-Borne Plant Disease Model with Discontinuous Treatment
AUTHORS:
Hengmin Lv, Lizhi Fei, Zhen Yuan, Fumin Zhang
KEYWORDS:
Vector-Borne, Plant Disease Model, Basic Reproduction Number, Discontinuous Treatment
JOURNAL NAME:
Applied Mathematics,
Vol.9 No.5,
May
28,
2018
ABSTRACT:
This paper proposes a vector-borne plant disease model with discontinuous
treatment strategies. Constructing Lyapunov function and applying
non-smooth theory to analyze discontinuous differential equations, the basic
reproductive number R0 is proved, which determines whether the plant disease
will be extinct or not. If R0 R0 > 1 , there exists a unique endemic
equilibrium which is globally stable. The numerical simulations are provided
to verify our theoretical results, which indicate that after infective individuals
reach some level, strengthening treatment measures is proved to be beneficial
in controlling disease transmission.