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Huang, L., Guo, Z. and Wang, J. (2011) Theory and Applications of Differential Equations with Discontinuous Righthand Sides. Science Press, Beijing. (In Chinese)

has been cited by the following article:

• 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.