Global Dynamic Analysis of a Vector-Borne Plant Disease Model with Discontinuous Treatment

Hengmin  Lv; Zhen  Yuan; Lizhi  Fei; Fumin  Zhang

doi:10.4236/am.2018.95036

Hengmin Lv¹^*, Lizhi Fei^1,2, Zhen Yuan¹, Fumin Zhang³

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 < 1 , the existence and global stability of disease-free equilibrium is established; If 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.

Keywords: Vector-Borne, Plant Disease Model, Basic Reproduction Number, Discontinuous Treatment

Cite this paper: Lv, H. , Fei, L. , Yuan, Z. and Zhang, F. (2018) Global Dynamic Analysis of a Vector-Borne Plant Disease Model with Discontinuous Treatment. Applied Mathematics, 9, 496-511. doi: 10.4236/am.2018.95036.

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