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

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DOI: 10.4236/am.2018.95036    863 Downloads   1,630 Views  Citations

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.

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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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