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Global Dynamic Analysis of a Vector-Borne Plant Disease Model with Discontinuous Treatment
Department of Basic Course Education, Ji’an College, Ji’an, China
College of Mathematics, Sichuan University, Chengdu, China
Department of Basic Course Education, Ji’an College, Ji’an, China
Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou, China
- 1 Department of Basic Course Education, Ji’an College, Ji’an, China
- 2 College of Mathematics, Sichuan University, Chengdu, China
- 3 Department of Basic Course Education, Ji’an College, Ji’an, China
- 4 Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Gannan Normal University, Ganzhou, China
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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 R 0 is proved, which determines whether the plant disease will be extinct or not. If R 0 < 1 , the existence and global stability of disease-free equilibrium is established; If R 0 > 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.
KeywordsVector-BornePlant Disease ModelBasic Reproduction NumberDiscontinuous Treatment
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