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.
Highlights
The plants play an important role in our lives, as most of our daily food, clothing and building materials come from plants
As for the plant infectious disease model, our main object is to investigate the effect of the insect vector and discontinuous treatment function on the dynamics of spreading the plant disease
We calculated the basic reproduction number R0, which is derived under some reasonable assumptions on the discontinuous treatment function
Summary
The plants play an important role in our lives, as most of our daily food, clothing and building materials come from plants. The vector-borne is a very important part of the transmission of plant diseases. Treatment plays a very important role to control the spread of diseases. When the number of infectives is large, the constant treatment is suitable for hypothesis of model. In [16], Shi and Zhao presented a vector-borne plant disease model, but they do not studied treatment to the infected plant host. Treating infected plant is a quite effective method which to control the outbreak of the plant disease. Continuous treatment is an effective method, the outbreak of the plant disease is periodic, and continuing treatment can be a huge waste of resources. In order to be realistic, we built a vector-borne plant disease model with discontinuous treatment.
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