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**Global dynamics of a vector-borne plant disease model with stage-structure.**
*(Chinese.
English summary)*
Zbl 07801531

Summary: In this paper, a time-delayed vector-borne plant disease model with state-structure is presented. Firstly, the analytical formula for the basic reproductive number \(R_0\) is given by using the next generation matrix method. Theoretical results show that the basic reproductive number serves as a threshold parameter provided that the invasion intensity is not strong: the disease dies out if \(R_0 < 1\), and breaks out if \(R_0 > 1\). Moreover, by means of fluctuation method, sufficient conditions for the global attractivity of the endemic equilibrium are obtained if removing infected trees is ignored. Finally, numerical simulations are given to verify the analytical results, and illustrate that spraying insecticides is a very effective control measure.

### MSC:

92D30 | Epidemiology |

92C80 | Plant biology |

34K60 | Qualitative investigation and simulation of models involving functional-differential equations |

### Keywords:

plant disease model; time delay; basic reproductive number; global attractivity; extinction### References:

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