Author(s)

Chunmei Zeng¹, Yujiang Liu¹, Shuixian Yan², Wenyan Fu²

¹Key Laboratory of Jiangxi Province for Numerical Simulation and Emulation Techniques, Ganzhou, China.
²Gannan Normal University, Ganzhou, China.

Incorporating plant-dependent saturated reproduction function, chemical insecticide, and its resistance, a plant-vector-virus model which describes the spread of infection throughout the plant by the insect is investigated in this paper. First of all, the basic reproduction number R₀ is obtained by using the method of the next generation matrix, and the existence of disease-free equilibrium and endemic equilibrium is examined. Then we show that the disease-free steady state is globally asymptotically stable if R₀ < 1, whereas if R₀ > 1, the system is uniformly persistent and the endemic equilibrium is local stability. Finally, numerical simulation is carried out to illustrate our theoretical results. Our result implies that insecticide resistance has a vital impact on the control of plant diseases.

Saturated Reproduction Rate, Vector-Borne Disease Model, Basic Reproduction Number, Sensitivity Analysis

Zeng, C. , Liu, Y. , Yan, S. and Fu, W. (2022) Global Dynamics of a New Huanglongbing Transmission Model with Quarantine Measures. Journal of Applied Mathematics and Physics, 10, 360-371. doi: 10.4236/jamp.2022.102028.