Thieme, H.R. (1993) Persistence under Relaxed Point-Dissipativity with Application to an Endemic Model. SIAM Journal on Mathematical Analysis, 24, 407-435.
https://doi.org/10.1137/0524026

has been cited by the following article:

• TITLE: Global Dynamics of a New Huanglongbing Transmission Model with Quarantine Measures

  AUTHORS: Chunmei Zeng, Yujiang Liu, Shuixian Yan, Wenyan Fu

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

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.10 No.2, February 21, 2022

  ABSTRACT: 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 0 > 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.