一类具有阶段结构的虫媒传播植物病模型的全局分析  

Global Dynamics of a Vector-borne Plant Disease Model with Stage-structure

作　　者：高淑京[1] 葛扬球 陈迪 GAO SHUJING;GE YANGQIU;CHEN DI(Key Laboratory of Jiangri Province for Numerical Simulation and Emulation Techniques,Gannan Normal University,Ganzhou 341000,China;Changshi High School,Kaiping 529300,China)

机构地区：[1]赣南师范大学江西省数值模拟与仿真技术重点实验室,赣州341000 [2]长师中学,开平529300

出　　处：《应用数学学报》2023年第3期457-477,共21页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:11961003);江西省自然科学基金(批准号:20224ACB201003)资助项目;江西省双千计划资助项目。

摘　　要：为了研究化学控制和移除病树对虫媒植物病传播控制的影响,本文建立了一类具有阶段结构的虫媒传播植物病时滞模型.首先,利用再生矩阵法计算得到了基本再生数R0.理论结果表明,在入侵强度不强的情况下,基本再生数是决定疾病是否流行的阈值条件,即当R0<1时疾病灭绝,而当R0>1时疾病爆发.进一步,如果不实施移除病树策略,利用振动逼近的方法我们得到了地方病平衡点全局吸引的充分条件.最后通过数值模拟验证了理论结果,并说明喷洒杀虫剂是一种非常有效的控制措施.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 Ro 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 R0<1,and breaks out if R0>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.

关 键 词：植物病模型 时滞 基本再生数 全局吸引 灭绝 

分 类 号：O175[理学—数学]