一类具有脉冲控制的非自治柑橘黄龙病数学模型研究

Study on a Sort of Non-autonomous Citrus Huanglongbing Mathematical Model with Impulsive Control

柑橘黄龙病是世界柑橘生产上的一种最具毁灭性的病害。为了防控黄龙病的传播,果农的主要措施是把染病的柑橘树拔除。该文建立了一个带有脉冲控制的非自治柑橘黄龙病动力学模型,并计算出了它的基本再生数R0。通过运用脉冲微分方程比较定理,证明了当R0<1时,无病周期解是全局渐进稳定的;当R0>1时,疾病持续存在。

Huanglongbing(HLB)is the most destructive plant disease in citrus industry around the world.In order to prevent and control the spreading of Huanglongbing,the main measure taken by farmers is to uproot the citrus trees suffered from this disease.In this paper,a dynamic model with impulsive control for non-autonomous citrus Huanglongbing is formed and its basic reproduction number has been worked out.Based on comparison theorem of impulsive differential equation,it is proved that the disease-free equilibrium is globally asymptotically stable if and the disease is permanence if.