具有疾病的棉铃虫—棉花SIS模型分析  

Analysis of Cotton Bollworm-Cotton SIS with Disease

作　　者：周英英 李鹏 李医民[1] ZHOU Ying-ying;LI Peng;LI YI-min(Faculty of Science,Jiangsu University,Zhenjiang Jiangsu 212013 China)

机构地区：[1]江苏大学理学院,江苏镇江212013

出　　处：《生物数学学报》2020年第1期49-59,共11页Journal of Biomathematics

基　　金：国家自然基金项目(11072090)

摘　　要：棉铃虫是棉花蕾铃期重要钻蛀性害虫,也是中国棉区蕾铃期害虫的优势种,近年为害十分猖獗,给棉花生产带来了巨大的损失.由于棉铃虫依附于棉花生长,所以研究棉花与棉铃虫之间的依存制约关系对棉铃虫的防治有着重要意义.本文研究易感棉铃虫、感染疾病的棉铃虫和棉花之间的关系,构建"棉铃虫—棉花"的具有疾病的SIS模型,研究了系统的正平衡点和基本再生数R0,利用了Hurwitz定理证明了正平衡点处渐进稳定性,通过构造Liapunov函数和Dulac定理说明了正平衡点的全局稳定性.数值模拟的结果也说明了所得结论的合理性,同时得出了当R0>1时,棉铃虫和棉花的数量达到平衡.Helicoverpa armigera is an important borer pest in cotton buds and a dominant species in the budding period of cotton in China.In recent years,the damage has been very severe,which has brought huge losses to cotton production.Because the cotton bollworm is attached to the growth of cotton,it is of great significance for the prevention and control of cotton bollworm to study the relationship between cotton and bollworm.In this paper,the cotton-cotton bollworm ecosystem was taken as the starting point to study the relationship between susceptible cotton bollworm and infected cotton bollworm and cotton,and the disease-prone SIS model of"cotton bollworm-cotton"was constructed and simulated by numerical simulationR0.The global asymptotic stability of the ill-posed equilibrium is simulated.The Hurwitz theorem is used to prove the asymptotic stability at the positive equilibrium point.The positive equilibrium point is illustrated by constructing the Liapunov function and Dulac theorem.The global stability.The results of the numerical simulation also illustrate the rationality of the conclusions obtained,and at the same time,we conciude that the amount of cotton bollworm and cotton reached equilibrium under the condition of Ro>1.

关 键 词：棉玲虫 棉花 SIS模型 基本再生数R0 稳定性 

分 类 号：S435.622.3[农业科学—农业昆虫与害虫防治] O175[农业科学—植物保护]