一类植物传染病模型的动力学分析  

Dynamics analysis of a class of plant epidemic model

作　　者：万槟萁 刘俊利[1] 刘文娟[1] WAN Bin-qi, LIU Jun-li, LIU Wen-juan(School of Science, Xi＇an Polytechnic University, Xi＇an 710048, Chin)

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《哈尔滨商业大学学报（自然科学版）》2017年第5期603-606,615,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金资助项目(11101323);陕西省自然科学基础研究计划资助项目(2014JQ1038);陕西省教育厅专项科研计划项目(16JK1331)

摘　　要：研究了一类植物传染病模型,计算了模型的基本再生数.当基本再生数小于1时,模型仅有唯一的无病平衡点,利用Routh-Hurwitz判据和Liapunov函数方法,讨论了无病平衡点的全局渐近稳定性.当基本再生数大于1时,无病平衡点不稳定,模型还存在唯一的地方病平衡点,借助复合矩阵证明了地方病平衡点的全局渐近稳定性.A class of plant disease model was studied,and the basic reproduction number was obtained. When the basic reproduction number was less than or equal to one,there was only the disease free equilibrium. The global stability of the disease-free equilibrium was obtained by the Routh-Hurwitz criteria and Liapunov function methods. When the basic reproduction number is greater than one,the disease free equilibrium was unstable,and there also existed an endemic equilibrium. The global stability of the endemic equilibrium was proved by the compound matrix.

关 键 词：基本再生数 全局稳定性 LIAPUNOV函数 第二加性复合矩阵 

分 类 号：O175.1[理学—数学]