具有预防接种且带隔离项的传染病模型的定性分析  

Qualitative Analysis of Epidemic Models with Vaccination and Isolation

作　　者：李冬梅[1] 刘伟华[1] 郑忠涛[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2012年第2期122-126,共5页Journal of Harbin University of Science and Technology

基　　金：黑龙江省自然基金(A200502);黑龙江省教育厅科学技术研究项目(12521099)

摘　　要：本文研究了一类具有预防接种且带隔离项的传染病模型,得到决定疾病流行与否的阈值,给出无病平衡点,地方病平衡点存在性的判定条件.利用Laslle不变原理证明了无病平衡点的全局渐近稳定.利用Hurwitz判别法得到地方病平衡点局部渐近稳定的充分条件,应用半流一致持久性的方法讨论解的一致持久性,应用复合矩阵得到了地方病平衡点的全局渐近稳定的充分条件.This paper studies infectious disease model with Vaccination and isolation. The threshold which determines the spread of the disease is found. The judgement conditions of the disease-free equilibrium point and the endemic equilibrium point is given. Using LaSalle Invariant theory, the global asymptotical stability of the diseasefree point is proved. Using Hurwitz criterion, the sufficient condition for the local stability of the endemic equilibrium point is obtained. The application of the method of flow uniform persistence Po（k/k＋d,）discusses the uniform persistence of solutions. Using compound matrix, the sufficient conditions for the global asymptotic stability of the endemic equilibrium is obtained.

关 键 词：预防接种 一致持久性 隔离 全局稳定性 

分 类 号：O175.1[理学—数学]