一类具有非线性传染率流行病模型的定性分析  

Qualitative Analysis of an Epidemic Model with Nonlinear Infection Rate

作　　者：林乾金[1] 董霖 叶星旸[3] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350007 [2]福州高级中学,福建福州350007 [3]集美大学理学院,福建厦门361021

出　　处：《集美大学学报（自然科学版）》2009年第2期190-194,共5页Journal of Jimei University：Natural Science

基　　金：福建省教育厅基金资助项目(JA05204);福建省科技厅(K类)基金资助项目(2005K027)

摘　　要：研究了一类具有非线性传染率βIpSq的SIQR传染病模型,确定了各类平衡点存在的条件阈值,研究了各平衡点的稳定性,最后讨论了模型的Hopf分支现象,并证明了当0<p≤1时地方病平衡点的全局稳定性.SIQR model with nonlinear infection rate βI^pSq was studied, and the conditions and threshold to the existence of various equilibriums were established. Finally, the stability of the equilibriums and Hopf bifurcations were discussed. It was also found that the endemic equilibriums were globally asymptotically stable when 0〈P≤1.

关 键 词：传染病模型 隔离 非线性传染率 稳定性 HOPF分支 

分 类 号：O175.1[理学—数学] Q141[理学—基础数学]