带有时滞的SIR模型的稳定性和Hopf分支  

Stability and Hopf bifurcation in an SIR model with delay

作　　者：刘洪涛[1] 李文龙[2] 李自珍[3] 

机构地区：[1]西安外事学院经济管理学院,陕西西安710077 [2]兰州大学草地农业科技学院,甘肃兰州730000 [3]兰州大学数学与统计学院,甘肃兰州730000

出　　处：《兰州大学学报（自然科学版）》2009年第5期99-104,共6页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项(30700100);国家社会科学重点基金项目(04AJL007)

摘　　要：考虑了一个具有非线性表现率且带有时滞的SIR模型。首先分析了无病平衡点和非平凡平衡点的稳定性;然后利用正规型理论和中心流行定理,得到了分支周期解的稳定性、方向和一些其他性质的条件;最后用数值模拟验证和支持了给出的理论结果。A time-delayed SIR model with a nonlinear incidence rate was considered. First, the stability of the disease-free and non-trivial equilibriums were studied and then the explicit formulas which determine the stability, direction and other properties of bifurcating periodic solution were derived. At last, numerical simulations supporting the theoretical analysis were also given.

关 键 词：HOPF分支 周期解 稳定性 带时滞微分方程 数值模拟 

分 类 号：O175.13[理学—数学] Q141[理学—基础数学]