| 一具有非线性发生率传染病模型的稳定性和霍普夫分支 |
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| 引用本文： | 宋礼,靳祯,孙桂全. 一具有非线性发生率传染病模型的稳定性和霍普夫分支[J]. 生物数学学报, 2009, 24(2): 207-212 |
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| 作者姓名： | 宋礼 靳祯 孙桂全 |
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| 作者单位： | 中北大学,理学院,山西,太原,030051 |
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| 基金项目： | the National Science Foundation of China，the Special Scientific Research Foundation for the Subjects of Doctors in University，the Program for New Century Excellent Talents in University |
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| 摘 要： | 在这篇文章中，我们研究了一具有非线性发生率的传染病模型．该模型经历了鞍结点分支和霍普夫分支．我们对模型的霍普夫分支进行了详细的分析，得知该霍普夫分支是超临界的．此外，我们给出了支持理论分析的数值模拟．
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| 关 键 词： | 非线性发生率 鞍结点分支 霍普夫分支 超临界 |
Stability and Hopf Bifurcation in a Epidemic Model with Non-linear Incidence Rate |
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| SONG Li,JIN Zhen,SUN Gui-quan. Stability and Hopf Bifurcation in a Epidemic Model with Non-linear Incidence Rate[J]. Journal of Biomathematics, 2009, 24(2): 207-212 |
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| Authors: | SONG Li JIN Zhen SUN Gui-quan |
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| Affiliation: | (Department of mathematics, North University of China, Taiyuan Shan＇xi 030051 China) |
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| Abstract: | In this paper, we investigate a epidemic model with nonlinear incidence rate β1/2I. It is shown that the model undergoes saddle-node bifurcation and Hopf bifurcation. We perform a detailed Hopf bifurcation analysis to the model, and derive that the direction of the Hopf bifurcation is supercritical. Further, the numerical simulations supporting the theoretical analysis are also given. |
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| Keywords: | Nonlinear incidence rate Saddle-node bifurcation Hopf bifurcation Supercritical |
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