| 具阶段结构的多时滞SIR模型的稳定性分析 |
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| 引用本文： | 江志超,曹建涛,程广涛,何春江. 具阶段结构的多时滞SIR模型的稳定性分析[J]. 数学年刊A辑(中文版), 2011, 32(1): 97-106 |
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| 作者姓名： | 江志超 曹建涛 程广涛 何春江 |
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| 作者单位： | 北华航天工业学院基础部;廊坊师范学院教育学院; |
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| 基金项目： | 河北省高等学校自然科学研究基金(No.2010105); 北华航天工业学院基金(No.ZKY-2009-02)资助的项目 |
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| 摘 要： | 考虑了一类具有两个阶段结构的SIR模型,得到了解的正性和有界性,通过分析特征方程根的分布,以(?)_1和(?)_2为参数分析了平衡点的稳定性和局部Hopf分支存在性.进一步地,利用规范型和中心流型理论,给出了决定Hopf分支方向和分支周期解的稳定性的隐式算法.最后利用一些数值模拟来支持所得到的理论分析结果.
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| 关 键 词： | SIR模型 稳定性 Hopf分支 |
Stability Analysis of a Stage-structured SIR Model with Time Delays |
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| JIANG Zhichao,CAO Jiantao,CHENG Guangtao and HE Chunjiang. Stability Analysis of a Stage-structured SIR Model with Time Delays[J]. Chinese Annals of Mathematics, 2011, 32(1): 97-106 |
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| Authors: | JIANG Zhichao CAO Jiantao CHENG Guangtao HE Chunjiang |
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| Affiliation: | JIANG Zhichao~1 CAO Jiantao~2 CHENG Guangtao~1 HE Chunjiang~1 1 Fundamental Science Department,North China Institute of Aerospace Engineering,Langfang 065000,Hebei,China. 2 Department of Education,Langfang Teachers College,China. |
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| Abstract: | The authors consider an SIR model with two stages, and obtain the positivity and boundedness of solutions. By analyzing the distribution of the roots of characteristic equations, the stability at the equilibria and the existence of local Hopf bifurcation under parameters $tau_1$ and $tau_2$ are analyzed. Furthermore, using the normal form theory and center manifold argument, an explicit formulas for determining the direction and the stability of periodic bifurcation solutions from Hopf bifurcations are derived. At last, some numerical simulations are carried out to support the analytical results. |
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| Keywords: | SIR model Stability Hopf bifurcation |
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