| 一类具有阶段结构的SIRS传染病模型的定性分析 |
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| 引用本文： | 江志超,聂铭玮,刘则红.一类具有阶段结构的SIRS传染病模型的定性分析[J].华北航天工业学院学报,2011(4):6-11. |
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| 作者姓名： | 江志超 聂铭玮 刘则红 |
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| 作者单位： | [1]北华航天工业学院基础部河北廊坊065000 [2]廊坊市卫生局,河北廊坊065000 |
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| 基金项目： | 廊坊市科学技术研究与发展计划项目（N0.2011013034） |
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| 摘 要： | 本文考虑了一类具有阶段结构和非线性传染率的SIRS传染病模型。通过考虑因病死亡,人口的输入和输出,出生率、自然死亡率,免疫周期等因素,分析了系统解的正性和有界性,进一步给出了系统一定条件下个平衡点的稳定性和分支情况分析。最后使用规范型和中心流形理论给出了决定Hopf分支方向和分支周期解稳定性的隐式算法。
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| 关 键 词： | 阶段结构 SIRS模型 稳定性 Hopf分支 |
Stability Analysis in a SIRS Epidemic Model with Stage Structure and Nonlinear Incidence Rate |
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| JIANG Zhi-chao,NIE Ming-wei,LIU Ze-hong.Stability Analysis in a SIRS Epidemic Model with Stage Structure and Nonlinear Incidence Rate[J].Journal of North China Institute of Astronautic Engineering,2011(4):6-11. |
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| Authors: | JIANG Zhi-chao NIE Ming-wei LIU Ze-hong |
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| Institution: | 1.Fundamental Science Department,North China Institute of Aerospace Engineering,Langfang 065000,China;2.Langfang Health Bureau,Langfang 065000,China) |
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| Abstract: | In this paper,we consider a SIRS epidemic model with stage structure and nonlinear incidence rate.By considering the following factors： death for disease,input and output from population,birth rate,natrual mortality rate,imunity period and so on.We analyse the positivity and boundedness of solutions.Furthermore,we give the stability and bifurcation analysis of equilibria under some conditions.At the end,an explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory. |
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| Keywords: | stage structure SIRS model stability hopf bifurcation |
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